- published: 21 Jun 2024
- views: 420645
Create your page here
Wilhelm Ackermann
Wilhelm Friedrich Ackermann (29 March 1896 – 24 December 1962) was a German mathematician best known for the Ackermann function, an important example in the theory of computation.
Ackermann was born in Herscheid municipality, Germany, and was awarded a Ph.D. by the University of Göttingen in 1925 for his thesis Begründung des "tertium non datur" mittels der Hilbertschen Theorie der Widerspruchsfreiheit, which was a consistency proof of arithmetic apparently without full Peano induction (although it did use e.g. induction over the length of proofs). From 1929 until 1948, he taught at the Arnoldinum Gymnasium in Burgsteinfurt, and then at Lüdenscheid until 1961. He was also a corresponding member of the Akademie der Wissenschaften (Academy of Sciences) in Göttingen, and was an honorary professor at the University of Münster.
In 1928, Ackermann helped David Hilbert turn his 1917 – 22 lectures on introductory mathematical logic into a text, Principles of Mathematical Logic. This text contained the first exposition ever of first-order logic, and posed the problem of its completeness and decidability (Entscheidungsproblem). Ackermann went on to construct consistency proofs for set theory (1937), full arithmetic (1940), type-free logic (1952), and a new axiomatization of set theory (1956).
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Wilhelm_Ackermann
Podcasts:
-
The Insane Ackermann Function
Researchers proved that navigating certain systems of vectors is among the most complex computational problems and involves a function called the Ackermann function. Find out how an easy-sounding problem yields numbers too big for our universe. Watch our full video explainer: https://www.youtube.com/watch?v=IzSs_gJDVzI Read the article: https://www.quantamagazine.org/an-easy-sounding-problem-yields-numbers-too-big-for-our-universe-20231204/ -------- - VISIT our website: https://www.quantamagazine.org - LIKE us on Facebook: https://www.facebook.com/QuantaNews - FOLLOW us Twitter: https://twitter.com/QuantaMagazine @QuantaScienceChannel #math #computerscience
published: 21 Jun 2024 -
Grandes Matemáticos - Wilhelm Ackermann
published: 11 Oct 2021 -
Ackermann Function
In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive
published: 21 Sep 2020 -
The Most Difficult Program to Compute? - Computerphile
The story of recursion continues as Professor Brailsford explains one of the most difficult programs to compute: Ackermann's function. Professor Brailsford's programs: http://bit.ly/1nhKtW4 Follow Up Film from the Prof in response to this film: https://www.youtube.com/watch?v=uNACwX-O5lk What on Earth is Recursion?: http://youtu.be/Mv9NEXX1VHc Fibonacci Programming: http://youtu.be/7t_pTlH9HwA Heartbleed, Running the Code: http://youtu.be/1dOCHwf8zVQ VR Series: COMING SOON! Please note, Ackermann is spelled incorrectly with one "n" on the title plate - Apologies http://www.facebook.com/computerphile https://twitter.com/computer_phile This video was filmed and edited by Sean Riley. Computer Science at the University of Nottingham: http://bit.ly/nottscomputer Computerphile is a ...
published: 01 Jul 2014 -
Ackermann function
If you find our videos helpful you can support us by buying something from amazon. https://www.amazon.com/?tag=wiki-audio-20 Ackermann function In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive.All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive. -Video is targeted to blind users Attribution: Article text available under CC-BY-SA image source in video https://www.youtube.com/watch?v=KV79PUX1iOM
published: 22 Jan 2016 -
Ackermannfunktion
Vielen Dank für Ihre Unterstützung: https://amzn.to/2UKHXys Ackermannfunktion Die Ackermannfunktion ist eine 1926 von Wilhelm Ackermann gefundene, extrem schnell wachsende mathematische Funktion, mit deren Hilfe in der theoretischen Informatik Grenzen von Computer- und Berechnungsmodellen aufgezeigt werden können.Heute gibt es eine ganze Reihe von Funktionen, die als Ackermannfunktion bezeichnet werden.Diese weisen alle ein ähnliches Bildungsgesetz wie die ursprüngliche Ackermannfunktion auf und haben auch ein ähnliches Wachstumsverhalten. ✪Video ist an blinde Nutzer gerichtet ✪Text verfügbar unter der Lizens CC-BY-SA ✪Bild Quelle im Video
published: 20 Jun 2016 -
Lawrence C. Paulson: Research Challenge + Ackermann's Function in Iterative Form (Isabelle 2020)
Presented at the Isabelle Workshop 2020, June 30, 2020
published: 21 Jul 2020 -
Ackermanns Function | GATE Lecture
In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive. After Ackermann's publication of his function (which had three nonnegative integer arguments), many authors modified it to suit various purposes, so that today "the Ackermann function" may refer to any of numerous variants of the original function. One common version, the two-argument Ackermann–Péter function, is defined as follows for nonnegative integers m and n: More in Details : https://en.wikipedia.org/wiki/Ackermann_function...
published: 21 Mar 2018 -
Principles of Mathematical Logic | Wikipedia audio article
This is an audio version of the Wikipedia Article: https://en.wikipedia.org/wiki/Principles_of_Mathematical_Logic Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago. Learning by listening is a great way to: - increases imagination and understanding - improves your listening skills - improves your own spoken accent - learn while on the move - reduce eye strain Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an ear...
