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14 (fourteen  /fɔərˈtiːn/) is the natural number following 13 and preceding 15. In speech, the numbers 14 and 40 are often confused. When carefully enunciated, they differ in which syllable is stressed: 14 /fɔərˈtiːn/ ( listen) vs 40 /ˈfɔrti/.^[1] However, in dates such as 1492 or when contrasting numbers in the teens, such as 13, 14, 15, the stress shifts to the first syllable: 14 /ˈfɔərtiːn/.

Look up fourteen in Wiktionary, the free dictionary.

In mathematics[link]

Fourteen is a composite number, its divisors being 1, 2, 7 and 14.

14 is the 3rd discrete semiprime ( 2 . 7 ) and the 3rd member of the (2.q) discrete semiprime family. The number following 14—15 is itself a discrete semiprime and this is the first such pair of discrete semiprimes. The next example is the pair commencing 21.

The aliquot sum σ(n) of 14 is 10, also a discrete semiprime and this is again the first example of a discrete semiprime having an aliquot sum in the same form. 14 has an aliquot sequence of 6 members ( 14,10,8,7,1,0) 14 is the third composite number in the 7-aliquot tree.

Fourteen is itself the Aliquot sum of two numbers; the discrete semiprime 22, and the square number 196.

It is the base of the tetradecimal notation.

In base fifteen and higher bases (such as hexadecimal), fourteen is represented as E.

Fourteen is the sum of the first three squares, which makes it a square pyramidal number.

This number is the lowest even n for which the equation φ(x) = n has no solution, making it the first even nontotient (see Euler's totient function).

14 is a Catalan number, the only semiprime among all Catalan numbers.

Take a set of real numbers and apply the closure and complement operations to it in any possible sequence. At most 14 distinct sets can be generated in this way. This holds even if the reals are replaced by a more general topological space. See Kuratowski's closure-complement problem.

Fourteen is a Keith number in base 10: 1, 4, 5, 9, 14, 23, 37, 60, 97, 157...

Fourteen is an open meandric number.

Fourteen is a Companion Pell number.

According to the Shapiro inequality 14 is the least number n such that there exist Failed to parse (Missing texvc executable; please see math/README to configure.): x_1, x_2, \dots, x_n

such that 

Failed to parse (Missing texvc executable; please see math/README to configure.): \sum_{i=1}^{n} \frac{x_i}{x_{i+1}+x_{i+2}} < \frac{n}{2}

where Failed to parse (Missing texvc executable; please see math/README to configure.): x_{n+1}=x_1, x_{n+2}=x_2 .

There are fourteen possible Bravais lattices that fill three-dimensional space.

The cuboctahedron, the truncated cube, and the truncated octahedron each have fourteen faces. The rhombic dodecahedron, which tessellates 3-dimensional space and is the dual of the cuboctahedron, has fourteen vertices. The truncated octahedron, which also tessellates 3-dimensional space, is the only permutohedron.

In science[link]

Chemistry[link]

• The atomic number of silicon
• The approximate atomic weight of nitrogen
• The maximum number of electrons that can fit in an f sublevel

Astronomy[link]

• Messier object M14, a magnitude 9.5 globular cluster in the constellation Ophiuchus

• The New General Catalogue object [NGC 14, a magnitude 12.5 irregular galaxy in the constellation Pegasus

• The Saros number of the solar eclipse series which began on July 31, 2568 B.C. and ended on February 6, B.C. 1035. The duration of Saros series 14 was 1532.5 years, and it contained 86 solar eclipses

• The Saros number of the lunar eclipse series which began on June 1, 2230 B.C. and ended on July 19, 932 B.C. The duration of Saros series 14 was 1298.1 years, and it contained 73 lunar eclipses.

In religion[link]

• The number of Stations of the Cross.
• The Fourteen Holy Helpers were a group of saints formerly venerated together by Roman Catholics.
• The number of muqatta'at in the Qur'an.
• The number of Infalliables (Masoomeen) in Shia Ithna-Asheri Islam.
• The number of pieces the body of Osiris was torn into by his fratricidal brother Set.

Age 14[link]

This unreferenced section requires citations to ensure verifiability.

• Age 14 is the earliest that the emancipation of minors can occur in the U.S.
• Minimum age a person can purchase, rent or buy tickets to a 14A rated movie in Canada without an adult. Rating are provincial, so ratings may vary. A movie can be 14A in one or some provinces and PG in other provinces. A movie can also be rated 14A in one or some provinces and 18A in other provinces. Quebec has a different rating system for films.
• Youngest age in Canada a person can watch a 14+ rated show without consent from a legal guardian.
• Minimum age at which one can view, rent, purchase, or buy tickets to an 18A rated movie with an accompanying adult in the Canadian provinces of the Maritimes and Manitoba.
• Minimum age at which one can work in many U.S states. Some require parental consent while others don't.
• Minimum age at which one can work in most Australian states with parent's consent.
• Minimum age at which one can drive a vehicle in the U.S. with a driver's license (with supervision of an adult over 18 years of age, and with a valid, unmarked driver's license, and at least 365 days of experience driving an actual automobile)
• The minimum age limit to drive a 50cc motorbike in Italy.

In Sports[link]

• The G-14 is a now-defunct union of eighteen football clubs.
• In Association football: The number 14, was the number for Johan Cruyff. Therefore he is often associated with that number and the football club AFC Ajax promised (in 2007) in his honour never to use it again.
• In rugby union:
  • The starting right wing wears the 14 shirt.
  • The Top 14 is the highest-level league in French rugby union.

• In the NASCAR Sprint Cup Series, the #14 car is currently owned by Stewart Haas Racing. Since 2009, it has been driven by team co-owner Tony Stewart.

• In the Division I (NCAA) of College Football
  • The number 14 equals the number of National Championships by the Alabama Crimson Tide.

• The jersey number 14 has been retired by several North American sports teams in honor of past playing greats or other key figures:
  • In Major League Baseball:
    • The Boston Red Sox, for Hall of Famer Jim Rice.
    • The Chicago Cubs, for Hall of Famer Ernie Banks.
    • The Cleveland Indians, for Hall of Fame player Larry Doby, who also managed the team.
    • The Minnesota Twins, for Kent Hrbek.
    • The New York Mets, for Gil Hodges, who both played for and managed the team.
    • The Philadelphia Phillies, for Hall of Famer Jim Bunning.
    • The St. Louis Cardinals, for Ken Boyer.
    • The Seattle Mariners have yet to retire any numbers, but have not issued #14 since Lou Piniella, manager from 1993 to 2002, left the team.
    • The Cincinnati Reds have taken #14 out of circulation since Pete Rose accepted a place on MLB's banned list in 1989 for allegedly betting on games (which he would admit to in 2004). Because of the ban, the Reds cannot retire the number for Rose during his lifetime; they have since only issued the number to his son.
  • In the NBA:
    • The Boston Celtics, for Hall of Famer Bob Cousy.
    • The Golden State Warriors, for Tom Meschery, who played for the team in its past incarnations as the Philadelphia and San Francisco Warriors.
    • The Milwaukee Bucks, for Jon McGlocklin.
    • The Portland Trail Blazers, for Lionel Hollins.
    • The Sacramento Kings, for Hall of Famer Oscar Robertson, who played for the team when it was known as the Cincinnati Royals.
    • The Utah Jazz, for Jeff Hornacek.
  • In the NFL:
    • The Cleveland Browns, for Hall of Famer Otto Graham.
    • The Green Bay Packers, for Hall of Famer Don Hutson.
    • The New York Giants, for Hall of Famer Y. A. Tittle.
    • The San Diego Chargers, for Hall of Famer Dan Fouts.
  • In the NHL:
    • The Buffalo Sabres, for René Robert.

White Pride symbol[link]

Among White Nationalists, 14 signifies the "Fourteen Words"—"We must secure the existence of our people and a future for white children"—attributed to David Lane. Often found in combination with 88 (1488, 8814, 14/88, etc.).

In other fields[link]

Fourteen is:

• The number of days in a fortnight.
• In traditional British units of weight, the number of pounds in a stone.
• A number 'encoded' in much of the music of Johann Sebastian Bach.^{[citation needed]} Bach may have considered this number a sort of signature, since given A = 1, B = 2, C = 3, etc., then B + A + C + H = 14. (See also 41)
• The number of points outlined by president Woodrow Wilson for reconstructing a new Europe following World War I, see Fourteen Points.
• The section that you go to when you die in the Grailquest books.
• The number of legs on a woodlouse, as well as on Hallucigenia.
• A common designation for the thirteenth floor in many buildings for superstitious reasons
• The number of points in a proposed republican constitution of the United Kingdom^{[citation needed]}
• The number of lines in a sonnet.
• The Number 14 airship by Alberto Santos Dumont that was used to test the aerodynamics of his 14-bis airplane.
• The number of the French department Calvados
• A Storage server manufactured by IBM. It goes by name of "XIV" and is pronounced as the separate letters "X", "I", "V".

