Archimedes was among the greatest mathematicians of antiquity.

Leonhard Euler is widely considered one of the greatest mathematicians.

Carl Friedrich Gauss was the foremost mathematician of the early 19th century.

Henri Poincaré is regarded as the last mathematician to excel in every field of the mathematics of his time.

David Hilbert was one of the most influential mathematicians of the late 19th and early 20th centuries.

Emmy Noether is possibly the most influential female mathematician to date.

Isaac Newton was a pioneering figure in the development of mathematical physics.

Ramanujan was an Indian mathematician who had no formal training in mathematics and yet made important contributions to the field.

A mathematician is a person with an extensive knowledge of mathematics, a field that has been informally defined as being concerned with numbers, data, collection, quantity, structure, space, and change.

Mathematicians involved with solving problems outside of pure mathematics are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their specialized knowledge and professional methodology, approach many of the imposing problems presented in related scientific fields. With professional focus on a wide variety of problems, theoretical systems, and localized constructs, applied mathematicians work regularly in the study and formulation of mathematical models.

The discipline of applied mathematics concerns itself with mathematical methods that are typically used in science, engineering, business, and industry; thus, "applied mathematics" is a mathematical science with specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on problems, often concrete but sometimes abstract. As professionals focused on problem solving, applied mathematicians look into the formulation, study, and use of mathematical models in science, engineering, business, and other areas of mathematical practice.

Education[link]

Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education, and then proceed to specialize in topics of their own choice at the graduate level. In some universities, a qualifying exam serves to test both the breadth and depth of a student's understanding of mathematics; the students who pass are permitted to work on a doctoral dissertation.

Motivation[link]

Mathematicians do research in fields such as logic, set theory, category theory, abstract algebra, number theory, analysis, geometry, topology, dynamical systems, combinatorics, game theory, information theory, numerical analysis, optimization, computation, probability and statistics. These fields comprise both pure mathematics and applied mathematics and establish links between the two. Some fields, such as the theory of dynamical systems, or game theory, are classified as applied mathematics due to the relationships they possess with physics, economics and the other sciences. Whether probability theory and statistics are of theoretical nature, applied nature, or both, is quite controversial among mathematicians. Other branches of mathematics, however, such as logic, number theory, category theory or set theory are accepted as part of pure mathematics, though they find application in other sciences (predominantly computer science and physics). Likewise, analysis, geometry and topology, although considered pure mathematics, find applications in theoretical physics—string theory, for instance.

Though it is true that mathematics finds diverse applications in many areas of research, a mathematician does not determine the value of an idea by the diversity of its applications. Mathematics is interesting in its own right, and a substantial minority of mathematicians investigate the diversity of structures studied in mathematics itself. However, among academic mathematics, the majority of mathematical papers published in the United States are written by academics outside of mathematics departments.

Furthermore, a mathematician is not someone who merely manipulates formulas, numbers or equations—the diversity of mathematics allows for research concerning how concepts in one area of mathematics can be used in other areas too. For instance, if one graphs a set of solutions of an equation in some higher dimensional space, he may ask about the geometric properties of the graph. Thus one can understand equations by a pure understanding of abstract topology or geometry—this idea is of importance in algebraic geometry. Similarly, a mathematician does not restrict his study of numbers to the integers; rather he considers more abstract structures such as rings, and in particular number rings in the context of algebraic number theory. This exemplifies the abstract nature of mathematics and how it is not restricted to questions one may ask in daily life.

In a different direction, mathematicians ask questions about space and transformations that are not restricted to geometric figures such as squares and circles. For instance, an active area of research in differential topology concerns itself with the ways one can "smooth" higher dimensional figures. In fact, whether one can smooth certain higher dimensional spheres was, until recently, an open problem — known as the smooth Poincaré conjecture. Another aspect of mathematics, set-theoretic topology and point-set topology, concerns objects of a different nature from objects in our universe, or in a higher dimensional analogue of our universe. These objects behave in a rather strange manner under deformations, and the properties they possess are completely different from those of objects in our universe. For instance, the "distance" between two points on such an object, may depend on the order in which you consider the pair of points. This is quite different from ordinary life, in which it is accepted that the straight line distance from person A to person B is the same as that between person B and person A.

Another aspect of mathematics, often referred to as "foundational mathematics", consists of the fields of logic and set theory. These explore various ideas regarding the ways one can prove certain claims. This theory is far more complex than it seems, in that the truth of a claim depends on the context in which the claim is made, unlike basic ideas in daily life where truth is absolute. In fact, although some claims may be true, it is impossible to prove or disprove them in rather natural contexts.

Category theory, another field within "foundational mathematics", is rooted on the abstract axiomatization of the definition of a "class of mathematical structures", referred to as a "category". A category intuitively consists of a collection of objects, and defined relationships between them. While these objects may be anything (such as "tables" or "chairs"), mathematicians are usually interested in particular, more abstract, classes of such objects. In any case, it is the relationships between these objects, and not the actual objects that are predominantly studied.

Differences with scientists[link]

Mathematics differs from natural science in that scientists subject truth claims to tests by experiments, while mathematical propositions are conclusions of mathematical proofs.