published: 31 Dec 2018 -
David Hilbert: Math's Modern Architect | PhilosophyStudent.org
Join us as we explore the remarkable life of David Hilbert, a towering figure in the world of mathematics and logic. This video highlights Hilbert's profound breakthroughs and ambitious program to axiomatize mathematics. Please Visit our Website to get more information: https://www.philosophystudent.org/ Discover his enduring influence on proof theory and his struggle with the challenges of his time. Witness the story of a man whose ideas transcended mathematics and touched the realms of philosophy. ✅Biography of David Hilbert’s Although identified primarily as a mathematician who made several fundamental breakthroughs in the field, David Hilbert’s work in proof theory and other aspects of mathematical logic has given him a significant place in logic and analytical philosophy. Of cent...
published: 30 Apr 2024
developed with YouTube
0:59
The Insane Ackermann Function
- Order: Reorder
- Duration: 0:59
- Uploaded Date: 21 Jun 2024
- views: 420645
Researchers proved that navigating certain systems of vectors is among the most complex computational problems and involves a function called the Ackermann func...
Researchers proved that navigating certain systems of vectors is among the most complex computational problems and involves a function called the Ackermann function. Find out how an easy-sounding problem yields numbers too big for our universe.
Watch our full video explainer: https://www.youtube.com/watch?v=IzSs_gJDVzI
Read the article: https://www.quantamagazine.org/an-easy-sounding-problem-yields-numbers-too-big-for-our-universe-20231204/
--------
- VISIT our website: https://www.quantamagazine.org
- LIKE us on Facebook: https://www.facebook.com/QuantaNews
- FOLLOW us Twitter: https://twitter.com/QuantaMagazine
@QuantaScienceChannel
#math #computerscience
https://wn.com/The_Insane_Ackermann_Function
Researchers proved that navigating certain systems of vectors is among the most complex computational problems and involves a function called the Ackermann function. Find out how an easy-sounding problem yields numbers too big for our universe.
Watch our full video explainer: https://www.youtube.com/watch?v=IzSs_gJDVzI
Read the article: https://www.quantamagazine.org/an-easy-sounding-problem-yields-numbers-too-big-for-our-universe-20231204/
--------
- VISIT our website: https://www.quantamagazine.org
- LIKE us on Facebook: https://www.facebook.com/QuantaNews
- FOLLOW us Twitter: https://twitter.com/QuantaMagazine
@QuantaScienceChannel
#math #computerscience
0:24
Grandes Matemáticos - Wilhelm Ackermann
- Order: Reorder
- Duration: 0:24
- Uploaded Date: 11 Oct 2021
- views: 22
- published: 11 Oct 2021
- views: 22
12:02
Ackermann Function
- Order: Reorder
- Duration: 12:02
- Uploaded Date: 21 Sep 2020
- views: 4723
In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable fu...
In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive
https://wn.com/Ackermann_Function
In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive
- published: 21 Sep 2020
- views: 4723
14:55
The Most Difficult Program to Compute? - Computerphile
- Order: Reorder
- Duration: 14:55
- Uploaded Date: 01 Jul 2014
- views: 1410371
The story of recursion continues as Professor Brailsford explains one of the most difficult programs to compute: Ackermann's function.
Professor Brailsford's p...
The story of recursion continues as Professor Brailsford explains one of the most difficult programs to compute: Ackermann's function.
Professor Brailsford's programs: http://bit.ly/1nhKtW4
Follow Up Film from the Prof in response to this film: https://www.youtube.com/watch?v=uNACwX-O5lk
What on Earth is Recursion?: http://youtu.be/Mv9NEXX1VHc
Fibonacci Programming: http://youtu.be/7t_pTlH9HwA
Heartbleed, Running the Code: http://youtu.be/1dOCHwf8zVQ
VR Series: COMING SOON!
Please note, Ackermann is spelled incorrectly with one "n" on the title plate - Apologies
http://www.facebook.com/computerphile
https://twitter.com/computer_phile
This video was filmed and edited by Sean Riley.
Computer Science at the University of Nottingham: http://bit.ly/nottscomputer
Computerphile is a sister project to Brady Haran's Numberphile. See the full list of Brady's video projects at: http://bit.ly/bradychannels
https://wn.com/The_Most_Difficult_Program_To_Compute_Computerphile
The story of recursion continues as Professor Brailsford explains one of the most difficult programs to compute: Ackermann's function.
Professor Brailsford's programs: http://bit.ly/1nhKtW4
Follow Up Film from the Prof in response to this film: https://www.youtube.com/watch?v=uNACwX-O5lk
What on Earth is Recursion?: http://youtu.be/Mv9NEXX1VHc
Fibonacci Programming: http://youtu.be/7t_pTlH9HwA
Heartbleed, Running the Code: http://youtu.be/1dOCHwf8zVQ
VR Series: COMING SOON!
Please note, Ackermann is spelled incorrectly with one "n" on the title plate - Apologies
http://www.facebook.com/computerphile
https://twitter.com/computer_phile
This video was filmed and edited by Sean Riley.