Historical years[link]

14 A.D., 14 B.C., 1914 etc.

References[link]

1. ^ The vowels of the syllables four- and for- are identical in many dialects, such as General American and younger speakers of Received Pronunciation.

vep:14 (lugu)

A number is a mathematical object used to count and measure. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers.

Mathematical operations are certain procedures that take one or more numbers as input and produce a number as output. Unary operations take a single input number and produce a single output number. For example, the successor operation adds one to an integer, thus the successor of 4 is 5. Binary operations take two input numbers and produce a single output number. Examples of binary operations include addition, subtraction, multiplication, division, and exponentiation. The study of numerical operations is called arithmetic.

A notational symbol that represents a number is called a numeral. In addition to their use in counting and measuring, numerals are often used for labels (telephone numbers), for ordering (serial numbers), and for codes (e.g., ISBNs).

In common use, the word number can mean the abstract object, the symbol, or the word for the number.

Classification of numbers[link]

Different types of numbers are used in many cases. Numbers can be classified into sets, called number systems. (For different methods of expressing numbers with symbols, such as the Roman numerals, see numeral systems.)

Natural numbers[link]

The most familiar numbers are the natural numbers or counting numbers: one, two, three, and so on. Traditionally, the sequence of natural numbers started with 1 (0 was not even considered a number for the Ancient Greeks.) However, in the 19th century, set theorists and other mathematicians started including 0 (cardinality of the empty set, i.e. 0 elements, where 0 is thus the smallest cardinal number) in the set of natural numbers.^{[citation needed]} Today, different mathematicians use the term to describe both sets, including zero or not. The mathematical symbol for the set of all natural numbers is N, also written Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbb{N} .

In the base ten numeral system, in almost universal use today for mathematical operations, the symbols for natural numbers are written using ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. In this base ten system, the rightmost digit of a natural number has a place value of one, and every other digit has a place value ten times that of the place value of the digit to its right.

In set theory, which is capable of acting as an axiomatic foundation for modern mathematics,^[1] natural numbers can be represented by classes of equivalent sets. For instance, the number 3 can be represented as the class of all sets that have exactly three elements. Alternatively, in Peano Arithmetic, the number 3 is represented as sss0, where s is the "successor" function (i.e., 3 is the third successor of 0). Many different representations are possible; all that is needed to formally represent 3 is to inscribe a certain symbol or pattern of symbols three times.

Integers[link]

The negative of a positive integer is defined as a number that produces zero when it is added to the corresponding positive integer. Negative numbers are usually written with a negative sign (a minus sign). As an example, the negative of 7 is written −7, and 7 + (−7) = 0. When the set of negative numbers is combined with the set of natural numbers (which includes zero), the result is defined as the set of integer numbers, also called integers, Z also written Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbb{Z} . Here the letter Z comes from German Zahl, meaning "number".

The set of integers forms a ring with operations addition and multiplication.^[2]

Rational numbers[link]

A rational number is a number that can be expressed as a fraction with an integer numerator and a non-zero natural number denominator. Fractions are written as two numbers, the numerator and the denominator, with a dividing bar between them. In the fraction written ^m⁄_n or

Failed to parse (Missing texvc executable; please see math/README to configure.): m \over n \,

m represents equal parts, where n equal parts of that size make up one whole. Two different fractions may correspond to the same rational number; for example ¹⁄₂ and ²⁄₄ are equal, that is:

Failed to parse (Missing texvc executable; please see math/README to configure.): {1 \over 2} = {2 \over 4}.\,

If the absolute value of m is greater than n, then the absolute value of the fraction is greater than 1. Fractions can be greater than, less than, or equal to 1 and can also be positive, negative, or zero. The set of all rational numbers includes the integers, since every integer can be written as a fraction with denominator 1. For example −7 can be written ⁻⁷⁄₁. The symbol for the rational numbers is Q (for quotient), also written Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbb{Q} .

Real numbers[link]

The real numbers include all of the measuring numbers. Real numbers are usually written using decimal numerals, in which a decimal point is placed to the right of the digit with place value one. Each digit to the right of the decimal point has a place value one-tenth of the place value of the digit to its left. Thus

Failed to parse (Missing texvc executable; please see math/README to configure.): 123.456\,

represents 1 hundred, 2 tens, 3 ones, 4 tenths, 5 hundredths, and 6 thousandths. In saying the number, the decimal is read "point", thus: "one two three point four five six ". In the US and UK and a number of other countries, the decimal point is represented by a period, whereas in continental Europe and certain other countries the decimal point is represented by a comma. Zero is often written as 0.0 when it must be treated as a real number rather than an integer. In the US and UK a number between −1 and 1 is always written with a leading zero to emphasize the decimal. Negative real numbers are written with a preceding minus sign:

Failed to parse (Missing texvc executable; please see math/README to configure.): -123.456.\,

Every rational number is also a real number. It is not the case, however, that every real number is rational. If a real number cannot be written as a fraction of two integers, it is called irrational. A decimal that can be written as a fraction either ends (terminates) or forever repeats, because it is the answer to a problem in division. Thus the real number 0.5 can be written as ¹⁄₂ and the real number 0.333... (forever repeating threes, otherwise written 0.3) can be written as ¹⁄₃. On the other hand, the real number π (pi), the ratio of the circumference of any circle to its diameter, is

Failed to parse (Missing texvc executable; please see math/README to configure.): \pi = 3.14159265358979\dots.\,

Since the decimal neither ends nor forever repeats, it cannot be written as a fraction, and is an example of an irrational number. Other irrational numbers include

Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt{2} = 1.41421356237 \dots\,

(the square root of 2, that is, the positive number whose square is 2).

Thus 1.0 and 0.999... are two different decimal numerals representing the natural number 1. There are infinitely many other ways of representing the number 1, for example ²⁄₂, ³⁄₃, 1.00, 1.000, and so on.

Every real number is either rational or irrational. Every real number corresponds to a point on the number line. The real numbers also have an important but highly technical property called the least upper bound property. The symbol for the real numbers is R, also written as Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbb{R} .

When a real number represents a measurement, there is always a margin of error. This is often indicated by rounding or truncating a decimal, so that digits that suggest a greater accuracy than the measurement itself are removed. The remaining digits are called significant digits. For example, measurements with a ruler can seldom be made without a margin of error of at least 0.001 meters. If the sides of a rectangle are measured as 1.23 meters and 4.56 meters, then multiplication gives an area for the rectangle of 5.6088 square meters. Since only the first two digits after the decimal place are significant, this is usually rounded to 5.61.

In abstract algebra, it can be shown that any complete ordered field is isomorphic to the real numbers. The real numbers are not, however, an algebraically closed field.

Complex numbers[link]

Moving to a greater level of abstraction, the real numbers can be extended to the complex numbers. This set of numbers arose, historically, from trying to find closed formulas for the roots of cubic and quartic polynomials. This led to expressions involving the square roots of negative numbers, and eventually to the definition of a new number: the square root of negative one, denoted by i, a symbol assigned by Leonhard Euler, and called the imaginary unit. The complex numbers consist of all numbers of the form

Failed to parse (Missing texvc executable; please see math/README to configure.): \,a + b i

where a and b are real numbers. In the expression a + bi, the real number a is called the real part and b is called the imaginary part. If the real part of a complex number is zero, then the number is called an imaginary number or is referred to as purely imaginary; if the imaginary part is zero, then the number is a real number. Thus the real numbers are a subset of the complex numbers. If the real and imaginary parts of a complex number are both integers, then the number is called a Gaussian integer. The symbol for the complex numbers is C or Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbb{C} .

In abstract algebra, the complex numbers are an example of an algebraically closed field, meaning that every polynomial with complex coefficients can be factored into linear factors. Like the real number system, the complex number system is a field and is complete, but unlike the real numbers it is not ordered. That is, there is no meaning in saying that i is greater than 1, nor is there any meaning in saying that i is less than 1. In technical terms, the complex numbers lack the trichotomy property.

Complex numbers correspond to points on the complex plane, sometimes called the Argand plane.

