Checking that a major mathematical proof is correct can take years. Formalization—converting the mathematical reasoning into a form computer proof assistants like Lean can verify—can help.
Last month, Claude completed the first formalized proof of Fermat’s Last Theorem, one of the most famous theorems of all time. This was a project experts thought would take many years. It is the largest Lean proof ever written.
Fermat’s Last Theorem was first proven in 1995 by Sir Andrew Wiles, more than 350 years after it was conjectured. Our proof, which totals over 13 million lines of code, provides machine verification. More importantly, it proves over 29,000 other theorems that the proof requires, across many areas of math which had never before been formalized.
We see this as a major step in the long process of firming up the core of mathematical knowledge, building on work from three centuries of mathematicians and hundreds of contributors to Lean and Mathlib. We are optimistic that AI-assisted verification of mathematical proofs will help reduce the burden of refereeing mathematics in an era where more proofs are being produced than ever before.
You can read about the process on our Science Blog: https://t.co/ryYnDEAU6J
And see the complete proof on GitHub: https://t.co/wlYMXYnofz
The green transition promises to upend labor markets, but it also presents untold opportunities for job creation across a number of sectors says @nyashry of @Kaust_News.
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#GLMC2023
🔬 Exciting News! Discover how we're modeling complex tissue structures & unlocking developmental insights in our new publication! A breakthrough in understanding breast tissue development! 🧬📖 #ScienceAdvances#TissueEngineering#OrganoidResearch
Excellent article by @DrM2theJ, I've rarely seen an article that integrates my love for genetics and gaming!
The very real concepts of “mutation” and genetic conditions are ... https://t.co/SnsqeBCsk6
This gave me a good laugh this morning! #Networking is super simple and a great way to connect personally and professionally! My go-to suggestion for people that think they hate networking is to establish a common link- (and keep it simple)! #princessbride
قدتسمع(والله ماتركت مستشفى ولاطبيب الا رحت له وما استفدت)! هذا التصرف ليس مبرر لعدم وجود علاج بل انه قد يكون(بإذن الله)سبب لعدم الشفاء!لاسباب كثيرة منهاعدم اعطاء الدواءوقت كافي ليبدأ مفعوله،أوعدم اكمال الفحوصات و(الاحتمالات):التنقل من مستشفى لآخر وطبيب لآخر جعل كلاً يبدأ من جديد
"“aggressively wrong” and unwilling to learn. They actively resisted facts that might alter their preexisting beliefs. They insisted that all opinions, however uninformed, be treated as equally serious."
The Mirage of Knowledge - Harvard Magazine https://t.co/2zLkBnZMEZ
For the first time, researchers have been able to use long read nanopore sequencing to assemble the genomic sequence of a human Y chromosome centromere. https://t.co/x402RsLuX1
2 excellent essays on ethics on genome editing @NatureNews #OA#CRISPR
1. call for an "observatory" by @SJasanoff B Hurlbut https://t.co/dOQ06Q6r9V
2. anticipate, map participation by @sburall https://t.co/shyt7yZ98v