Computer Science at the University of Nottingham: http://bit.ly/nottscomputer
Computerphile is a sister project to Brady Haran's Numberphile. See the full list of Brady's video projects at: http://bit.ly/bradychannels
- published: 01 Jul 2014
- views: 1410371
9:38
Ackermann function
- Order: Reorder
- Duration: 9:38
- Uploaded Date: 22 Jan 2016
- views: 9796
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Ackermann function
In computabil...
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Ackermann function
In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive.All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive.
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=KV79PUX1iOM
https://wn.com/Ackermann_Function
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Ackermann function
In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive.All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive.
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=KV79PUX1iOM
- published: 22 Jan 2016
- views: 9796
5:01
Ackermannfunktion
- Order: Reorder
- Duration: 5:01
- Uploaded Date: 20 Jun 2016
- views: 3895
Vielen Dank für Ihre Unterstützung:
https://amzn.to/2UKHXys
Ackermannfunktion
Die Ackermannfunktion ist eine 1926 von Wilhelm Ackermann gefundene, extrem schne...
Vielen Dank für Ihre Unterstützung:
https://amzn.to/2UKHXys
Ackermannfunktion
Die Ackermannfunktion ist eine 1926 von Wilhelm Ackermann gefundene, extrem schnell wachsende mathematische Funktion, mit deren Hilfe in der theoretischen Informatik Grenzen von Computer- und Berechnungsmodellen aufgezeigt werden können.Heute gibt es eine ganze Reihe von Funktionen, die als Ackermannfunktion bezeichnet werden.Diese weisen alle ein ähnliches Bildungsgesetz wie die ursprüngliche Ackermannfunktion auf und haben auch ein ähnliches Wachstumsverhalten.
✪Video ist an blinde Nutzer gerichtet
✪Text verfügbar unter der Lizens CC-BY-SA
✪Bild Quelle im Video
https://wn.com/Ackermannfunktion
Vielen Dank für Ihre Unterstützung:
https://amzn.to/2UKHXys
Ackermannfunktion
Die Ackermannfunktion ist eine 1926 von Wilhelm Ackermann gefundene, extrem schnell wachsende mathematische Funktion, mit deren Hilfe in der theoretischen Informatik Grenzen von Computer- und Berechnungsmodellen aufgezeigt werden können.Heute gibt es eine ganze Reihe von Funktionen, die als Ackermannfunktion bezeichnet werden.Diese weisen alle ein ähnliches Bildungsgesetz wie die ursprüngliche Ackermannfunktion auf und haben auch ein ähnliches Wachstumsverhalten.
✪Video ist an blinde Nutzer gerichtet
✪Text verfügbar unter der Lizens CC-BY-SA
✪Bild Quelle im Video
- published: 20 Jun 2016
- views: 3895
33:19
Lawrence C. Paulson: Research Challenge + Ackermann's Function in Iterative Form (Isabelle 2020)
- Order: Reorder
- Duration: 33:19
- Uploaded Date: 21 Jul 2020
- views: 437
Presented at the Isabelle Workshop 2020, June 30, 2020
Presented at the Isabelle Workshop 2020, June 30, 2020
https://wn.com/Lawrence_C._Paulson_Research_Challenge_Ackermann's_Function_In_Iterative_Form_(Isabelle_2020)
Presented at the Isabelle Workshop 2020, June 30, 2020
- published: 21 Jul 2020
- views: 437
21:25
Ackermanns Function | GATE Lecture
- Order: Reorder
- Duration: 21:25
- Uploaded Date: 21 Mar 2018
- views: 6943
In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable fu...
In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive.
After Ackermann's publication of his function (which had three nonnegative integer arguments), many authors modified it to suit various purposes, so that today "the Ackermann function" may refer to any of numerous variants of the original function. One common version, the two-argument Ackermann–Péter function, is defined as follows for nonnegative integers m and n:
More in Details : https://en.wikipedia.org/wiki/Ackermann_function
https://wn.com/Ackermanns_Function_|_Gate_Lecture
In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive.
After Ackermann's publication of his function (which had three nonnegative integer arguments), many authors modified it to suit various purposes, so that today "the Ackermann function" may refer to any of numerous variants of the original function. One common version, the two-argument Ackermann–Péter function, is defined as follows for nonnegative integers m and n:
More in Details : https://en.wikipedia.org/wiki/Ackermann_function
- published: 21 Mar 2018
- views: 6943
1:39
Principles of Mathematical Logic | Wikipedia audio article
- Order: Reorder
- Duration: 1:39
- Uploaded Date: 31 Dec 2018
- views: 12
This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Principles_of_Mathematical_Logic
Listening is a more natural way of...
This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Principles_of_Mathematical_Logic
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain
Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.
Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.7251380574054289
Voice name: en-AU-Wavenet-D
"I cannot teach anybody anything, I can only make them think."
- Socrates
SUMMARY
=======
Principles of Mathematical Logic is the 1950 American translation of the 1938 second edition of David Hilbert's and Wilhelm Ackermann's classic text Grundzüge der theoretischen Logik, on elementary mathematical logic. The 1928 first edition thereof is considered the first elementary text clearly grounded in the formalism now known as first-order logic (FOL). Hilbert and Ackermann also formalized FOL in a way that subsequently achieved canonical status. FOL is now a core formalism of mathematical logic, and is presupposed by contemporary treatments of Peano arithmetic and nearly all treatments of axiomatic set theory.