If a definite statement is believed plausible by some mathematicians but has been neither proved nor disproved, it is called a conjecture, as opposed to an ultimate goal: a theorem that has been proved.

Scientific theories change when new information about the world is discovered. Mathematics changes in a similar way: New ideas do not falsify old ones, but new concepts refine old concepts and old theories, attaining a better approximation to the truth. One method of refinement is generalization, for example widening the scope of a concept. For instance, calculus (in one variable) generalizes to multivariable calculus, which generalizes to analysis on manifolds. The development of algebraic geometry from its classical to modern forms is a particularly striking example of the way an area of mathematics can change radically in its viewpoint, without making what was correctly proved before in any way incorrect; of course mathematical progress clarifies gaps in previous proofs, often by exposing hidden assumptions, which progress has revealed worth conceptualizing.

A theorem is true, and was true before we knew it and will be true after humans are extinct. Of course, our understanding of what the theorem really means gains in profundity as the mathematics around the theorem grows. A mathematician feels that a theorem is better understood when it can be extended to apply in a broader setting than previously known. For instance, Fermat's little theorem for the nonzero integers modulo a prime generalizes to Euler's theorem for the invertible numbers modulo any nonzero integer, which generalizes to Lagrange's theorem for finite groups.

Women in mathematics[link]

While the majority of mathematicians are male, there have been some demographic changes since World War II. Some prominent female mathematicians are Hypatia of Alexandria (ca. 400 AD), Ada Lovelace (1815–1852), Maria Gaetana Agnesi (1718–1799), Emmy Noether (1882–1935), Sophie Germain (1776–1831), Sofia Kovalevskaya (1850–1891), Alicia Boole Stott (1860–1940), Rózsa Péter (1905–1977), Julia Robinson (1919–1985), Olga Taussky-Todd (1906–1995), Émilie du Châtelet (1706–1749), Mary Cartwright (1900–1998), Olga Ladyzhenskaya (1922–2004), and Olga Oleinik (1925–2001).

The Association for Women in Mathematics is a professional society whose purpose is "to encourage women and girls to study and to have active careers in the mathematical sciences, and to promote equal opportunity and the equal treatment of women and girls in the mathematical sciences." The American Mathematical Society and other mathematical societies offer several prizes aimed at increasing the representation of women and minorities in the future of mathematics.

Prizes in mathematics[link]

There is no Nobel Prize in mathematics, though sometimes mathematicians have won the Nobel Prize in a different field, such as economics. Prominent prizes in mathematics include the Abel Prize, the Chern Medal, the Fields Medal, the Gauss Prize, the Nemmers Prize, the Balzan Prize, the Crafoord Prize, the Shaw Prize, the Wolf Prize, the Schock Prize, and the Nevanlinna Prize.

Quotations about mathematicians[link]

Wikiquote has a collection of quotations related to: Mathematician

The following are quotations about mathematicians, or by mathematicians.

A mathematician is a device for turning coffee into theorems.

—Attributed to both Alfréd Rényi^[1] and Paul Erdős

Die Mathematiker sind eine Art Franzosen; redet man mit ihnen, so übersetzen sie es in ihre Sprache, und dann ist es alsobald ganz etwas anderes. (Mathematicians are [like] a sort of Frenchmen; if you talk to them, they translate it into their own language, and then it is immediately something quite different.)

—Johann Wolfgang von Goethe

Each generation has its few great mathematicians...and [the others'] research harms no one.

—Alfred W. Adler (1930- ), "Mathematics and Creativity"^[2]

In short, I never yet encountered the mere mathematician who could be trusted out of equal roots, or one who did not clandestinely hold it as a point of his faith that x squared + px was absolutely and unconditionally equal to q. Say to one of these gentlemen, by way of experiment, if you please, that you believe occasions may occur where x squared + px is not altogether equal to q, and, having made him understand what you mean, get out of his reach as speedily as convenient, for, beyond doubt, he will endeavor to knock you down.

—Edgar Allan Poe, The purloined letter

A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.

—G. H. Hardy, A Mathematician's Apology

Some of you may have met mathematicians and wondered how they got that way.

—Tom Lehrer

It is impossible to be a mathematician without being a poet in soul.

—Sofia Kovalevskaya

There are two ways to do great mathematics. The first is to be smarter than everybody else. The second way is to be stupider than everybody else—but persistent.

—Raoul Bott

See also[link]

Some notable mathematicians include Archimedes of Syracuse, Leonhard Euler, Carl Gauss, Johann Bernoulli, Jacob Bernoulli, Aryabhatta, Brahmagupta, Bhaskara II, Nilakantha Somayaji, Omar Khayyám, Muhammad ibn Mūsā al-Khwārizmī, Bernhard Riemann, Gottfried Leibniz, Andrey Kolmogorov, Euclid of Alexandria, Jules Henri Poincaré, Srinivasa Ramanujan, Alexander Grothendieck, David Hilbert, Alan Turing, von Neumann, Kurt Gödel, Joseph-Louis Lagrange, Georg Cantor, William Rowan Hamilton, Carl Jacobi, Évariste Galois, Nikolay Lobachevsky, Rene Descartes, Joseph Fourier, Pierre-Simon Laplace, Alonzo Church, Nikolay Bogolyubov and Pierre de Fermat.

