OpenAI produced two versions of its proof of the Navier-Stokes problem. Historical mathematical milestones date back to 350 BC, when Aristotle described a proof that an isosceles triangle always has two equal sides and two equal angles at the base.
Around 300 BC, Euclid described a similar proof regarding the equal sides and base angles of an isosceles triangle. Euclid also recorded a proof establishing that there are infinitely many primes.
A 2023 survey identified 200 different proofs of Euclid's theorem. In 1737, Leonhard Euler published a formula relating the sum of all numbers to the product of all primes.
Bernard Riemann proposed the Riemann hypothesis over a century after Euler's formula. Wilhelm Grunwald published a proof in 1933 showing a number a with a certain property must be written as x^n.
George Whaples gave a new proof of the same property in 1942. Shianghao Wang found the property was not true for 16 in 1948.
The result is now known as the Grunwald-Wang theorem. Scott Viteri and Simon DeDeo published a paper in 2022 regarding mathematical proof journeys.
Scott Viteri at Stanford University and Simon DeDeo at Carnegie Mellon University in Pennsylvania claim a mathematical proof is structured like a network where truth is transmitted along paths. Viteri and DeDeo also claim the network of a proof undergoes an epistemic phase transition.