The 1928 edition included a clear statement of the Entscheidungsproblem (decision problem) for FOL, and also asked whether that logic was complete (i.e., whether all semantic truths of FOL were theorems derivable from the FOL axioms and rules). The former problem was answered in the negative first by Alonzo Church and independently by Alan Turing in 1936. The latter was answered affirmatively by Kurt Gödel in 1929.
The text also touched on set theory and relational algebra as ways of going beyond FOL. Contemporary notation for logic owes more to this text than it does to the notation of Principia Mathematica, long popular in the English speaking world.
https://wn.com/Principles_Of_Mathematical_Logic_|_Wikipedia_Audio_Article
This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Principles_of_Mathematical_Logic
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain
Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.
Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.7251380574054289
Voice name: en-AU-Wavenet-D
"I cannot teach anybody anything, I can only make them think."
- Socrates
SUMMARY
=======
Principles of Mathematical Logic is the 1950 American translation of the 1938 second edition of David Hilbert's and Wilhelm Ackermann's classic text Grundzüge der theoretischen Logik, on elementary mathematical logic. The 1928 first edition thereof is considered the first elementary text clearly grounded in the formalism now known as first-order logic (FOL). Hilbert and Ackermann also formalized FOL in a way that subsequently achieved canonical status. FOL is now a core formalism of mathematical logic, and is presupposed by contemporary treatments of Peano arithmetic and nearly all treatments of axiomatic set theory.
The 1928 edition included a clear statement of the Entscheidungsproblem (decision problem) for FOL, and also asked whether that logic was complete (i.e., whether all semantic truths of FOL were theorems derivable from the FOL axioms and rules). The former problem was answered in the negative first by Alonzo Church and independently by Alan Turing in 1936. The latter was answered affirmatively by Kurt Gödel in 1929.
The text also touched on set theory and relational algebra as ways of going beyond FOL. Contemporary notation for logic owes more to this text than it does to the notation of Principia Mathematica, long popular in the English speaking world.
- published: 31 Dec 2018
- views: 12
3:47
David Hilbert: Math's Modern Architect | PhilosophyStudent.org
- Order: Reorder
- Duration: 3:47
- Uploaded Date: 30 Apr 2024
- views: 50
Join us as we explore the remarkable life of David Hilbert, a towering figure in the world of mathematics and logic. This video highlights Hilbert's profound br...
Join us as we explore the remarkable life of David Hilbert, a towering figure in the world of mathematics and logic. This video highlights Hilbert's profound breakthroughs and ambitious program to axiomatize mathematics. Please Visit our Website to get more information: https://www.philosophystudent.org/
Discover his enduring influence on proof theory and his struggle with the challenges of his time. Witness the story of a man whose ideas transcended mathematics and touched the realms of philosophy.
✅Biography of David Hilbert’s
Although identified primarily as a mathematician who made several fundamental breakthroughs in the field, David Hilbert’s work in proof theory and other aspects of mathematical logic has given him a significant place in logic and analytical philosophy.
Of central importance was “Hilbert’s Program,” a call to formalize all mathematics in axiomatic form, thereby bringing mathematics and philosophy under the same intellectual umbrella. David Hilbert was born in Prussia (either in Königsberg or Wehlau [modern Znamensk]) on January 23, 1862.
He enrolled in the Friedrichskolleg Gymnasium in 1872 but, in 1879, transferred to the more science-intensive Wilhelm Gymnasium, from which he graduated. He then enrolled in 1880 at the University of Königsberg, earning a doctorate in 1885 with a dissertation titled “On the Invariant Properties of Special Binary Forms, in Particular the Spherical Harmonic Functions.”
The university appointed him a Privatdozent (lecturer), a post in which he served from 1886 to 1895 before being appointed Professor of Mathematics at the University of Göttingen. Hilbert remained at that institution for the rest of his life and was instrumental in elevating it to recognition as the foremost center of mathematics in the world.
From 1925 until the end of his long life, Hilbert suffered from debilitating pernicious anemia, which diminished his creativity. He died on February 14, 1943, having lived long enough to witness the dismantling of Göttingen’s mathematics department by the Nazi purge of Jewish faculty. In the early 1920s, Hilbert published his proposal to formalize all of mathematics in axiomatic form, together with a proof that the axiomatization of mathematics is consistent.
This bold step forward in epistemology and mathematics was known as Hilbert’s Program. Eminent logicians, including Paul Bernays, Wilhelm Ackermann, John von Neumann, and Jacques Herbrand, were drawn into furthering Hilbert’s Program.
But in 1930-1931, Kurt Gödel published his two “incompleteness theorems,” demonstrating that even elementary axiomatic systems such as Peano arithmetic are either self-contradicting or contain logical propositions that are impossible to prove or disprove.
To many, this seemed the death blow to Hilbert’s Program—and to what might have been a major pillar of epistemology. Still, Hilbert’s work has continued to drive the development of proof theory, one of the central interests of analytic philosophy.”