Mathematics portal

• List of amateur mathematicians
• List of female mathematicians
• List of mathematicians
• Mathematical joke
• Men of mathematics (book)
• A Mathematician's Apology

Notes[link]

References[link]

External links[link]

Wikiquote has a collection of quotations related to: Mathematicians

Wikimedia Commons has media related to: Mathematicians

• Occupational Outlook: Mathematicians. Information on the occupation of mathematician from the US Department of Labor.
• Sloan Career Cornerstone Center: Careers in Mathematics. Although US-centric, a useful resource for anyone interested in a career as a mathematician. Learn what mathematicians do on a daily basis, where they work, how much they earn, and more.
• The MacTutor History of Mathematics archive. A comprehensive list of detailed biographies.
• The Mathematics Genealogy Project. Allows to follow the succession of thesis advisors for most mathematicians, living or dead.
• Weisstein, Eric W., "Unsolved Problems" from MathWorld.
• Middle School Mathematician Project Short biographies of select mathematicians assembled by middle school students.
• Career Information for Students of Math and Aspiring Mathematicians from MathMajor

This article contains Japanese text. Without proper rendering support, you may see question marks, boxes, or other symbols instead of kanji and kana.

Michio Kaku (加来 道雄, Kaku Michio^?, born January 24, 1947) is an American theoretical physicist, the Henry Semat Professor of Theoretical Physics in the City College of New York of City University of New York, a co-founder of string field theory,^[1] a futurist, and a "communicator" and "popularizer" of science. He has written several books about physics and related topics; he has made frequent appearances on radio, television, and film; and he writes extensive online blogs and articles. He has written two New York Times best sellers, Physics of the Impossible (2008) and Physics of the Future (2011). He has hosted several TV specials for BBC-TV, the Discovery Channel, and the Science Channel.

Early life and education[link]

Kaku was born in San Jose, California to Japanese immigrant parents. His grandfather came to the United States to take part in the clean-up operation after the 1906 San Francisco Earthquake^{[citation needed]}. His father was born in California but was educated in Japan and spoke little English. Both his parents were put in the Tule Lake War Relocation Center, where they met and where his two brothers were born.

At Cubberley High School in Palo Alto, Kaku assembled an atom smasher in his parents' garage for a science fair project.^[2] At the National Science Fair in Albuquerque, New Mexico, he attracted the attention of physicist Edward Teller, who took Kaku as a protégé, awarding him the Hertz Engineering Scholarship. Kaku graduated summa cum laude from Harvard University in 1968 and was first in his physics class. He attended the Berkeley Radiation Laboratory at the University of California, Berkeley and received a Ph.D. in 1972, and in 1972 he held a lectureship at Princeton University.

During the Vietnam War, Kaku completed his U.S. Army basic training at Fort Benning, Georgia and his advanced individual training at Fort Lewis, Washington.^[3] However, the Vietnam War ended before he was deployed as an infantryman.

Academic career[link]

Kaku became a visiting professor at the Institute for Advanced Study in Princeton,^[4] and New York University.^[5] He currently holds the Henry Semat Chair and Professorship in theoretical physics at the City College of New York.^[6]

Kaku has had over 70 articles published in physics journals such as Physical Review, covering topics such as superstring theory, supergravity, supersymmetry, and hadronic physics.^[7] In 1974, along with Prof. Keiji Kikkawa of Osaka University, he authored the first papers describing string theory in a field form.^[8][9]

Kaku is the author of several textbooks on string theory and quantum field theory.

Popular science[link]

Kaku is most widely known as a popularizer of science.^[10] He has written books and appeared on many television programs as well as film. He also hosts a weekly radio program.

Books[link]

Kaku is the author of various popular science books.

• Hyperspace (1994)
• Beyond Einstein (with Jennifer Thompson) (1995)
• Visions: How Science Will Revolutionize the 21st Century^[11] (1998)
• Einstein's Cosmos (2004)
• Parallel Worlds (2004)
• Physics of the Impossible (2008)
• Physics of the Future (2011)

Hyperspace was a best-seller and was voted one of the best science books of the year by both The New York Times^[10] and The Washington Post. Parallel Worlds was a finalist for the Samuel Johnson Prize for non-fiction in the UK.^[12]

Radio[link]

Kaku is the host of the weekly, one-hour radio program Explorations, produced by the Pacifica Foundation's WBAI in New York. "Explorations" is syndicated to community and independent radio stations and makes previous broadcasts available on the program's website. Kaku defines the show as dealing with the general topics of science, war, peace, and the environment.

In April 2006, Kaku began broadcasting Science Fantastic on 90 commercial radio stations, the only nationally syndicated science program on commercial radio in the United States. It is syndicated by Talk Radio Network and now reaches 130 radio stations and America's Talk on XM. The program is formatted as a live listener call-in show, focusing on "futurology," which he defines as the future of science.^{[citation needed]} Featured guests include Nobel laureates and top researchers on the topics of string theory, time travel, black holes, gene therapy, aging, space travel, artificial intelligence, and SETI. When Kaku is busy filming for television, Science Fantastic goes on hiatus, sometimes for several months. Kaku is also a frequent guest on many programs, where he is outspoken in all areas and issues he considers of importance, such as the program Coast to Coast AM, where on 30 November 2007, he reaffirmed his belief that there is a 100% probability of extraterrestrial life in the universe.^[13]

Kaku has appeared on The Opie and Anthony Show a number of times, discussing popular fiction such as Back to The Future, Lost, and the theories behind time-travel that these and other fictional entertainment focus on.