Each of the number systems mentioned above is a proper subset of the next number system. Symbolically, Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R} \subset \mathbb{C} .

Computable numbers[link]

Moving to problems of computation, the computable numbers are determined in the set of the real numbers. The computable numbers, also known as the recursive numbers or the computable reals, are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm. Equivalent definitions can be given using μ-recursive functions, Turing machines or λ-calculus as the formal representation of algorithms. The computable numbers form a real closed field and can be used in the place of real numbers for many, but not all, mathematical purposes.

Other types[link]

Algebraic numbers are those that can be expressed as the solution to a polynomial equation with integer coefficients. The complement of the algebraic numbers are the transcendental numbers.

Hyperreal numbers are used in non-standard analysis. The hyperreals, or nonstandard reals (usually denoted as *R), denote an ordered field that is a proper extension of the ordered field of real numbers R and satisfies the transfer principle. This principle allows true first order statements about R to be reinterpreted as true first order statements about *R.

Superreal and surreal numbers extend the real numbers by adding infinitesimally small numbers and infinitely large numbers, but still form fields.

The p-adic numbers may have infinitely long expansions to the left of the decimal point, in the same way that real numbers may have infinitely long expansions to the right. The number system that results depends on what base is used for the digits: any base is possible, but a prime number base provides the best mathematical properties.

For dealing with infinite collections, the natural numbers have been generalized to the ordinal numbers and to the cardinal numbers. The former gives the ordering of the collection, while the latter gives its size. For the finite set, the ordinal and cardinal numbers are equivalent, but they differ in the infinite case.

A relation number is defined as the class of relations consisting of all those relations that are similar to one member of the class.^[3]

Sets of numbers that are not subsets of the complex numbers are sometimes called hypercomplex numbers. They include the quaternions H, invented by Sir William Rowan Hamilton, in which multiplication is not commutative, and the octonions, in which multiplication is not associative. Elements of function fields of non-zero characteristic behave in some ways like numbers and are often regarded as numbers by number theorists.

Specific uses[link]

There are also other sets of numbers with specialized uses. Some are subsets of the complex numbers. For example, algebraic numbers are the roots of polynomials with rational coefficients. Complex numbers that are not algebraic are called transcendental numbers.

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without remainder; an odd number is an integer that is not evenly divisible by 2. (The old-fashioned term "evenly divisible" is now almost always shortened to "divisible".) A formal definition of an odd number is that it is an integer of the form n = 2k + 1, where k is an integer. An even number has the form n = 2k where k is an integer.

A perfect number is a positive integer that is the sum of its proper positive divisors—the sum of the positive divisors not including the number itself. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors, or σ(n) = 2 n. The first perfect number is 6, because 1, 2, and 3 are its proper positive divisors and 1 + 2 + 3 = 6. The next perfect number is 28 = 1 + 2 + 4 + 7 + 14. The next perfect numbers are 496 and 8128 (sequence A000396 in OEIS). These first four perfect numbers were the only ones known to early Greek mathematics.

A figurate number is a number that can be represented as a regular and discrete geometric pattern (e.g. dots). If the pattern is polytopic, the figurate is labeled a polytopic number, and may be a polygonal number or a polyhedral number. Polytopic numbers for r = 2, 3, and 4 are:

• P₂(n) = ¹⁄₂ n(n + 1) (triangular numbers)
• P₃(n) = ¹⁄₆ n(n + 1)(n + 2) (tetrahedral numbers)
• P₄(n) = ¹⁄₂₄ n(n + 1)(n + 2)(n + 3) (pentatopic numbers)

Numerals[link]

Numbers should be distinguished from numerals, the symbols used to represent numbers. Boyer showed that Egyptians created the first ciphered numeral system.^{[citation needed]} Greeks followed by mapping their counting numbers onto Ionian and Doric alphabets. The number five can be represented by both the base ten numeral '5', by the Roman numeral 'Ⅴ' and ciphered letters. Notations used to represent numbers are discussed in the article numeral systems. An important development in the history of numerals was the development of a positional system, like modern decimals, which can represent very large numbers. The Roman numerals require extra symbols for larger numbers.

History[link]

First use of numbers[link]

Bones and other artifacts have been discovered with marks cut into them that many believe are tally marks.^[4] These tally marks may have been used for counting elapsed time, such as numbers of days, lunar cycles or keeping records of quantities, such as of animals.

A tallying system has no concept of place value (as in modern decimal notation), which limits its representation of large numbers. Nonetheless tallying systems are considered the first kind of abstract numeral system.

The first known system with place value was the Mesopotamian base 60 system (ca. 3400 BC) and the earliest known base 10 system dates to 3100 BC in Egypt.^[5]

[edit] Zero

The use of zero as a number should be distinguished from its use as a placeholder numeral in place-value systems. Many ancient texts used zero. Babylonian and Egyptian texts used it. Egyptians used the word nfr to denote zero balance in double entry accounting entries. Indian texts used a Sanskrit word Shunye to refer to the concept of void. In mathematics texts this word often refers to the number zero.^[6]

Records show that the Ancient Greeks seemed unsure about the status of zero as a number: they asked themselves "how can 'nothing' be something?" leading to interesting philosophical and, by the Medieval period, religious arguments about the nature and existence of zero and the vacuum. The paradoxes of Zeno of Elea depend in large part on the uncertain interpretation of zero. (The ancient Greeks even questioned whether 1 was a number.)

The late Olmec people of south-central Mexico began to use a true zero (a shell glyph) in the New World possibly by the 4th century BC but certainly by 40 BC, which became an integral part of Maya numerals and the Maya calendar. Mayan arithmetic used base 4 and base 5 written as base 20. Sanchez in 1961 reported a base 4, base 5 'finger' abacus.

By 130 AD, Ptolemy, influenced by Hipparchus and the Babylonians, was using a symbol for zero (a small circle with a long overbar) within a sexagesimal numeral system otherwise using alphabetic Greek numerals. Because it was used alone, not as just a placeholder, this Hellenistic zero was the first documented use of a true zero in the Old World. In later Byzantine manuscripts of his Syntaxis Mathematica (Almagest), the Hellenistic zero had morphed into the Greek letter omicron (otherwise meaning 70).

Another true zero was used in tables alongside Roman numerals by 525 (first known use by Dionysius Exiguus), but as a word, nulla meaning nothing, not as a symbol. When division produced zero as a remainder, nihil, also meaning nothing, was used. These medieval zeros were used by all future medieval computists (calculators of Easter). An isolated use of their initial, N, was used in a table of Roman numerals by Bede or a colleague about 725, a true zero symbol.

An early documented use of the zero by Brahmagupta (in the Brahmasphutasiddhanta) dates to 628. He treated zero as a number and discussed operations involving it, including division. By this time (the 7th century) the concept had clearly reached Cambodia as Khmer numerals, and documentation shows the idea later spreading to China and the Islamic world.

[edit] Negative numbers

The abstract concept of negative numbers was recognised as early as 100 BC – 50 BC. The Chinese Nine Chapters on the Mathematical Art (Chinese: Jiu-zhang Suanshu) contains methods for finding the areas of figures; red rods were used to denote positive coefficients, black for negative.^[7] This is the earliest known mention of negative numbers in the East; the first reference in a Western work was in the 3rd century in Greece. Diophantus referred to the equation equivalent to Failed to parse (Missing texvc executable; please see math/README to configure.): 4x + 20 = 0

(the solution is negative) in Arithmetica, saying that the equation gave an absurd result.

During the 600s, negative numbers were in use in India to represent debts. Diophantus’ previous reference was discussed more explicitly by Indian mathematician Brahmagupta, in Brahma-Sphuta-Siddhanta 628, who used negative numbers to produce the general form quadratic formula that remains in use today. However, in the 12th century in India, Bhaskara gives negative roots for quadratic equations but says the negative value "is in this case not to be taken, for it is inadequate; people do not approve of negative roots."

European mathematicians, for the most part, resisted the concept of negative numbers until the 17th century, although Fibonacci allowed negative solutions in financial problems where they could be interpreted as debts (chapter 13 of Liber Abaci, 1202) and later as losses (in Flos). At the same time, the Chinese were indicating negative numbers either by drawing a diagonal stroke through the right-most nonzero digit of the corresponding positive number's numeral.^[8] The first use of negative numbers in a European work was by Chuquet during the 15th century. He used them as exponents, but referred to them as “absurd numbers”.