This video is about David Hilbert: Math's Modern Architect. But It also covers the following topics:
David Hilbert's Mathematical Journey
Hilbert's Contributions To Mathematics
David Hilbert's Proof Theory
Video Title: David Hilbert: Math's Modern Architect | PhilosophyStudent.org
🔔 Hit Subscribe for everything you need about philosophy, from history to theory to exam tips! https://www.youtube.com/@PhilosophyStudentOrg/sub_confirmation=1
✅ Stay Connected With Us.
👉Facebook:https://www.facebook.com/people/Philosophy-Student/100095368029438/
👉Website: https://www.philosophystudent.org/
=============================
✅ Recommended Playlists
👉Philosophical Terms Definitions
https://www.youtube.com/watch?v=vAlR6PPrUT4&list;=PLpxz2tR-XHQMO4tlfZ6aVqWgUggaeNKSI
👉BIOGRAPHIES
https://www.youtube.com/watch?v=37TI2KOGwrc&list;=PLpxz2tR-XHQOrLFN0PnpPY7_yx9X-yPIw
✅ Other Videos You Might Be Interested In Watching:
✅ About Philosophy Student.
This channel has one goal: to help philosophy students learn about philosophical concepts and familiarize themselves with their history, terms, theories, and thoughts. Here, you will find videos on the history of philosophy, biographies of philosophical figures, and explanation videos on philosophical terms, concepts, and theories.
We also do videos on philosophy books and popular papers. A special emphasis is placed on helping you to learn how to be your very best at philosophy. How to write better papers, how to learn better, and how to get great grades in your philosophy courses. We hope you enjoy it, and look forward to your comments!
🔔 Master the art of philosophy with our comprehensive library of educational videos. Subscribe Now:
https://www.youtube.com/@PhilosophyStudentOrg/sub_confirmation=1
=================================
#davidhilbert #mathematics #prooftheory #philosophy #biography #logic
© Philosophy Student
https://wn.com/David_Hilbert_Math's_Modern_Architect_|_Philosophystudent.Org
Join us as we explore the remarkable life of David Hilbert, a towering figure in the world of mathematics and logic. This video highlights Hilbert's profound breakthroughs and ambitious program to axiomatize mathematics. Please Visit our Website to get more information: https://www.philosophystudent.org/
Discover his enduring influence on proof theory and his struggle with the challenges of his time. Witness the story of a man whose ideas transcended mathematics and touched the realms of philosophy.
✅Biography of David Hilbert’s
Although identified primarily as a mathematician who made several fundamental breakthroughs in the field, David Hilbert’s work in proof theory and other aspects of mathematical logic has given him a significant place in logic and analytical philosophy.
Of central importance was “Hilbert’s Program,” a call to formalize all mathematics in axiomatic form, thereby bringing mathematics and philosophy under the same intellectual umbrella. David Hilbert was born in Prussia (either in Königsberg or Wehlau [modern Znamensk]) on January 23, 1862.
He enrolled in the Friedrichskolleg Gymnasium in 1872 but, in 1879, transferred to the more science-intensive Wilhelm Gymnasium, from which he graduated. He then enrolled in 1880 at the University of Königsberg, earning a doctorate in 1885 with a dissertation titled “On the Invariant Properties of Special Binary Forms, in Particular the Spherical Harmonic Functions.”
The university appointed him a Privatdozent (lecturer), a post in which he served from 1886 to 1895 before being appointed Professor of Mathematics at the University of Göttingen. Hilbert remained at that institution for the rest of his life and was instrumental in elevating it to recognition as the foremost center of mathematics in the world.
From 1925 until the end of his long life, Hilbert suffered from debilitating pernicious anemia, which diminished his creativity. He died on February 14, 1943, having lived long enough to witness the dismantling of Göttingen’s mathematics department by the Nazi purge of Jewish faculty. In the early 1920s, Hilbert published his proposal to formalize all of mathematics in axiomatic form, together with a proof that the axiomatization of mathematics is consistent.
This bold step forward in epistemology and mathematics was known as Hilbert’s Program. Eminent logicians, including Paul Bernays, Wilhelm Ackermann, John von Neumann, and Jacques Herbrand, were drawn into furthering Hilbert’s Program.
But in 1930-1931, Kurt Gödel published his two “incompleteness theorems,” demonstrating that even elementary axiomatic systems such as Peano arithmetic are either self-contradicting or contain logical propositions that are impossible to prove or disprove.
To many, this seemed the death blow to Hilbert’s Program—and to what might have been a major pillar of epistemology. Still, Hilbert’s work has continued to drive the development of proof theory, one of the central interests of analytic philosophy.”
This video is about David Hilbert: Math's Modern Architect. But It also covers the following topics:
David Hilbert's Mathematical Journey
Hilbert's Contributions To Mathematics
David Hilbert's Proof Theory
Video Title: David Hilbert: Math's Modern Architect | PhilosophyStudent.org
🔔 Hit Subscribe for everything you need about philosophy, from history to theory to exam tips! https://www.youtube.com/@PhilosophyStudentOrg/sub_confirmation=1
✅ Stay Connected With Us.