Television and film[link]

Kaku has appeared in many forms of media and on many programs and networks, including Good Morning America, The Screen Savers, Larry King Live, 60 Minutes, Nightline, 20/20, Naked Science, CNN, ABC News, CBS News, NBC News, Al Jazeera English, Fox News Channel, The History Channel, Conan, The Science Channel, The Discovery Channel, TLC, Countdown with Keith Olbermann, The Colbert Report, The Art Bell Show and its successor, Coast To Coast AM, BBC World News America, The Opie & Anthony Show, The Covino & Rich Show, Head Rush, The Late Show with David Letterman, and Real Time with Bill Maher.

In 1999, Kaku was one of the scientists profiled in the feature-length film Me and Isaac Newton, directed by Michael Apted. It played theatrically in the United States, was later broadcast on national TV, and won several film awards.^{[citation needed]}

In 2005, Kaku appeared in the short documentary Obsessed & Scientific. The film is about the possibility of time travel and the people who dream about it. It screened at the Montreal World Film Festival and a feature film expansion is in development talks. Kaku also appeared in the ABC documentary UFOs: Seeing Is Believing, in which he suggested that while he believes it is extremely unlikely that extraterrestrials have ever actually visited Earth, we must keep our minds open to the possible existence of civilizations a million years ahead of us in technology, where entirely new avenues of physics open up. He also discussed the future of interstellar exploration and alien life in the Discovery Channel special Alien Planet as one of the multiple speakers who co-hosted the show, and Einstein's Theory of Relativity on The History Channel.

In February 2006, Kaku appeared as presenter in the BBC-TV four-part documentary Time which seeks to explore the mysterious nature of time. Part one of the series concerns personal time, and how we perceive and measure the passing of time. The second in the series deals with cheating time, exploring possibilities of extending the lifespan of organisms. The geological time covered in part three explores the ages of the earth and the sun. Part four covers the topics of cosmological time, the beginning of time and the events that occurred at the instant of the big bang.

On January 28, 2007, Kaku hosted the Discovery Channel series 2057. This three-hour program discussed how medicine, the city, and energy could change over the next 50 years.

In 2008, Kaku hosted the three-hour BBC-TV documentary Visions of the Future, on the future of computers, medicine, and quantum physics, and he appeared in several episodes of the History Channel's Universe series.

On December 1, 2009, he began hosting a 12-episode weekly TV series for the Science Channel at 10 pm, called Sci Fi Science: Physics of the Impossible, based on his best-selling book. Each 30-minute episode discusses the scientific basis behind imaginative schemes, such as time travel, parallel universes, warp drive, star ships, light sabers, force fields, teleportation, invisibility, death stars, and even superpowers and flying saucers. Each episode includes interviews with the world's top scientists working on prototypes of these technologies, interviews with science fiction fans, clips from science fiction movies, and special effects and computer graphics. Although these inventions are impossible today, the series discusses when these technologies might become feasible in the future.^[14]

In 2010, he began to appear in a series on the website Gametrailers.com called Science of Games, discussing the scientific aspects of various popular video games such as Mass Effect 2 and Star Wars: The Force Unleashed.

Kaku is popular in mainstream media because of his knowledge and his accessible approach to presenting complex subjects in science. While his technical writings are confined to theoretical physics, his public speaking and media appearances cover a broad range of topics, from the Kardashev scale to more esoteric subjects such as wormholes and time travel. In January 2007, Kaku visited Oman. While there, he talked at length to select members of that country's decision makers. In an interview with local media, Dr Kaku elaborated on his vision of mankind's future. Kaku considers climate change and terrorism as serious threats in man's evolution from a Type 0 civilization to Type 1.^[15]

He is pictured in Symphony of Science's newest song (as of September 6, 2011), 'The Quantum World.'

On October 11, 2010, Michio Kaku appeared in the BBC program "What Happened Before the Big Bang" (along with Laura Mersini-Houghton, Andrei Linde, Roger Penrose, Lee Smolin, Neil Turok, and other notable cosmologists and physicists), where he propounded his theory of the universe created out of nothing.^[16]

Social policy advocacy[link]

Kaku has publicly stated his concerns over matters including the anthropogenic cause of global warming, nuclear armament, nuclear power and the general misuse of science.^[17] He was critical of the Cassini–Huygens space probe because of the 72 pounds (33 kg) of plutonium contained in the craft for use by its radioisotope thermoelectric generator. Conscious of the possibility of casualties if the probe's fuel were dispersed into the environment during a malfunction and crash as the probe was making a 'sling-shot' maneuver around earth, Kaku publicly criticized NASA's risk assessment.^[18] He has also spoken on the dangers of space junk and called for more and better monitoring. Kaku is generally a vigorous supporter of the exploration of outer space, believing that the ultimate destiny of the human race may lie in extrasolar planets; but he is critical of some of the cost-ineffective missions and methods of NASA.