As recently as the 18th century, it was common practice to ignore any negative results returned by equations on the assumption that they were meaningless, just as René Descartes did with negative solutions in a Cartesian coordinate system.

[edit] Rational numbers

It is likely that the concept of fractional numbers dates to prehistoric times. The Ancient Egyptians used their Egyptian fraction notation for rational numbers in mathematical texts such as the Rhind Mathematical Papyrus and the Kahun Papyrus. Classical Greek and Indian mathematicians made studies of the theory of rational numbers, as part of the general study of number theory. The best known of these is Euclid's Elements, dating to roughly 300 BC. Of the Indian texts, the most relevant is the Sthananga Sutra, which also covers number theory as part of a general study of mathematics.

The concept of decimal fractions is closely linked with decimal place-value notation; the two seem to have developed in tandem. For example, it is common for the Jain math sutras to include calculations of decimal-fraction approximations to pi or the square root of two. Similarly, Babylonian math texts had always used sexagesimal (base 60) fractions with great frequency.

[edit] Irrational numbers

The earliest known use of irrational numbers was in the Indian Sulba Sutras composed between 800–500 BC.^[9] The first existence proofs of irrational numbers is usually attributed to Pythagoras, more specifically to the Pythagorean Hippasus of Metapontum, who produced a (most likely geometrical) proof of the irrationality of the square root of 2. The story goes that Hippasus discovered irrational numbers when trying to represent the square root of 2 as a fraction. However Pythagoras believed in the absoluteness of numbers, and could not accept the existence of irrational numbers. He could not disprove their existence through logic, but he could not accept irrational numbers, so he sentenced Hippasus to death by drowning.

The sixteenth century brought final European acceptance of negative integral and fractional numbers. By the seventeenth century, mathematicians generally used decimal fractions with modern notation. It was not, however, until the nineteenth century that mathematicians separated irrationals into algebraic and transcendental parts, and once more undertook scientific study of irrationals. It had remained almost dormant since Euclid. 1872 brought publication of the theories of Karl Weierstrass (by his pupil Kossak), Heine (Crelle, 74), Georg Cantor (Annalen, 5), and Richard Dedekind. In 1869, Méray had taken the same point of departure as Heine, but the theory is generally referred to the year 1872. Weierstrass's method was completely set forth by Salvatore Pincherle (1880), and Dedekind's has received additional prominence through the author's later work (1888) and endorsement by Paul Tannery (1894). Weierstrass, Cantor, and Heine base their theories on infinite series, while Dedekind founds his on the idea of a cut (Schnitt) in the system of real numbers, separating all rational numbers into two groups having certain characteristic properties. The subject has received later contributions at the hands of Weierstrass, Kronecker (Crelle, 101), and Méray.

Continued fractions, closely related to irrational numbers (and due to Cataldi, 1613), received attention at the hands of Euler, and at the opening of the nineteenth century were brought into prominence through the writings of Joseph Louis Lagrange. Other noteworthy contributions have been made by Druckenmüller (1837), Kunze (1857), Lemke (1870), and Günther (1872). Ramus (1855) first connected the subject with determinants, resulting, with the subsequent contributions of Heine, Möbius, and Günther, in the theory of Kettenbruchdeterminanten. Dirichlet also added to the general theory, as have numerous contributors to the applications of the subject.

[edit] Transcendental numbers and reals

The first results concerning transcendental numbers were Lambert's 1761 proof that π cannot be rational, and also that eⁿ is irrational if n is rational (unless n = 0). (The constant e was first referred to in Napier's 1618 work on logarithms.) Legendre extended this proof to show that π is not the square root of a rational number. The search for roots of quintic and higher degree equations was an important development, the Abel–Ruffini theorem (Ruffini 1799, Abel 1824) showed that they could not be solved by radicals (formula involving only arithmetical operations and roots). Hence it was necessary to consider the wider set of algebraic numbers (all solutions to polynomial equations). Galois (1832) linked polynomial equations to group theory giving rise to the field of Galois theory.

The existence of transcendental numbers^[10] was first established by Liouville (1844, 1851). Hermite proved in 1873 that e is transcendental and Lindemann proved in 1882 that π is transcendental. Finally Cantor shows that the set of all real numbers is uncountably infinite but the set of all algebraic numbers is countably infinite, so there is an uncountably infinite number of transcendental numbers.

[edit] Infinity and infinitesimals

The earliest known conception of mathematical infinity appears in the Yajur Veda, an ancient Indian script, which at one point states, "If you remove a part from infinity or add a part to infinity, still what remains is infinity." Infinity was a popular topic of philosophical study among the Jain mathematicians c. 400 BC. They distinguished between five types of infinity: infinite in one and two directions, infinite in area, infinite everywhere, and infinite perpetually.

Aristotle defined the traditional Western notion of mathematical infinity. He distinguished between actual infinity and potential infinity—the general consensus being that only the latter had true value. Galileo's Two New Sciences discussed the idea of one-to-one correspondences between infinite sets. But the next major advance in the theory was made by Georg Cantor; in 1895 he published a book about his new set theory, introducing, among other things, transfinite numbers and formulating the continuum hypothesis. This was the first mathematical model that represented infinity by numbers and gave rules for operating with these infinite numbers.

In the 1960s, Abraham Robinson showed how infinitely large and infinitesimal numbers can be rigorously defined and used to develop the field of nonstandard analysis. The system of hyperreal numbers represents a rigorous method of treating the ideas about infinite and infinitesimal numbers that had been used casually by mathematicians, scientists, and engineers ever since the invention of infinitesimal calculus by Newton and Leibniz.

A modern geometrical version of infinity is given by projective geometry, which introduces "ideal points at infinity," one for each spatial direction. Each family of parallel lines in a given direction is postulated to converge to the corresponding ideal point. This is closely related to the idea of vanishing points in perspective drawing.

[edit] Complex numbers

The earliest fleeting reference to square roots of negative numbers occurred in the work of the mathematician and inventor Heron of Alexandria in the 1st century AD, when he considered the volume of an impossible frustum of a pyramid. They became more prominent when in the 16th century closed formulas for the roots of third and fourth degree polynomials were discovered by Italian mathematicians such as Niccolo Fontana Tartaglia and Gerolamo Cardano. It was soon realized that these formulas, even if one was only interested in real solutions, sometimes required the manipulation of square roots of negative numbers.

This was doubly unsettling since they did not even consider negative numbers to be on firm ground at the time. When René Descartes coined the term "imaginary" for these quantities in 1637, he intended it as derogatory. (See imaginary number for a discussion of the "reality" of complex numbers.) A further source of confusion was that the equation

Failed to parse (Missing texvc executable; please see math/README to configure.): \left ( \sqrt{-1}\right )^2 =\sqrt{-1}\sqrt{-1}=-1

seemed capriciously inconsistent with the algebraic identity

Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt{a}\sqrt{b}=\sqrt{ab},

which is valid for positive real numbers a and b, and was also used in complex number calculations with one of a, b positive and the other negative. The incorrect use of this identity, and the related identity

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{1}{\sqrt{a}}=\sqrt{\frac{1}{a}}

in the case when both a and b are negative even bedeviled Euler. This difficulty eventually led him to the convention of using the special symbol i in place of Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt{-1}

to guard against this mistake.

The 18th century saw the work of Abraham de Moivre and Leonhard Euler. de Moivre's formula (1730) states:

Failed to parse (Missing texvc executable; please see math/README to configure.): (\cos \theta + i\sin \theta)^{n} = \cos n \theta + i\sin n \theta \,

and to Euler (1748) Euler's formula of complex analysis:

Failed to parse (Missing texvc executable; please see math/README to configure.): \cos \theta + i\sin \theta = e ^{i\theta }. \,

The existence of complex numbers was not completely accepted until Caspar Wessel described the geometrical interpretation in 1799. Carl Friedrich Gauss rediscovered and popularized it several years later, and as a result the theory of complex numbers received a notable expansion. The idea of the graphic representation of complex numbers had appeared, however, as early as 1685, in Wallis's De Algebra tractatus.

Also in 1799, Gauss provided the first generally accepted proof of the fundamental theorem of algebra, showing that every polynomial over the complex numbers has a full set of solutions in that realm. The general acceptance of the theory of complex numbers is due to the labors of Augustin Louis Cauchy and Niels Henrik Abel, and especially the latter, who was the first to boldly use complex numbers with a success that is well known.