👉Facebook:https://www.facebook.com/people/Philosophy-Student/100095368029438/
👉Website: https://www.philosophystudent.org/
=============================
✅ Recommended Playlists
👉Philosophical Terms Definitions
https://www.youtube.com/watch?v=vAlR6PPrUT4&list;=PLpxz2tR-XHQMO4tlfZ6aVqWgUggaeNKSI
👉BIOGRAPHIES
https://www.youtube.com/watch?v=37TI2KOGwrc&list;=PLpxz2tR-XHQOrLFN0PnpPY7_yx9X-yPIw
✅ Other Videos You Might Be Interested In Watching:
✅ About Philosophy Student.
This channel has one goal: to help philosophy students learn about philosophical concepts and familiarize themselves with their history, terms, theories, and thoughts. Here, you will find videos on the history of philosophy, biographies of philosophical figures, and explanation videos on philosophical terms, concepts, and theories.
We also do videos on philosophy books and popular papers. A special emphasis is placed on helping you to learn how to be your very best at philosophy. How to write better papers, how to learn better, and how to get great grades in your philosophy courses. We hope you enjoy it, and look forward to your comments!
🔔 Master the art of philosophy with our comprehensive library of educational videos. Subscribe Now:
https://www.youtube.com/@PhilosophyStudentOrg/sub_confirmation=1
=================================
#davidhilbert #mathematics #prooftheory #philosophy #biography #logic
© Philosophy Student
- published: 30 Apr 2024
- views: 50
0:59
The Insane Ackermann Function
Researchers proved that navigating certain systems of vectors is among the most complex co...
published: 21 Jun 2024
The Insane Ackermann Function
The Insane Ackermann Function
- Report rights infringement
- published: 21 Jun 2024
- views: 420645
Researchers proved that navigating certain systems of vectors is among the most complex computational problems and involves a function called the Ackermann function. Find out how an easy-sounding problem yields numbers too big for our universe.
Watch our full video explainer: https://www.youtube.com/watch?v=IzSs_gJDVzI
Read the article: https://www.quantamagazine.org/an-easy-sounding-problem-yields-numbers-too-big-for-our-universe-20231204/
--------
- VISIT our website: https://www.quantamagazine.org
- LIKE us on Facebook: https://www.facebook.com/QuantaNews
- FOLLOW us Twitter: https://twitter.com/QuantaMagazine
@QuantaScienceChannel
#math #computerscience
0:24
Grandes Matemáticos - Wilhelm Ackermann
published: 11 Oct 2021
Grandes Matemáticos - Wilhelm Ackermann
Grandes Matemáticos - Wilhelm Ackermann
- Report rights infringement
- published: 11 Oct 2021
- views: 22
12:02
Ackermann Function
In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of ...
published: 21 Sep 2020
Ackermann Function
Ackermann Function
- Report rights infringement
- published: 21 Sep 2020
- views: 4723
In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive
14:55
The Most Difficult Program to Compute? - Computerphile
The story of recursion continues as Professor Brailsford explains one of the most difficul...
published: 01 Jul 2014
The Most Difficult Program to Compute? - Computerphile
The Most Difficult Program to Compute? - Computerphile
- Report rights infringement
- published: 01 Jul 2014
- views: 1410371
The story of recursion continues as Professor Brailsford explains one of the most difficult programs to compute: Ackermann's function.
Professor Brailsford's programs: http://bit.ly/1nhKtW4
Follow Up Film from the Prof in response to this film: https://www.youtube.com/watch?v=uNACwX-O5lk
What on Earth is Recursion?: http://youtu.be/Mv9NEXX1VHc
Fibonacci Programming: http://youtu.be/7t_pTlH9HwA
Heartbleed, Running the Code: http://youtu.be/1dOCHwf8zVQ
VR Series: COMING SOON!
Please note, Ackermann is spelled incorrectly with one "n" on the title plate - Apologies
http://www.facebook.com/computerphile
https://twitter.com/computer_phile
This video was filmed and edited by Sean Riley.
Computer Science at the University of Nottingham: http://bit.ly/nottscomputer
Computerphile is a sister project to Brady Haran's Numberphile. See the full list of Brady's video projects at: http://bit.ly/bradychannels
9:38
Ackermann function
If you find our videos helpful you can support us by buying something from amazon.
https:/...
published: 22 Jan 2016
Ackermann function
Ackermann function
- Report rights infringement
- published: 22 Jan 2016
- views: 9796
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Ackermann function
In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive.All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive.
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=KV79PUX1iOM
5:01
Ackermannfunktion
Vielen Dank für Ihre Unterstützung:
https://amzn.to/2UKHXys
Ackermannfunktion
Die Ackerma...
published: 20 Jun 2016
Ackermannfunktion
Ackermannfunktion
- Report rights infringement
- published: 20 Jun 2016
- views: 3895
Vielen Dank für Ihre Unterstützung:
https://amzn.to/2UKHXys
Ackermannfunktion
Die Ackermannfunktion ist eine 1926 von Wilhelm Ackermann gefundene, extrem schnell wachsende mathematische Funktion, mit deren Hilfe in der theoretischen Informatik Grenzen von Computer- und Berechnungsmodellen aufgezeigt werden können.Heute gibt es eine ganze Reihe von Funktionen, die als Ackermannfunktion bezeichnet werden.Diese weisen alle ein ähnliches Bildungsgesetz wie die ursprüngliche Ackermannfunktion auf und haben auch ein ähnliches Wachstumsverhalten.