Kaku credits his anti-nuclear war position to programs he heard on the Pacifica Radio network, during his student years in California. It was during this period that he made the decision to turn away from a career developing the next generation of nuclear weapons in association with Edward Teller and focused on research, teaching, writing and media.^{[citation needed]} Kaku joined with others such as Helen Caldicott, Jonathan Schell, Peace Action and was instrumental in building a global anti-nuclear weapons movement that arose in the 1980s, during the administration of U.S. President Ronald Reagan.

Kaku was a board member of Peace Action and on the board of radio station WBAI-FM in New York City where he originated his long running program, Explorations, that focused on the issues of science, war, peace and the environment.

His remark from an interview in support of SETI, "We could be in the middle of an intergalactic conversation...and we wouldn't even know.", is used in the third Symphony of Science installment "Our Place in the Cosmos".

Personal life[link]

Kaku is married to Shizue Kaku and has two daughters.^[19]

Bibliography[link]

References[link]

External links[link]

Wikimedia Commons has media related to: Michio Kaku

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• Official website
• Michio Kaku on Twitter
• Getting Physical: Dr. Michio Kaku Explains Einstein's Genius
• Russia Takes Aim at Asteroids, op-ed on asteroid defense, Wall St. Journal, Jan. 5, 2010
• The Skeptics' Guide To The Universe interview
• Michio Kaku at the Internet Movie Database
• Michio Kaku on National Public Radio
• About Michio Kaku
• Video: Michio Kaku discusses Physics of the Future on March 23, 2011, on Forum Network.
• In Depth interview with Kaku, October 3, 2010

This article's factual accuracy is disputed. Please help to ensure that disputed facts are reliably sourced. See the relevant discussion on the talk page. (December 2011)

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Keith J. Devlin
Keith Devlin (2011)
Born	East Hull, England
Nationality	English and American
Fields	Mathematics
Institutions	Stanford University, Kings College London, University of Bristol, University of Manchester, University of Aberdeen, University of Oslo, University of Heidelberg, University of Bonn, University of Toronto, University of Lancaster, Colby College, St. Mary's College of California
Alma mater	Kings College London, University of Bristol
Doctoral advisor	Frederick Rowbottom[1]

Keith J. Devlin is a British mathematician and popular science writer. He has lived in the United States since 1987 and has dual American-British citizenship.

Biography[link]

Devlin earned a B.Sc. (Special) in Mathematics at Kings College London and a Ph.D. in Mathematics at the University of Bristol under the supervision of Frederick Rowbottom.^[1] He is co-founder and Executive Director of Stanford University's Human-Sciences and Technologies Advanced Research Institute (H-STAR), a co-founder of Stanford Media X university-industry research partnership program, and a Senior Researcher in the Center for the Study of Language and Information (CSLI). He is a commentator on National Public Radio's Weekend Edition Saturday, where he is known as "The Math Guy."^[2]

As of 2011, he is the author of 31 books and over 80 research articles.^[3] Several of his books are aimed at an audience of the general public, as opposed to much academic work.

His recent research work has focused on the development of new tools and protocols to assist intelligence analysis and the development and use of videogames in mathematics education.

Devlin is also creator of the concept "soft mathematics," introduced in the final chapter of his book Goodbye, Descartes.

Research publications[link]

• Devlin, Keith I.; Jensen, R. Björn (1975), "Marginalia to a theorem of Silver", ISILC Logic Conference (Proc. Internat. Summer Inst. and Logic Colloq., Kiel, 1974), Lecture notes in mathematics, 499, Berlin, New York: Springer-Verlag, pp. 115–142, DOI:10.1007/BFb0079419, ISBN 978-3-540-07534-9, MR 0480036, http://books.google.com/books?id=9UHU_bq-wc8C&dq=Marginalia+to+a+theorem+of+Silver  [First proof of Jensen's covering theorem; Keith J. Devlin is credited as Keith I. Devlin in the paper.]

List of books[link]

This list is incomplete; you can help by expanding it.

• Mathematics Education for a New Era: Video Games as a Medium for Learning. A K Peters. 2011. ISBN 978-1-56881-431-5. 
• The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern. Basic Books. 2008. ISBN 978-0-465-00910-7. 
• The Numbers Behind NUMB3RS: Solving Crime with Mathematics. Plume. 2007. ISBN 0-452-28857-6.  with coauthor Gary Lorden
• The Math Instinct: Why You're a Mathematical Genius (Along with Lobsters, Birds, Cats, and Dogs). Thunder's Mouth Press. 2006. ISBN 1-56025-839-X. 
• The Millennium Problems: the Seven Greatest Unsolved Mathematical Puzzles of Our Time. Basic Books. 2002. ISBN 0-465-01730-4. 
• The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip. Basic Books. 2000. ISBN 0-465-01619-7. 
• Mathematics: The New Golden Age. Columbia University Press. 1999. ISBN 0-231-11639-X. 
• The Language of Mathematics: Making the Invisible Visible. Holt Paperbacks. 1998. ISBN 0-8050-7254-3. 
• Mathematics: The Science of Patterns. Holt Paperbacks. 1996. ISBN 0-8050-7344-2. 
• The Joy of Sets: Fundamentals of Contemporary Set Theory. Springer. 1993. ISBN 0-387-94094-4. 
• Logic and Information. Cambridge University Press. 1991. ISBN 0-521-49971-2. 
• Constructibility. Springer. 1984. ISBN 3-540-13258-9. 
• The Man of Numbers: Fibonacci's Arithmetic Revolution. Walker Publishing Co. 2011. ISBN 978-0-8027-7812-3. 