Gauss studied complex numbers of the form a + bi, where a and b are integral, or rational (and i is one of the two roots of x² + 1 = 0). His student, Gotthold Eisenstein, studied the type a + bω, where ω is a complex root of x³ − 1 = 0. Other such classes (called cyclotomic fields) of complex numbers derive from the roots of unity x^k − 1 = 0 for higher values of k. This generalization is largely due to Ernst Kummer, who also invented ideal numbers, which were expressed as geometrical entities by Felix Klein in 1893. The general theory of fields was created by Évariste Galois, who studied the fields generated by the roots of any polynomial equation F(x) = 0.

In 1850 Victor Alexandre Puiseux took the key step of distinguishing between poles and branch points, and introduced the concept of essential singular points. This eventually led to the concept of the extended complex plane.

[edit] Prime numbers

Prime numbers have been studied throughout recorded history. Euclid devoted one book of the Elements to the theory of primes; in it he proved the infinitude of the primes and the fundamental theorem of arithmetic, and presented the Euclidean algorithm for finding the greatest common divisor of two numbers.

In 240 BC, Eratosthenes used the Sieve of Eratosthenes to quickly isolate prime numbers. But most further development of the theory of primes in Europe dates to the Renaissance and later eras.

In 1796, Adrien-Marie Legendre conjectured the prime number theorem, describing the asymptotic distribution of primes. Other results concerning the distribution of the primes include Euler's proof that the sum of the reciprocals of the primes diverges, and the Goldbach conjecture, which claims that any sufficiently large even number is the sum of two primes. Yet another conjecture related to the distribution of prime numbers is the Riemann hypothesis, formulated by Bernhard Riemann in 1859. The prime number theorem was finally proved by Jacques Hadamard and Charles de la Vallée-Poussin in 1896. Goldbach and Riemann's conjectures remain unproven and unrefuted.

Word alternatives[link]

Some numbers traditionally have alternative words to express them, including the following:

• Nothing: 0
• Single: 1
• Pair, couple, brace: 2
• Trio: 3
• Half-Dozen: 6
• Decade: 10
• Dozen: 12
• Baker's dozen: 13
• Score: 20
• Half-century: 50
• Century: 100
• Gross: 144
• Ream: 480 (old measure) 500 (new measure)
• Millenium: 1000
• Great gross: 1728
• "n-figure", as in digit, generally for larger-number ranges, also written without a hyphen; often used in financial discussion. For example

• "five-figure": 10,000 to 99,999 (five digits); ten-thousands
• "six-figure": 100,000 to 999,999 (six digits); hundred-thousands
• "seven-figure": 1,000,000 to 9,999,999 (seven digits); millions

See also[link]

Wikimedia Commons has media related to: Numbers

Notes[link]

References[link]

• Tobias Dantzig, Number, the language of science; a critical survey written for the cultured non-mathematician, New York, The Macmillan company, 1930.
• Erich Friedman, What's special about this number?
• Steven Galovich, Introduction to Mathematical Structures, Harcourt Brace Javanovich, 23 January 1989, ISBN 0-15-543468-3.
• Paul Halmos, Naive Set Theory, Springer, 1974, ISBN 0-387-90092-6.
• Morris Kline, Mathematical Thought from Ancient to Modern Times, Oxford University Press, 1972.
• Alfred North Whitehead and Bertrand Russell, Principia Mathematica to *56, Cambridge University Press, 1910.
• George I. Sanchez, Arithmetic in Maya,Austin-Texas, 1961.

External links[link]

Look up number in Wiktionary, the free dictionary.

Wikiversity has learning materials about Primary mathematics:Numbers

• Nechaev, V.I. (2001), "Number", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4, http://www.encyclopediaofmath.org/index.php?title=Number 
• Mesopotamian and Germanic numbers
• BBC Radio 4, In Our Time: Negative Numbers
• '4000 Years of Numbers', lecture by Robin Wilson, 07/11/07, Gresham College (available for download as MP3 or MP4, and as a text file).
• http://planetmath.org/encyclopedia/MayanMath2.html
• "What's the World's Favorite Number?". 2011-06-22. http://www.npr.org/blogs/krulwich/2011/07/22/138493147/what-s-your-favorite-number-world-wide-survey-v1. Retrieved 2011-09-17. ; "Cuddling With 9, Smooching With 8, Winking At 7". 2011-08-11. http://www.npr.org/templates/transcript/transcript.php?storyId=139797360. Retrieved 2011-09-17. 

Ron Paul
Member of the U.S. House of Representatives from Texas's 14th district
Incumbent
Assumed office January 3, 1997
Preceded by	Greg Laughlin
Member of the U.S. House of Representatives from Texas's 22nd district
In office January 3, 1979 – January 3, 1985
Preceded by	Robert Gammage
Succeeded by	Tom DeLay
In office April 3, 1976 – January 3, 1977
Preceded by	Robert Casey
Succeeded by	Robert Gammage
Personal details
Born	Ronald Ernest Paul (1935-08-20) August 20, 1935 (age 76) Pittsburgh, Pennsylvania, U.S.
Political party	Republican Party (1976–1988, 1988–present)
Other political affiliations	Libertarian Party (1988 election)
Spouse(s)	Carol Wells
Children	Ronnie Lori Rand Robert Joy
Alma mater	Gettysburg College (B.S.) Duke University (M.D.)
Religion	Southern Baptist
Signature
Website	Congressional website Campaign website
Military service
Service/branch	United States Air Force Texas Air National Guard
Years of service	1963–1965 1965–1968
Rank	Captain[1]
This article is part of a series about Ron Paul 2012 presidential campaign 2008 presidential campaign 1988 presidential campaign Political positions · Electoral history List of legislation sponsored by Ron Paul Ron Paul newsletters Ron Paul bibliography

Ronald Ernest "Ron" Paul (born August 20, 1935) is an American politician who has been the U.S. Representative for Texas's 14th congressional district, which includes Galveston, since 1997, and a three-time candidate for President of the United States, as a Libertarian in 1988 and as a Republican in 2008 and currently 2012. He is an outspoken critic of American foreign and monetary policies, including the Military–industrial complex and the Federal Reserve, and is known for his libertarian-leaning views, often differing from his own party on certain issues.

A native of Pittsburgh, Pennsylvania, Paul is a graduate of Gettysburg College and Duke University School of Medicine, where he earned his medical degree. He served as a medical officer in the United States Air Force from 1963 until 1968. He worked as an obstetrician-gynecologist from the 1960s to the 1980s, delivering more than 4,000 babies. He became the first Representative in history to serve concurrently with a child in the Senate when his son Rand Paul was elected to the United States Senate for Kentucky in 2010.^[2]

Ron Paul has been an active writer and publisher since the late 1970s, when he created the first of several newsletters bearing his name. He has published many books, beginning with The Case for Gold (1982) and including Liberty Defined: 50 Essential Issues That Affect Our Freedom (2011), End The Fed (2009), The Revolution: A Manifesto (2008), Pillars of Prosperity (2008), and A Foreign Policy of Freedom: Peace, Commerce, and Honest Friendship (2007). Paul has been characterized as the "intellectual godfather" of the Tea Party movement.^[3][4]

On July 12, 2011, Paul announced that he would forego seeking another term in Congress in order to focus on his presidential bid.^[5] On May 14, 2012, Paul announced that he would not be competing in any other Presidential primaries, though he is still competing for delegates in states where the primary election have already been held.^[6]

Early life, education, and medical career[link]

Ronald Ernest Paul was born on August 20, 1935, in Pittsburgh,^[7] the son of Howard Caspar Paul, who ran a small dairy company, and Margaret (née Dumont) Paul. His paternal great-grandparents emigrated from Germany, and his mother was of German and Irish ancestry.^[8][9]

As a junior at suburban Dormont High School, he was the 220-yard dash state champion.^[10] He graduated from Gettysburg College with a B.S. degree in Biology in 1957.^[10]

Paul earned a Doctor of Medicine degree from Duke University's School of Medicine in 1961, and completed his medical internship at the Henry Ford Hospital in Detroit and his residency in obstetrics and gynecology at Magee-Womens Hospital in Pittsburgh.^[11] Paul served as a flight surgeon in the United States Air Force from 1963 to 1965 and then in the United States Air National Guard from 1965 to 1968.^[12]

Paul and his wife then relocated to Texas, where he began a private practice in obstetrics and gynecology.^[13] He refused to accept Medicaid or Medicare payments, but routinely lowered fees for patients who could not afford to pay.^[14][15]

Early congressional career (1976–1985)[link]

While still a medical resident in the 1960s, Paul was influenced by Friedrich Hayek's The Road to Serfdom, which caused him to read many publications by Ludwig von Mises and Ayn Rand. He came to know economists Hans Sennholz and Murray Rothbard well, and credits to them his interest in the study of economics.^[16]

When President Richard Nixon "closed the gold window" by ending American participation in the Bretton Woods System, thus ending U.S. dollar's loose association with gold^[16] on August 15, 1971, Paul decided to enter politics^[17] and became a Republican candidate for the United States Congress.^[18]

Elections[link]

In 1974, incumbent Robert R. Casey defeated him for the 22nd district. President Gerald Ford later appointed Casey to direct the Federal Maritime Commission, and Paul won an April 1976 special election to the vacant office.^[19] Paul lost the next regular election to Democrat Robert Gammage by fewer than 300 votes (0.2%), but defeated Gammage in a 1978 rematch, and was reelected in 1980 and 1982.^[20] Gammage underestimated Paul's popularity among local mothers: "I had real difficulty down in Brazoria County, where he practiced, because he'd delivered half the babies in the county. There were only two obstetricians in the county, and the other one was his partner."^[21]

Tenure[link]

Paul has served in Congress three different periods: first from 1976 to 1977, after he won a special election, then from 1979 to 1985, and finally since 1997.