✪Video ist an blinde Nutzer gerichtet
✪Text verfügbar unter der Lizens CC-BY-SA
✪Bild Quelle im Video
33:19
Lawrence C. Paulson: Research Challenge + Ackermann's Function in Iterative Form (Isabelle 2020)
Presented at the Isabelle Workshop 2020, June 30, 2020
published: 21 Jul 2020
Lawrence C. Paulson: Research Challenge + Ackermann's Function in Iterative Form (Isabelle 2020)
Lawrence C. Paulson: Research Challenge + Ackermann's Function in Iterative Form (Isabelle 2020)
- Report rights infringement
- published: 21 Jul 2020
- views: 437
Presented at the Isabelle Workshop 2020, June 30, 2020
21:25
Ackermanns Function | GATE Lecture
In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of ...
published: 21 Mar 2018
Ackermanns Function | GATE Lecture
Ackermanns Function | GATE Lecture
- Report rights infringement
- published: 21 Mar 2018
- views: 6943
In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive.
After Ackermann's publication of his function (which had three nonnegative integer arguments), many authors modified it to suit various purposes, so that today "the Ackermann function" may refer to any of numerous variants of the original function. One common version, the two-argument Ackermann–Péter function, is defined as follows for nonnegative integers m and n:
More in Details : https://en.wikipedia.org/wiki/Ackermann_function
1:39
Principles of Mathematical Logic | Wikipedia audio article
This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Principl...
published: 31 Dec 2018
Principles of Mathematical Logic | Wikipedia audio article
Principles of Mathematical Logic | Wikipedia audio article
- Report rights infringement
- published: 31 Dec 2018
- views: 12
This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Principles_of_Mathematical_Logic
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain
Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.
Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.7251380574054289
Voice name: en-AU-Wavenet-D
"I cannot teach anybody anything, I can only make them think."
- Socrates
SUMMARY
=======
Principles of Mathematical Logic is the 1950 American translation of the 1938 second edition of David Hilbert's and Wilhelm Ackermann's classic text Grundzüge der theoretischen Logik, on elementary mathematical logic. The 1928 first edition thereof is considered the first elementary text clearly grounded in the formalism now known as first-order logic (FOL). Hilbert and Ackermann also formalized FOL in a way that subsequently achieved canonical status. FOL is now a core formalism of mathematical logic, and is presupposed by contemporary treatments of Peano arithmetic and nearly all treatments of axiomatic set theory.
The 1928 edition included a clear statement of the Entscheidungsproblem (decision problem) for FOL, and also asked whether that logic was complete (i.e., whether all semantic truths of FOL were theorems derivable from the FOL axioms and rules). The former problem was answered in the negative first by Alonzo Church and independently by Alan Turing in 1936. The latter was answered affirmatively by Kurt Gödel in 1929.
The text also touched on set theory and relational algebra as ways of going beyond FOL. Contemporary notation for logic owes more to this text than it does to the notation of Principia Mathematica, long popular in the English speaking world.
3:47
David Hilbert: Math's Modern Architect | PhilosophyStudent.org
Join us as we explore the remarkable life of David Hilbert, a towering figure in the world...
published: 30 Apr 2024
David Hilbert: Math's Modern Architect | PhilosophyStudent.org
David Hilbert: Math's Modern Architect | PhilosophyStudent.org
- Report rights infringement
- published: 30 Apr 2024
- views: 50
Join us as we explore the remarkable life of David Hilbert, a towering figure in the world of mathematics and logic. This video highlights Hilbert's profound breakthroughs and ambitious program to axiomatize mathematics. Please Visit our Website to get more information: https://www.philosophystudent.org/
Discover his enduring influence on proof theory and his struggle with the challenges of his time. Witness the story of a man whose ideas transcended mathematics and touched the realms of philosophy.
✅Biography of David Hilbert’s
Although identified primarily as a mathematician who made several fundamental breakthroughs in the field, David Hilbert’s work in proof theory and other aspects of mathematical logic has given him a significant place in logic and analytical philosophy.
Of central importance was “Hilbert’s Program,” a call to formalize all mathematics in axiomatic form, thereby bringing mathematics and philosophy under the same intellectual umbrella. David Hilbert was born in Prussia (either in Königsberg or Wehlau [modern Znamensk]) on January 23, 1862.
He enrolled in the Friedrichskolleg Gymnasium in 1872 but, in 1879, transferred to the more science-intensive Wilhelm Gymnasium, from which he graduated. He then enrolled in 1880 at the University of Königsberg, earning a doctorate in 1885 with a dissertation titled “On the Invariant Properties of Special Binary Forms, in Particular the Spherical Harmonic Functions.”
The university appointed him a Privatdozent (lecturer), a post in which he served from 1886 to 1895 before being appointed Professor of Mathematics at the University of Göttingen. Hilbert remained at that institution for the rest of his life and was instrumental in elevating it to recognition as the foremost center of mathematics in the world.