Awards[link]

• Joint Policy Board for Mathematics Communications Award^[4]
• In 2007 he received Wonderfest's Carl Sagan Prize for Science Popularization.^[5]
• 2004 International Pythagoras Prize in Mathematics, in the category Best Expository Text in the Mathematical Sciences for the Italian translation of The Millennium Problems^[6]

References[link]

1. ^ ^{a b} Devlin, K. (1973). "Some weak versions of large cardinal axioms". Annals of Mathematical Logic 5 (4): 291–325. DOI:10.1016/0003-4843(73)90010-7.  edit
2. ^ Archive of The Math Guy series from NPR's Weekend Edition accessed 2007-11-09
3. ^ http://www.stanford.edu/~kdevlin/
4. ^ Keith Devlin at Stanford University
5. ^ "Sagan Prize Recipients". wonderfest.org. 2011 [last update]. http://wonderfest.org/sagan-prize/sagan-prize-recipients/. Retrieved 10 September 2011. 
6. ^ Stanford Report—2 November 2005

External links[link]

• Official website including his curriculum vitae
• Devlin's Angle — column at the Mathematical Association of America
• Radio interview on Philosophy Talk
• The Unfinished Game, Google Authors talk, 9 October 2008.
• Keith Devlin at the Mathematics Genealogy Project

Paul Halmos
Born	(1916-03-03)March 3, 1916 Budapest
Died	October 2, 2006(2006-10-02) (aged 90) Los Gatos, California, U.S.
Nationality	Hungarian American
Fields	Mathematics
Institutions	Syracuse University University of Chicago University of Michigan Indiana University Santa Clara University
Alma mater	Institute for Advanced Study University of Illinois
Doctoral advisor	Joseph Leo Doob
Doctoral students	H. Arlen Brown Bernard Galler Eric Nordgren Herman Rubin Donald Sarason

Paul Richard Halmos (March 3, 1916 – October 2, 2006) was a Hungarian-born American mathematician who made fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces). He was also recognized as a great mathematical expositor.

Career[link]

Halmos obtained his B.A. from the University of Illinois, majoring in philosophy and minoring in mathematics. He took only three years to obtain the degree, and was only 19 when he graduated. He then began a Ph.D. in philosophy, but after failing his masters' oral exams,^[1] shifted to mathematics, graduating in 1938. Joseph Doob supervised his dissertation, titled Invariants of Certain Stochastic Transformations: The Mathematical Theory of Gambling Systems. Shortly thereafter, Halmos left for the Institute for Advanced Study, lacking both job and grant money. Six months later, he was working under John von Neumann, which proved a decisive experience. While at the Institute, Halmos wrote his first book, Finite Dimensional Vector Spaces, which immediately established his reputation as a fine expositor of mathematics.

Halmos taught at Syracuse University, the University of Chicago (1946–60), the University of Michigan, the University of California at Santa Barbara (about 1977), the University of Hawaii, and Indiana University. From his 1985 retirement from Indiana until his death, he was affiliated with the Mathematics department at Santa Clara University.

Accomplishments[link]

In a series of papers reprinted in his 1962 Algebraic Logic, Halmos devised polyadic algebras, an algebraic version of first-order logic differing from the better known cylindric algebras of Alfred Tarski and his students. An elementary version of polyadic algebra is described in monadic Boolean algebra.

In addition to his original contributions to mathematics, Halmos was an unusually clear and engaging expositor of university mathematics. This was so even though Halmos arrived in the USA at 13 years of age and never lost his Hungarian accent. He chaired the American Mathematical Society committee that wrote the AMS style guide for academic mathematics, published in 1973. In 1983, he received the AMS's Steele Prize for exposition. Some of his classics were:

• How to read mathematics
• How to write mathematics
• How to speak mathematics.

In the American Scientist 56(4): 375–389, Halmos argued that mathematics is a creative art, and that mathematicians should be seen as artists, not number crunchers. He discussed the division of the field into mathology and mathophysics, further arguing that mathematicians and painters think and work in related ways.

Halmos's 1985 "automathography" I Want to Be a Mathematician is an account of what it was like to be an academic mathematician in 20th century America. He called the book “automathography” rather than “autobiography”, because its focus is almost entirely on his life as a mathematician, not his personal life. The book contains the following quote on Halmos' view of what doing mathematics means:

In these memoirs, Halmos claims to have invented the "iff" notation for the words "if and only if" and to have been the first to use the “tombstone” notation to signify the end of a proof, and this is generally agreed to be the case. The tombstone symbol ∎ (Unicode U+220E) is sometimes called a halmos.^[2]

In 2005, Halmos and his wife Viriginia funded the Euler Book Prize, an annual award given by the Mathematical Association of America for a book that is likely to improve the view of mathematics among the public. The first prize was given in 2007, the 300th anniversary of Leonhard Euler's birth, to John Derbyshire for his book about Riemann and the Riemann hypothesis: Prime Obsession.^[3]