In his early years, Paul served on the House Banking Committee, where he blamed the Federal Reserve for inflation and spoke against the banking mismanagement that resulted in the savings and loan crisis.^[22][8] Paul argued for a return to the gold standard maintained by the US from 1873-1933, and with Senator Jesse Helms convinced the Congress to study the issue.^[16] He spoke against the reinstatement of registration for the military draft in 1980, in opposition to President Jimmy Carter and the majority of his fellow Republican members of Congress.^[23]

During his first term, Paul founded the Foundation for Rational Economics and Education (FREE), a non-profit "think tank" dedicated to promoting principles of limited government and free-market economics.^[24]

Paul proposed term-limit legislation multiple times, while himself serving four terms in the House of Representatives.^[23] In 1984, he decided to retire from the House in order to run for the U.S. Senate, complaining in his House farewell address that "Special interests have replaced the concern that the Founders had for general welfare.... It's difficult for one who loves true liberty and utterly detests the power of the state to come to Washington for a period of time and not leave a true cynic."^[25][26] (On Paul's departure from the House, his congressional seat was assumed by former state representative Tom DeLay, who would eventually become Speaker of the House.)^[27]

Committee assignments[link]

• House Banking Committee

1984 U.S. Senate election[link]

In 1984, Paul campaigned for the U.S. Senate, but lost the Republican primary to Phil Gramm, who had switched parties the previous year from Democrat to Republican.^[28] Another candidate of the senatorial primary was Henry Grover, a conservative former state legislator who had lost the 1972 gubernatorial general election to the Democrat Dolph Briscoe, Jr.

Inter-congressional years[link]

1985–1997[link]

Following the loss of the 1984 senate race, Paul returned to his obstetrics practice and took part in a number of other business ventures.^[8][29] Along with his former congressional chief of staff, Lew Rockwell, Paul founded a for-profit enterprise, Ron Paul & Associates, Inc. (RP&A) in 1984, with Paul serving as president, Rockwell as vice president, Paul's wife Carol as secretary, and daughter Lori Pyeatt as treasurer.^[30] The company published a variety of political and investment-oriented newsletters including Ron Paul Freedom Report and Ron Paul Survival Report, and by 1993 was generating revenues in excess of $900,000.^[31][32]

Paul also co-owned a mail-order coin dealership, Ron Paul Coins, for twelve years with Burt Blumert, who continued to operate the dealership after Paul resumed office in 1996.^[33][34] Paul spoke multiple times at the American Numismatic Association's 1988 convention.^[33] He worked with his Foundation for Rational Economics and Education on such projects as establishing the National Endowment for Liberty, producing the At Issue public policy series that was broadcast on the Discovery Channel and CNBC,^[24] and continuing publication of newsletters.

1988 presidential campaign[link]

Paul resigned from the Republican Party in 1987 and launched a bid for the presidency running on the Libertarian Party ticket. At the 1987 Libertarian National Convention, the party was split between a Conservative and Liberal wing. Paul represented the conservative wing, which was successful in fundraising, while the liberal wing claimed to have received ten times more (and more favorable) press coverage.^{[citation needed]} Paul argued, "Pro-life libertarians have a vital task to perform: to persuade the many abortion-supporting libertarians of the contradiction between abortion and individual liberty; and to sever the mistaken connection in many minds between individual freedom and the 'right' to extinguish individual life."^[35][36]

In the 1988 presidential election, Paul was on the ballot in 46 States,^[37] scoring third in the popular vote with 432,179 votes (0.5%).^[38] Paul was kept off the ballot in Missouri, and received votes there only when written in, due to what the St. Louis Post-Dispatch termed a "technicality".^[39]

According to Paul, his presidential campaign was about more than obtaining office; he sought to promote his libertarian ideas, often to school and university groups regardless of vote eligibility. He said, "We're just as interested in the future generation as this election. These kids will vote eventually, and maybe, just maybe, they'll go home and talk to their parents."^[37]

Paul considered campaigning for President during 1992,^[40] but instead chose to endorse Pat Buchanan that year, and served as an adviser to Buchanan's Republican presidential primary campaign against incumbent President George H. W. Bush.^[41]

Later congressional career (1997–present)[link]

An earlier congressional portrait of Paul

Elections[link]

1996 campaign

During 1996, Paul was re-elected to Congress after a difficult campaign. The Republican National Committee endorsed incumbent Greg Laughlin in the primary; Paul won with assistance from baseball pitcher, constituent, and friend Nolan Ryan, tax activist and publisher Steve Forbes^[8] and conservative commentator Pat Buchanan (both of whom had had presidential campaigns that year). Paul narrowly defeated Democratic attorney Charles "Lefty" Morris in the fall election, despite Morris' criticism over controversial statements in several newsletters that Ron Paul published.

1998–present

In 1998 and 2000, Paul defeated Loy Sneary, a Democratic Bay City, Texas, rice farmer and former Matagorda County judge.^[17] In the 2008 Republican primary,^[42] he defeated Friendswood city councilman Chris Peden,^[43] with over 70 percent of the vote^[44] and ran unopposed in the general election.^[45] In the 2010 Republican primary, Paul defeated three opponents with 80 percent of the vote.^[46]

On July 12, 2011, Paul announced that he would not seek re-election to the House in order to pursue the 2012 presidential election.^[47][48]

Tenure[link]

Legislation

Of the 620 bills that Paul had sponsored through December 2011, over a period of more than 22 years in Congress, only one had been signed into law – a lifetime success rate of less than 0.3%.^[49] The sole measure authored by Paul that was ultimately enacted allowed for a federal customhouse to be sold to a local historic preservation society (H.R. 2121 in 2009).^[49]

By amending other legislation, he has helped prohibit funding for national identification numbers, funding for federal teacher certification,^[17] International Criminal Court jurisdiction over the U.S. military, American participation with any U.N. global tax, and surveillance of peaceful First Amendment activities by citizens.^[50]

Affiliations

Paul was honorary chairman of, and is a member of the Republican Liberty Caucus, a political action committee that describes its goal as electing "liberty-minded, limited-government individuals".^[51] He is an initiating member of the Congressional Rural Caucus, which deals with agricultural and rural issues, and the 140-member Congressional Wildlife Refuge Caucus.^[52]

Committee assignments[link]

Rep. Paul serves on the following committee and subcommittees.^[53]

• Committee on Financial Services
  • Subcommittee on Domestic Monetary Policy and Technology (Chairman)
  • Subcommittee on International Monetary Policy and Trade
• Committee on Foreign Affairs
  • Subcommittee on Oversight and Investigations

With the election of the 112th Congress, and a resulting GOP majority in the House, Paul became the chairman of the Subcommittee on Domestic Monetary Policy and Technology starting in January 2011.^[54]

2008 presidential campaign[link]

Ron Paul being interviewed the day of the New Hampshire primary in Manchester

2008 Republican primary campaign[link]

Paul formally declared his candidacy for the 2008 Republican nomination on March 12, 2007, on C-SPAN.^[55] Few major politicians endorsed him, and his campaign was largely ignored by traditional media.^[56] However, he attracted an intensely loyal grassroots following, in large part energized by "iconoclastic white men"^[57] interacting through internet social media.^[58][59][60] In May 2007, shortly after the first televised primary debates, the blogs search engine site Technorati.com listed Paul's name as the term most frequently searched for;^[58] and Paul's campaign claimed that Paul had more YouTube channel subscribers than Barack Obama or any other candidate for president.^[61] For a candidate who had had relatively low national name recognition prior to entering the race, Paul did surprisingly well in fundraising, taking in more money than any other Republican candidate in the fourth quarter of 2007, as the primary season headed into the Iowa caucuses.^[62][63]

Despite benefiting from large numbers of campaign contributions from individual donors,^[64] and the efforts of tech-savvy supporters determined to keep his name a frequent topic of discussion on the internet,^[58] over the course of the campaign Paul was unable to translate the enthusiasm of his core supporters into large enough numbers of actual primary votes to unseat his rivals.

