P ≠ NP. It's easy to verify the truth, but it's hard to solve problems to find the truth.

#PNP #ComputerScience #Algorithms #Complexity #Math #Computation #Theory #MillenniumPrize #Cryptography #Optimization #Science #Tech #Unsolved #Mathematics #Computing #Innovation #Logic #ProblemSolving #AI #Knowledge

P ≠ NP: Checking a solution is easy; finding it is hard. Still the greatest unsolved mystery in computation.

#PNP #ComputerScience #Algorithms #Complexity #Math #Computation #Theory #MillenniumPrize #Cryptography #Optimization #Science #Tech #Unsolved #Mathematics #Computing #Innovation #Logic #ProblemSolving #AI #Knowledge

MillenniumPrizeProblemBench: Thử thách AI với những bài toán khó nhất lịch sử

Một hệ thống benchmark mới vừa ra đời nhằm đánh giá khả năng giải toán của AI thông qua các Bài toán Thiên niên kỷ (Millennium Prize Problems). Đây là những đề bài toán học chưa có lời giải với phần thưởng 1 triệu USD mỗi bài. Liệu AI có thể vượt qua giới hạn tư duy của con người để giải quyết những bí ẩn này?

#AI #Mathematics #MillenniumPrize #MachineLearning #Toanhoc #Congnghe #TriTueNhanTao #MPPBench

https://www.

Blow-Up or Not? - Terence Tao on Lex Fridman

#navierstokes #blowup #millenniumprize

Nine years ago on a defunct platform I wrote this (and I made a big statement, now-deleted, more below)

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What do you think of this explanation of the Hodge conjecture by Melbourne mathematician Arun Ram?

https://theconversation.com/millennium-prize-the-hodge-conjecture-4243

I think it's great: the right level of metaphor and concrete examples that arise from simple cases of the problem.

[...]

#mathematics #millenniumprize #hodge #algebraicgeometry
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Last week I was asked to explain off the cuff the Hodge conjecture by a colleague who is an engineer of some kind. I had recalled from a more recent peep into a certain pop-maths book (mentioned in the [...] above) that the author kinda wimped out, leaving the Hodge conjecture for last and then admitting it was rather complicated. I think I was a bit harsh in what I said in the redacted bit. But that may have been because I don't have the expertise in writing for a popular audience, and this certain person very much did, and held themselves to a higher standard of exposition in both detail and clarity than I would have, nine years ago.

I'm also slightly cooler on the metaphor in the linked post — it's still a good metaphor, but it doesn't work so well for me now as when I first wrote the above.