Books by Halmos[link]

• 1942. Finite-Dimensional Vector Spaces. Springer-Verlag.
• 1950. Measure Theory. Springer Verlag.
• 1951. Introduction to Hilbert Space and the Theory of Spectral Multiplicity. Chelsea.
• 1956. Lectures on Ergodic Theory. Chelsea.
• 1960. Naive Set Theory. Springer Verlag.
• 1962. Algebraic Logic. Chelsea.
• 1963. Lectures on Boolean Algebras. Van Nostrand.
• 1967. A Hilbert Space Problem Book. Springer-Verlag.
• 1978 (with V. Sunder). Bounded Integral Operators on L² Spaces. Springer Verlag
• 1985. I Want to Be a Mathematician. Springer-Verlag.
• 1987. I Have a Photographic Memory. Mathematical Association of America.
• 1991. Problems for Mathematicians, Young and Old, Dolciani Mathematical Expositions, Mathematical Association of America.
• 1996. Linear Algebra Problem Book, Dolciani Mathematical Expositions, Mathematical Association of America.
• 1998 (with Steven Givant). Logic as Algebra, Dolciani Mathematical Expositions No. 21, Mathematical Association of America.

See also[link]

• Criticism of non-standard analysis
• Halmos symbol

Notes[link]

References[link]

• J. H. Ewing; F. W. Gehring, F. W. (1991). Paul Halmos: Celebrating 50 Years of Mathematics. Springer-Verlag. ISBN 0-387-97509-8. OCLC 22859036.  Includes a bibliography of Halmos's writings through 1991.
• John Ewing (October 2007). "Paul Halmos: In His Own Words" (PDF). Notices of the American Mathematical Society 54 (9): pp.1136–1144. http://www.ams.org/notices/200709/tx070901136p.pdf. Retrieved 2008-01-15. 
• Paul Halmos (1985). I want to be a Mathematician: An Automathography. Springer-Verlag. ISBN 0-387-96470-3. OCLC 230812318. 

External links[link]

Wikiquote has a collection of quotations related to: Paul Halmos

• O'Connor, John J.; Robertson, Edmund F., "Paul Halmos", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Halmos.html .
• "Paul Halmos: A Life in Mathematics", Mathematical Association of America (MAA)
• Paul Halmos at the Mathematics Genealogy Project

Danica McKellar
at a book signing, October 2007
Born	Danica Mae McKellar (1975-01-03) January 3, 1975 (age 37) La Jolla, California, U.S.
Education	Bachelor's degree (summa cum laude)
Alma mater	UCLA
Occupation	Actress, author, education advocate and director
Years active	1985–present
Spouse	Mike Verta (2009–present)
Website
www.danicamckellar.com

Danica Mae McKellar (born January 3, 1975) is an American actress, academic, and education advocate. She is best known for her role as Winnie Cooper in the television show The Wonder Years,^[1] and later as author of three popular^[2][3] non-fiction books: Math Doesn't Suck, Kiss My Math, and Hot X: Algebra Exposed, which encourage middle-school girls to have confidence and succeed in mathematics.^[4]

Early life[link]

Born in La Jolla, California, McKellar moved with her family to Los Angeles when she was eight. Her mother Mahalia is a homemaker; her father Christopher is a real estate developer.^[5] Her family is "a big mix of Western Europe":^[6] Her mother's ancestry is Portuguese (via the Azores and Madeira islands); her father's ancestry is Scottish, Irish, French, German and Dutch.^[6] McKellar and her sister Crystal McKellar (who is loosely named after their dad) both maintained professional acting careers as children, but with a strong emphasis on education as a priority. As a result, Crystal became a corporate lawyer (her family nicknamed her "Legally Blonde" because of her hair color), while Danica majored in mathematics. Danica and Crystal also have two half-brothers, Chris Junior and Connor McKellar.

Acting career[link]

[edit] The Wonder Years and early acting career

McKellar had a leading role in The Wonder Years, an American television comedy-drama that ran for six seasons on ABC, from 1988 to 1993.^[1]

McKellar played Gwendolyn "Winnie" Cooper,^[1] the main love interest of Kevin Arnold (played by Fred Savage) on the show.

McKellar's first kiss was with Fred Savage in an episode of The Wonder Years.^[7] She later said, "My first kiss was a pretty nerve-wracking experience! But we never kissed off screen, and pretty quickly our feelings turned into brother/sister, and stayed that way."^[8] McKellar also had a role in the film Sidekicks, directed by Aaron Norris.