From 1925 until the end of his long life, Hilbert suffered from debilitating pernicious anemia, which diminished his creativity. He died on February 14, 1943, having lived long enough to witness the dismantling of Göttingen’s mathematics department by the Nazi purge of Jewish faculty. In the early 1920s, Hilbert published his proposal to formalize all of mathematics in axiomatic form, together with a proof that the axiomatization of mathematics is consistent.
This bold step forward in epistemology and mathematics was known as Hilbert’s Program. Eminent logicians, including Paul Bernays, Wilhelm Ackermann, John von Neumann, and Jacques Herbrand, were drawn into furthering Hilbert’s Program.
But in 1930-1931, Kurt Gödel published his two “incompleteness theorems,” demonstrating that even elementary axiomatic systems such as Peano arithmetic are either self-contradicting or contain logical propositions that are impossible to prove or disprove.
To many, this seemed the death blow to Hilbert’s Program—and to what might have been a major pillar of epistemology. Still, Hilbert’s work has continued to drive the development of proof theory, one of the central interests of analytic philosophy.”
This video is about David Hilbert: Math's Modern Architect. But It also covers the following topics:
David Hilbert's Mathematical Journey
Hilbert's Contributions To Mathematics
David Hilbert's Proof Theory
Video Title: David Hilbert: Math's Modern Architect | PhilosophyStudent.org
🔔 Hit Subscribe for everything you need about philosophy, from history to theory to exam tips! https://www.youtube.com/@PhilosophyStudentOrg/sub_confirmation=1
✅ Stay Connected With Us.
👉Facebook:https://www.facebook.com/people/Philosophy-Student/100095368029438/
👉Website: https://www.philosophystudent.org/
=============================
✅ Recommended Playlists
👉Philosophical Terms Definitions
https://www.youtube.com/watch?v=vAlR6PPrUT4&list;=PLpxz2tR-XHQMO4tlfZ6aVqWgUggaeNKSI
👉BIOGRAPHIES
https://www.youtube.com/watch?v=37TI2KOGwrc&list;=PLpxz2tR-XHQOrLFN0PnpPY7_yx9X-yPIw
✅ Other Videos You Might Be Interested In Watching:
✅ About Philosophy Student.
This channel has one goal: to help philosophy students learn about philosophical concepts and familiarize themselves with their history, terms, theories, and thoughts. Here, you will find videos on the history of philosophy, biographies of philosophical figures, and explanation videos on philosophical terms, concepts, and theories.
We also do videos on philosophy books and popular papers. A special emphasis is placed on helping you to learn how to be your very best at philosophy. How to write better papers, how to learn better, and how to get great grades in your philosophy courses. We hope you enjoy it, and look forward to your comments!
🔔 Master the art of philosophy with our comprehensive library of educational videos. Subscribe Now:
https://www.youtube.com/@PhilosophyStudentOrg/sub_confirmation=1
=================================
#davidhilbert #mathematics #prooftheory #philosophy #biography #logic
© Philosophy Student
Wilhelm Ackermann
Wilhelm Friedrich Ackermann (29 March 1896 – 24 December 1962) was a German mathematician best known for the Ackermann function, an important example in the theory of computation.
Ackermann was born in Herscheid municipality, Germany, and was awarded a Ph.D. by the University of Göttingen in 1925 for his thesis Begründung des "tertium non datur" mittels der Hilbertschen Theorie der Widerspruchsfreiheit, which was a consistency proof of arithmetic apparently without full Peano induction (although it did use e.g. induction over the length of proofs). From 1929 until 1948, he taught at the Arnoldinum Gymnasium in Burgsteinfurt, and then at Lüdenscheid until 1961. He was also a corresponding member of the Akademie der Wissenschaften (Academy of Sciences) in Göttingen, and was an honorary professor at the University of Münster.
In 1928, Ackermann helped David Hilbert turn his 1917 – 22 lectures on introductory mathematical logic into a text, Principles of Mathematical Logic. This text contained the first exposition ever of first-order logic, and posed the problem of its completeness and decidability (Entscheidungsproblem). Ackermann went on to construct consistency proofs for set theory (1937), full arithmetic (1940), type-free logic (1952), and a new axiomatization of set theory (1956).
This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Wilhelm_Ackermann
The Insane Ackermann Function...
Grandes Matemáticos - Wilhelm Ackermann...
Ackermann Function...
The Most Difficult Program to Compute? - Computerp...
Ackermann function...
Ackermannfunktion...
Lawrence C. Paulson: Research Challenge + Ackerman...
Ackermanns Function | GATE Lecture...
Principles of Mathematical Logic | Wikipedia audio...
David Hilbert: Math's Modern Architect | Philosoph...
Latest News for: wilhelm ackermann
Edit
Eagle-Tribune
20 Oct 2022
HMNC Brain Health Raises EUR 14.3 million to Advance Precision Psychiatry Therapies
Eagle-Tribune
20 Oct 2022
Josef Ackermann, Wilhelm Beier, Toni Kroos, and Carsten Maschmeyer ... Josef Ackermann (formerly CEO of Deutsche Bank), Toni Kroos (Real Madrid), Wilhelm Beier (Dermapharm) and Hans Kompernaß (Hans Kompernaß GmbH).
- 1