The contributions of Kurt Gödel in 1940 and Paul Cohen in 1963 showed that the hypothesis can neither be disproved nor be proved using the axioms of Zermelo – Fraenkel set theory, the standard foundation of modern mathematics, provided ZF set theory is consistent.

One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when many, such as Bertrand Russell, A. N. Whitehead and David Hilbert, were pioneering the use of logic and set theory to understand the foundations of mathematics.

Gödel attended the Evangelische Volksschule, a Lutheran school in Brünn from 1912 to 1916, and was enrolled in the Deutsches Staats-Realgymnasium from 1916 to 1924, excelling with honors in all his subjects, particularly in mathematics, languages and religion.

The theorems were proven by Kurt Gödel in 1931, and are important in the philosophy of mathematics.

** Kurt Gödel, Austrian logician, mathematician, and philosopher of mathematics ( d. 1978 )

Gödel showed that mathematics and logic contain Strange Loops: propositions that not only refer to mathematical / logical truths, but also to the symbol systems expressing those truths.

The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics.

One of the earliest attempts to use incompleteness to reason about human intelligence was by Gödel himself in his 1951 Gibbs lecture entitled " Some basic theorems on the foundations of mathematics and their philosophical implications ".

In the foundations of mathematics, von Neumann – Bernays – Gödel set theory ( NBG ) is an axiomatic set theory that is a conservative extension of the canonical axiomatic set theory ZFC.

Most of his academic life, from 1912 to 1938, was spent at the University of Vienna, where he taught for example Kurt Gödel, who later said that Furtwängler's lectures on number theory were the best mathematical lectures that he ever heard ; Gödel had originally intended to become a physicist but turned to mathematics partly as a result of Furtwängler's lectures.

The paper is famous for the theorems it contains, which have many implications for consistency proofs in mathematics, and for the techniques that Gödel invented to prove these theorems.

In addition to his work in logic and the philosophy of mathematics, Parsons was an editor, with Solomon Feferman and others, of the posthumous works of Kurt Gödel.

It is an international organization aimed at promoting research primarily on logic, philosophy and the history of mathematics, with special attention to connections with Kurt Gödel, in whose honour it was named.

This modern Platonism ( sometimes rendered " platonism ," with a lower-case p, to distinguish it from the ancient schools ) has been endorsed in one way or another at one time or another by numerous philosophers ( most of whom taking a particular interest in the philosophy and foundations of logic and mathematics ), including Bernard Bolzano, Gottlob Frege, Edmund Husserl, Bertrand Russell, Alonzo Church, Kurt Gödel, W. V.

In the foundation of mathematics, Morse – Kelley set theory ( MK ) or Kelley – Morse set theory ( KM ) is a first order axiomatic set theory that is closely related to von Neumann – Bernays – Gödel set theory ( NBG ).

Blind students also complete mathematical assignments using a braille-writer and Nemeth code ( a type of braille code for mathematics ) but large multiplication and long division problems can be long and difficult.

For instance, instead of a hardware multiplier, a calculator might implement floating point mathematics with code in ROM, and compute trigonometric functions with the CORDIC algorithm because CORDIC does not require hardware floating-point.

Much of ML code is similar to mathematics in facility and syntax.

Professor Thomas Nicely, a professor of mathematics at Lynchburg College, had written code to enumerate primes, twin primes, prime triplets, and prime quadruplets.

One of the first court cases regarding the nature of source code as free speech involved University of California mathematics professor Dan Bernstein, who had published on the Internet the source code for an encryption program that he created.

In mathematics, Fibonacci coding is a universal code which encodes positive integers into binary code words.

Computer code is regarded by some as a form of mathematics.

Unicode discourages their use for mathematics and in Western texts because they are canonically equivalent to the CJK code points U + 300x and thus likely to render as double-width symbols.

The 49G incorporated many of the most powerful interface and mathematics tools available on the HP-48 series into the firmware of the new 49G, including the ability to easily decompile and compile both SysRPL and Saturn assembly code on the unit.

In mathematics and electronics engineering, a binary Golay code is a type of error-correcting code used in digital communications.

The binary Golay code, along with the ternary Golay code, has a particularly deep and interesting connection to the theory of finite sporadic groups in mathematics.

Nemeth Braille is just one code used to write mathematics in braille.