Later career[link]

McKellar has admitted the transition from "child actor to adult actor was a little bumpy."^[8] Since leaving The Wonder Years, McKellar has had several guest roles in television series (including one with former co-star Fred Savage on Working), and has written and directed two short films. She played Kristin Guthrie in a 1994 Lifetime TV movie, Moment of Truth: Cradle of Conspiracy. In 1996, she played the character Annie Mills Carman in the Lifetime Moment of Truth movie Justice For Annie.^[9] She briefly returned to regular television with a recurring role in the 2002–03 season of The West Wing, portraying Elsie Snuffin, the stepsister and assistant of Deputy White House Communications Director Will Bailey.^[10]

McKellar appeared in lingerie in the July 2005 edition of Stuff magazine^[11] after readers voted her the '90s star they would most like to see in lingerie. McKellar explained that she agreed to the shoot in part to obtain "grittier roles".^[8]

In June 2006, Lifetime Television announced that McKellar would star in a Lifetime movie and web-based series titled Inspector Mom about a mother who solves mysteries.^[12] In an interview in the November 17, 2006 issue of TV Guide, McKellar said that two TV movies and ten webisodes of Inspector Mom were being produced.^[13]

McKellar has provided the voices for two characters in three video games: Jubilee in X-Men Legends (2004), and Invisible Woman in Marvel: Ultimate Alliance (2006) and Marvel: Ultimate Alliance 2 (2009).

On the August 1, 2007, edition of the Don and Mike Show, a WJFK-FM radio program out of Washington, D.C., McKellar announced plans that the producers of How I Met Your Mother were planning to bring her back for a recurring role (she guest-starred on the show in late 2005 in "The Pineapple Incident" and again in early 2007 in "Third Wheel"). She also made an appearance on the show The Big Bang Theory.

In 2008, she starred in Heatstroke, a Sci-Fi Channel original movie about searching for alien life on Earth.^[14]

McKellar, as of June 23, 2008 (2008 -06-23)^[update], is one of the stars commenting on the occurrences of the new millennium in VH1's I Love the New Millennium, and as of 2009 is the math correspondent for Brink, a program by the Science Channel about upcoming technology.^[10]

McKellar has also become a very experienced voice actress.^{[citation needed]}

Mathematics[link]

McKellar studied mathematics at UCLA, graduating with highest honors (summa cum laude) in 1998. As an undergraduate, she coauthored a scientific paper^[15] with Professor Lincoln Chayes and fellow student Brandy Winn. Their results are termed the 'Chayes–McKellar–Winn theorem'.^[16][17] Referring to the mathematical abilities of his student coauthors, Chayes was quoted in The New York Times^[18] as saying, "I thought that the two were really, really first-rate." McKellar's Erdős number is four.^[19] She is even one of the few people with an Erdős-Bacon number, which combines an Erdős number with a Bacon Number (as in the game Six Degrees of Kevin Bacon) since she also has a Bacon number of 2,^[20] making her Erdos-Bacon number a 6.

Books[link]

McKellar is the author of The New York Times^[2] bestselling book Math Doesn't Suck: How to Survive Middle-School Math without Losing Your Mind or Breaking a Nail,^[21] that encourages girls in middle school to enjoy and succeed at mathematics.^[22] The book has been favorably reviewed by Tara C. Smith, the founder of Iowa Citizens for Science and a professor of epidemiology at the University of Iowa.^[23] In an interview with Smith, McKellar said that she wrote the book "to show girls that math is accessible and relevant, and even a little glamorous" and to counteract "damaging social messages telling young girls that math and science aren't for them".^[24]

McKellar was named Person of the Week^[25] on World News with Charles Gibson for the week ending August 10, 2007. The news segment highlighted her book Math Doesn't Suck and her efforts to help girls develop an interest in mathematics, especially during the middle school years.

McKellar's second book, Kiss My Math: Showing Pre-Algebra Who's Boss,^[26] was released on August 5, 2008. The book's target audience is girls in the 7th through 9th grades. Her third book, Hot X: Algebra Exposed!^[27][28][29] was published on August 3, 2010, and is aimed at girls in the 8th-10th grade, or even adults who want to learn algebra.

All three of McKellar's books made it to The New York Times children's bestseller list.^[3][30]

Personal life[link]

She married composer Mike Verta on March 22, 2009, in La Jolla, California; the couple had dated since 2001. They had their first child on September 7, 2010, a boy they named Draco.^[31][32]

Filmography[link]

References[link]

Further reading[link]

• Chayes, L; McKellar, D; Winn, B (1998). "Percolation and Gibbs states multiplicity for ferromagnetic Ashkin-Teller models on Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbb{Z}^2

". Journal of Physics A: Mathematical and General 31 (45): 9055–9063. Bibcode 1998JPhA...31.9055C. DOI:10.1088/0305-4470/31/45/005. http://www.danicamckellar.com/math/percolation.pdf. 

• Danica McKellar (2007). Math Doesn't Suck: How to Survive Middle-School Math without Losing Your Mind or Breaking a Nail. Hudson Street Press. ISBN 978-1-59463-039-2. 
• Danica McKellar (2008). Kiss My Math: Showing Pre-Algebra Who's Boss. Hudson Street Press. ISBN 978-1-59463-049-1. 
• Danica McKellar (2010). Hot X: Algebra Exposed. Hudson Street Press. ISBN 978-1-59463-070-5. 

External links[link]

Wikimedia Commons has media related to: Danica McKellar

• Danica McKellar at the Internet Movie Database
• Interview with McKellar about her theorem at NPR
• February 2006 Proof and Prejudice: Women in Mathematics Conference, at which McKellar was a speaker
• Official website of her book, Math Doesn't Suck
• Official website of her book, Kiss My Math
• Science Friday for September 21, 2007 with McKellar among the guests
• Public School Insights Interview with McKellar about girls and math
• Danica McKeller's blog
• Official Website