Paul came in 5th place in both the January 4 Iowa caucuses (10% of votes cast)^[65] and the January 8 New Hampshire primary (8%).^[66] With the exception of the Nevada caucuses January 19, where he came in 2nd (14%) behind Romney (51%), he did little better through the rest of January: Michigan 4th (6%), South Carolina 5th (4%), Florida 5th (3%). On SuperTuesday, February 5, he placed 4th in almost every state, generally taking in a mere 3–6% of the votes (although he did better in the mountain states of North Dakota (21%, 3rd place) and Montana (25%, 2nd place).^[67][68]

By March, front-runner John McCain had secured enough pledged delegates to guarantee that he would win the nomination, and Romney and Huckabee had both formally withdrawn from the race. Paul, who had won no state primaries, knew that it was now mathematically impossible for him to win the nomination, as he had captured only 20^[69] – 40 pledged delegates compared to more than 1,191 for McCain, yet he refused to concede the race and said that it was unlikely that he would ultimately endorse McCain.^[70][71][72] Over the next few weeks, Paul's supporters clashed with establishment Republicans at several county and state party conventions over state party rules, the party platforms, and selection of delegates for the national convention.^[73][74][75] In one of the more dramatic moments, Nevada's state party leaders, outmaneuvered by Paul supporters at the state nominating convention, resorted to the highly unusual measure of prematurely and abruptly shutting down the convention before selecting national delegates, with a plan to reconvene at a later date.^[76][77]

On June 12, 2008, Paul finally withdrew his bid for the Republican nomination. He later said that one of the reasons he did not run in the general election as a third-party candidate, after losing the primary election, was that, as a concession to gain ballot access in certain states, he had signed legally-binding agreements to not run a third-party campaign if he lost the primary.^[78] Some of the $4 million remaining campaign contributions was invested into the new political action and advocacy group called Ron Paul's Campaign for Liberty.^[79]

Refusal to endorse the Republican candidate[link]

At a September 10, 2008, press conference, Paul announced his general support of four third-party candidates: Cynthia McKinney (Green Party); Bob Barr (Libertarian Party); Chuck Baldwin (Constitution Party); and Ralph Nader (independent). He said that each of them had pledged to adhere to a policy of balancing budgets, bringing the troops home, defending privacy and personal liberties, and investigating the Federal Reserve. Paul also said that under no circumstances would he be endorsing either of the two dominant parties' candidates (McCain – Republican Party, or Obama – Democratic Party) because there were no real differences between them, and because neither of them, if elected, would seek to make the fundamental changes in governance that were necessary. He urged instead that, rather than contribute to the “charade” that the two-party election system had become, the voters support the third-party candidates as a protest vote, to force change in the election process.^[80][81] Later that same day, Paul gave a televised interview with Nader saying much the same again.^[82]

Two weeks later, "shocked and disappointed" that Bob Barr (the Libertarian candidate) had pulled out of attending the press conference at the last minute and had admonished Paul for remaining neutral and failing to say which specific candidate Paul would vote for in the general election, Paul released a statement saying that he had decided to endorse Chuck Baldwin, the Constitution Party candidate, for president.^[83]

In the November 2008 general election, Paul received 41,905 votes despite not actively campaigning.^[84][85]

2012 presidential campaign[link]

Ron Paul during his 2012 presidential election campaign in Las Vegas, Nevada.

Paul is a candidate for the Republican Party nomination for President of the United States in the 2012 election.

He won several early straw polls for the 2012 Republican presidential nomination ^[86] and in late April, 2011, he formed an official exploratory committee.^[87][88] He participated in the first Republican presidential debate on May 5, 2011.^[89] and on May 13, 2011, Paul formally announced his candidacy in an interview on ABC's Good Morning America.^[90] He placed second in the 2011 Ames Straw Poll, missing first by 0.9%.^[91]

In December 2011, with Ron Paul's increased support, the controversy over allegedly racist and homophobic statements in several Ron Paul newsletters in the 1980s and early 1990s once again gained media attention.^[92] During this time Paul supporters asserted that he was continually ignored by the media despite his significant support, citing examples of where television news shows would fail to mention Paul in discussions of the Republican presidential hopefuls even when he was polling second.^{[93][94][95][96]}

Paul came in third in the Iowa Republican Caucus held on January 3, 2012. Out of a turnout of 121,503 votes, Paul took 26,036 (21%) of the certified votes. Rick Santorum and Mitt Romney finished in a virtual tie for first place with 25% each.^[97] In the New Hampshire Primary held on January 10, 2012, Paul received 23% of the votes and came in second after Romney's 39%.^[98]

Ron Paul's results then declined, despite the withdrawal of candidates Michele Bachmann, Jon Huntsman and Rick Perry. He had fourth place finishes in the next two primaries, on January 21st in South Carolina (with 13% of the vote^[99]) and on January 31st in Florida (where he received 7% of the vote.^{[100][101][102]})

On February 4, Paul finished third in Nevada with 18.8% of the vote.^[103] Three non-binding primaries were held on February 7th; Paul took 3rd place in Colorado^[104] and Missouri^[105] with 13% and 12% of the vote respectively. He fared better in Minnesota^[106] with 27%, finishing second to Rick Santorum.

On May 14, Paul's campaign announced that due to lack of funds he would no longer actively campaign for votes in the 11 remaining primary states, including Texas and California, that had not yet voted.^[6][107] He would, however, continue to seek to win delegates for the national party convention in the states that had already voted.

Political party identification[link]

Throughout his entire tenure in Congress, Paul has represented his district as a member of the Republican Party. However, he has frequently taken positions in direct opposition to the other members and the leadership of the party, and he has sometimes publicly questioned whether he really belonged in the party.

He had been a lifelong supporter of the Republican Party by the time he entered politics in the mid 1970s.^[108] He was one of the first elected officials in the nation to support Ronald Reagan's presidential campaign,^[109] and he actively campaigned for Reagan in 1976 and 1980.^[110] After Reagan's election in 1980, Paul quickly became disillusioned with the Reagan administration's policies. He later recalled being the only Republican to vote against Reagan budget proposals in 1981,^[111][112] aghast that "in 1977, Jimmy Carter proposed a budget with a $38 billion deficit, and every Republican in the House voted against it. In 1981, Reagan proposed a budget with a $45 billion deficit – which turned out to be $113 billion – and Republicans were cheering his great victory. They were living in a storybook land."^[109] He expressed his disgust with the political culture of both major parties in a speech delivered in 1984 upon resigning from the House of Representatives to prepare for a (failed) run for the Senate, and he eventually apologized to his Libertarian friends for having supported Reagan.^[111]

Wikisource has original text related to this article: Ron Paul's 1987 Resignation Letter to the RNC

By 1987, Paul was ready to sever all ties to the Republican Party, as he explained in a blistering resignation letter: "Since [1981] Ronald Reagan and the Republican Party have given us skyrocketing deficits, and astoundingly a doubled national debt. How is it that the party of balanced budgets, with control of the White House and Senate, accumulated red ink greater than all previous administrations put together? ... There is no credibility left for the Republican Party as a force to reduce the size of government. That is the message of the Reagan years."^[110][108] A month later he announced he would seek the 1988 Libertarian Party nomination for president.