* Covering code for the mathematics behind continental European pools

* Reed – Muller code ( mathematics )

STOS 2. 4 also fixed a few bugs and had faster floating point mathematics code, but the floating point numbers had a smaller range.

In combinatorial mathematics, the Prüfer sequence ( also Prüfer code or Prüfer numbers ) of a labeled tree is a unique sequence associated with the tree.

The major criticism against the code is that it fails to handle mathematics or computer science as compactly as codes designed to be optimal for those disciplines.

The Gray code, or reflected binary code, appearing in Gray's 1953 patent, is a binary numeral system often used in electronics, but with many applications in mathematics.

Pythagoras believed that behind the appearance of things, there was the permanent principle of mathematics, and that the forms were based on a transcendental mathematical relation.

Another possibility, raised in an essay by the Swedish fantasy writer and editor Rickard Berghorn, is that the name Alhazred was influenced by references to two historical authors whose names were Latinized as Alhazen: Alhazen ben Josef, who translated Ptolemy into Arabic ; and Abu ' Ali al-Hasan ibn al-Haytham, who wrote about optics, mathematics and physics.

George W. Snedecor, the head of Iowa State's Statistics Department, was very likely the first user of an electronic digital computer to solve real world mathematics problems.

In later life Ampère claimed that he knew as much about mathematics and science when he was eighteen as ever he knew ; but, a polymath, his reading embraced history, travels, poetry, philosophy, and the natural sciences.

Despite his lack of formal qualifications, Ampère was appointed a professor of mathematics at the school in 1809.

Despite being quite religious, he was also interested in mathematics and science, and sometimes is claimed to have contradicted the teachings of the Church in favour of scientific theories.

From the ages of 6 to 9, Alexei was educated by his tutor Vyazemsky, but after the removal of his mother by Peter the Great to the Suzdal Intercession Convent, Alexei was confined to the care of educated foreigners, who taught him history, geography, mathematics and French.

He was educated at the Collège des Quatre-Nations ( also known as Collège Mazarin ) from 1754 to 1761, studying chemistry, botany, astronomy, and mathematics.

Many of the refugee children being hidden in Chambon attended Cévenol and it was at this school that Grothendieck apparently first became fascinated with mathematics.

He was, however, able to play a dominant role in mathematics for around a decade, gathering a strong school.

This program culminated in the proofs of the Weil conjectures, the last of which was settled by Grothendieck's student Pierre Deligne in the early 1970s after Grothendieck had largely withdrawn from mathematics.

In mathematics, the axiom of regularity ( also known as the axiom of foundation ) is one of the axioms of Zermelo – Fraenkel set theory and was introduced by.

" The Four Books on Measurement " were published at Nuremberg in 1525 and was the first book for adults on mathematics in German, as well as being cited later by Galileo and Kepler.

It was published in Des Moines, Iowa, and was the earliest American mathematics journal to be published continuously for more than a year or two.

On the Infinite was Hilbert ’ s most important paper on the foundations of mathematics, serving as the heart of Hilbert's program to secure the foundation of transfinite numbers by basing them on finite methods.

Stroustrup has a master's degree in mathematics and computer science ( 1975 ) from the University of Aarhus, Denmark, and a Ph. D. in computer science ( 1979 ) from the University of Cambridge, England, where he was a student at Churchill College.

His father, Étienne Pascal ( 1588 – 1651 ), who also had an interest in science and mathematics, was a local judge and member of the " Noblesse de Robe ".

Following Desargues ' thinking, the sixteen-year-old Pascal produced, as a means of proof, a short treatise on what was called the " Mystic Hexagram ", Essai pour les coniques (" Essay on Conics ") and sent it — his first serious work of mathematics — to Père Mersenne in Paris ; it is known still today as Pascal's theorem.

William Frederick Schelter ( 1947 – July 30, 2001 ) was a professor of mathematics at The University of Texas at Austin and a Lisp developer and programmer.

The Demolished Man was a novel that had fascinated De Palma since the late 1950s and appealed to his background in mathematics and avant-garde storytelling.

The first person to describe the mathematics behind Brownian motion was Thorvald N. Thiele in a paper on the method of least squares published in 1880.

Their cognitive science of mathematics was a study of the embodiment of basic symbols and properties including those studied in the philosophy of mathematics, via embodied philosophy, using cognitive science.