Anthropic announced that its artificial intelligence model, Cloud, was able, almost independently, to formulate the Great Fermat Theorem into code within 11 days.
It is worth noting that the French mathematician Pierre de Fermat formulated the theorem in the seventeenth century, but proving it remained elusive for more than three centuries, until the British mathematician Andrew Wiles was able to prove it in 1995, after about seven years of working on it in secret.
Formal formulation, on the other hand, means translating the mathematical proof into computer code that allows the computer to verify the correctness of each step in it.
Many mathematicians tried to find a proof for this problem, but their attempts ended in failure. Wiles worked on the problem in secret for seven years before announcing a major breakthrough in 1993. Mathematical proofs often consist of long chains of logical deductions that depend on each other, such that if an error creeps into one of the steps, the entire proof may collapse.
This is exactly what happened with Wiles, when a flaw was discovered in his proof, and it took about a year to close it.
The digitization, or formalization, of mathematical theories transfers them from the world of "pen and paper" to the world of programming code, allowing computers to process them, verify their logic step by step, and uncover any errors or flaws. The central repository "Mathlib" contains approximately two million lines of formally formulated mathematics.
Professor Kevin Buzzard of Imperial College London spent five years working on this task, while the "Claude" model completed it in 11 days. According to Buzzard, the proof "relies on nothing but the axioms of mathematics."
The task was divided between AI agents who received general guidance periodically, and the "Prove2Me" tool, originally designed to help human mathematicians, helped them coordinate the work.
If these results become reliably reproducible, artificial intelligence may be able to accelerate the process of translating modern mathematics into formulas that can be automatically verified.
what is your opinion on this news ?do let us know in the comments on tha comment box
if you liked this news article please share on friends & family & don't forget to follow on website & social media