During the 1988 campaign, Paul called Reagan "a dramatic failure"^[110] and complained that "Reagan's record is disgraceful. He starts wars, breaks the law, supplies terrorists with guns made at taxpayers' expense and lies about it to the American people."^[113] Paul predicted that "the Republicans are on their way out as a major party,"^[111] and he said that, although registered as a Republican, he had always been a Libertarian at heart.^[112][111]

Paul returned to his private medical practice and managing several business ventures after losing the 1988 election; but by 1996, he was ready to return to politics, this time running on the Republican Party ticket again. He said that he had never read the entire Libertarian platform when he ran for president as a Libertarian in 1988, and that "I worked for the Libertarians on my terms, not theirs."^[114] He added that in terms of a political label he preferred to call himself "a constitutionalist. In Congress I took an oath to uphold the Constitution, not the (Republican) platform."^[114]

When he lost the Republican Party presidential primary election in 2008, Paul criticized the two major political parties, saying that there was no real difference between the parties and that neither of them truly intended to challenge the status quo. He refused to endorse the Republican Party's nominee for president, John McCain, and lent his support to third-party candidates instead.^[115][116]

In 2012 presidential campaign, during which he acknowledged it was unlikely that he would win the Republican Party nomination,^[117] Paul again asserted that he was participating in the Republican Party on his own terms, trying to persuade the rest of the party to move toward his positions rather than joining in with theirs.^[118] He expressed doubt that he would support any of his rivals should they win the nomination, warning that, “If the policies of the Republican Party are the same as the Democrat Party and they don't want to change anything on foreign policy, they don't want to cut anything, they don't want to audit the Fed and find out about monetary policy, they don't want to have actual change in government, that is a problem for me."^[119] On that same theme he said in another interview, "I would be reluctant to jump on board and tell all of the supporters that have given me trust and money that all of a sudden, I'd say, [all] we've done is for naught. So, let's support anybody at all ... even if they disagree with everything that we do."^[120]

Political positions[link]

Paul at the 2007 National Right to Life Committee Convention in Kansas City, Missouri, June 15, 2007.

Paul has been described as conservative and libertarian.^[8] According to University of Georgia political scientist Keith Poole, Paul had the most conservative voting record of any member of Congress from 1937 to 2002,^[121] and is the most conservative of the candidates seeking the 2012 Republican nomination for president,^[122] on a scale primarily measuring positions on the role of government in managing the economy – not positions on social issues or foreign policy matters.^[123] Other analyses, in which key votes on domestic social issues and foreign policy factor more heavily, have judged Paul much more moderate. The National Journal, for instance, rated Paul only the 145th most conservative member of the House of Representatives based on votes cast in 2010.^[124][125]

The foundation of Paul's political philosophy is the conviction that "the proper role for government in America is to provide national defense, a court system for civil disputes, a criminal justice system for acts of force and fraud, and little else."^[126] He has been nicknamed "Dr. No,"^[17] reflecting both his medical degree and his insistence that he will "never vote for legislation unless the proposed measure is expressly authorized by the Constitution."^[22]

Paul is a proponent of Austrian School economics; he has authored six books on the subject, and displays pictures of Austrian School economists Friedrich Hayek, Murray Rothbard, and Ludwig von Mises (as well as of Grover Cleveland)^[127] on his office wall. He regularly votes against almost all proposals for new government spending, initiatives, or taxes;^[128] he cast two thirds of all the lone negative votes in the House during a 1995–1997 period.^[17]

He has pledged never to raise taxes^[129] and states he has never voted to approve a budget deficit. Paul believes that the country could abolish the individual income tax by scaling back federal spending to its fiscal year 2000 levels;^[130][131] financing government operations would be primarily by excise taxes and non-protectionist tariffs. He endorses eliminating most federal government agencies, terming them unnecessary bureaucracies.

On April 15, 2011, Paul was one of four Republican members of Congress to vote against Rep. Paul Ryan's budget proposal, known as "The Path to Prosperity."^[132]

Paul has a consistent record as an inflation hawk, having warned of hyperinflation as far back as 1981.^[133] While Paul believes the longterm decrease of the U.S. dollar's purchasing power by inflation is attributable to its lack of any commodity backing, he does not endorse a "return" to a gold standard – as the U.S. government has established during the past – but instead prefers to eliminate legal tender laws and to remove the sales tax on gold and silver, so that the market may freely decide what type of monetary standard(s) there shall be.^[134] Since 1999, he has introduced bills into each Congress seeking to eliminate the Federal Reserve System in a single year.^{[135][136][137]}

Paul's foreign policy of nonintervention^[138] made him the only 2008 Republican presidential candidate to have voted against the Iraq War Resolution in 2002. He advocates withdrawal from the United Nations, and from the North Atlantic Treaty Organization, for reasons of maintaining strong national sovereignty.^[139]

He endorses free trade, rejecting membership in the North American Free Trade Agreement (NAFTA) and the World Trade Organization as "managed trade". He endorses increased border security and opposes welfare for illegal aliens, birthright citizenship and amnesty;^[140] he voted for the Secure Fence Act of 2006. He voted for the Authorization for Use of Military Force Against Terrorists in response to the September 11 attacks, but suggested war alternatives such as authorizing the president to grant Letters of Marque and Reprisal targeting specific terrorists. An opponent of the Iraq War and potential war with Iran, he has also criticized neoconservatism and U.S. foreign policy in the Middle East, arguing that both inadvertently cause terrorist reprisals against Americans. Paul has stated that "Israel is our close friend" and that it is not the place of the United States to "dictate how Israel runs her affairs".^[141]

Paul endorses constitutional rights, such as the right to keep and bear arms, and habeas corpus for political detainees. He opposes the Patriot Act, federal use of torture, presidential autonomy, a national identification card, warrantless domestic surveillance, and the draft. Paul also believes that the notion of the separation of church and state is currently misused by the court system: "In case after case, the Supreme Court has used the infamous 'separation of church and state' metaphor to uphold court decisions that allow the federal government to intrude upon and deprive citizens of their religious liberty."^[142]

Citing the Ninth and Tenth Amendments, Paul advocates states' rights to decide how to regulate social matters not cited directly by the Constitution. He opposes federal regulation of the death penalty^[143] (although he opposes capital punishment),^[144] of education,^[145] and of marriage, and endorsed revising the military's "don't ask, don't tell" policy to concern mainly disruptive sexual behavior (whether heterosexual or homosexual).^[146]

Paul says his years as an obstetrician led him to believe life begins at conception.^[147]

He terms himself "strongly pro-life",^[148] "an unshakable foe of abortion",^[149] and believes regulation or ban^[150] on medical decisions about maternal or fetal health is "best handled at the state level".^[143][151] His abortion-related legislation, like the Sanctity of Life Act, is intended to negate Roe v. Wade and to get "the federal government completely out of the business of regulating state matters."^[152]

Paul has stated that "The government shouldn't be in the medical business." He pushes to eliminate federal involvement with and management of health care, which he argues would allow prices to decrease due to the fundamental dynamics of a free market.^[153] Paul also opposes the federal War on Drugs,^[154] and believes the states should decide whether to regulate or deregulate drugs such as medical marijuana.^[155] He also opposes federal government influenza inoculation programs.^[156]

As a free-market environmentalist, he asserts private property rights in relation to environmental protection and pollution prevention.^{[citation needed]} He called global warming a hoax in a 2009 Fox Business interview, saying, "You know, the greatest hoax I think that has been around in many, many years if not hundreds of years has been this hoax on the environment and global warming."^[157] He acknowledges there is clear evidence of rising temperatures in some parts of the globe, but says that temperatures are cooling in other parts.^[158]

Paul was critical of the Civil Rights Act of 1964, arguing that it sanctioned federal interference in the labor market and did not improve race relations. He once remarked: "The Civil Rights Act of 1964 not only violated the Constitution and reduced individual liberty; it also failed to achieve its stated goals of promoting racial harmony and a color-blind society".^[159] Paul opposes affirmative action.^[160]

He is an outspoken proponent of increased ballot access for 3rd party candidates,^[161] but has sought to repeal the National Voter Registration Act of 1993, also known as the Motor Voter law.^[162]

Newsletters controversy[link]

Beginning in 1978, for more than two decades Paul and his associates published a number of political and investment-oriented newsletters bearing his name (Dr. Ron Paul's Freedom Report, The Ron Paul Survival Report, the Ron Paul Investment Letter, and the Ron Paul Political Report).^[163] By 1993, a business through which Paul was publishing the newsletters was earning in excess of $900,000 per year.^[163]

A number of the newsletters, particularly in the period between 1988 and 1994 when Paul was no longer in Congress, contained material that later proved highly controversial, dwelling on conspiracy theories, praising anti-government militia movements, and warning of coming race wars.^[163][164] During Paul's 1996 congressional election campaign, and his 2008 and 2012 presidential primary campaigns, critics charged that some of the passages reflected racist, anti-Semitic, and homophobic bigotry.^{[165][166][167][168][169][170][171]}

The newsletters included statements such as: