Perfect rigor

What Hacker News says

1. xabushAug 2026
   "To me it would be more impressive if we could define hard problems that need to be solved up front and see how the models deal with that."

   I was recently listening to BBC Radio 4's episode on the Poincare Conjecture[1] and the guests on the program were discussing how the problem that looked deceptively simple eluded the great mathematicians of the time (including Poincare himself) for nearly a century and how Grigori Perelman cleverly came up with the proof. It took other mathematicians working in groups years after Perelman's publication to understand and validate his proof. The mathematicians on the program were speaking of highly of his proofs and admiring the originality of his work. This made me think of one neat experiment where if we cut-off a frontier model's training data 2002 or anytime before Perelman posted his proofs on arXiv and check if it can come up with the solution by itself. That would surely be a great signal to see if these LLMs aren't just solving interesting puzzles and that they can came up with something truly novel.

   P.S I highly recommend Misha Green's "Perfect Rigor" for anyone interested in the history of the problem and the genius behind the proofs of the conjecture - Perleman. I found it an entertaining read and could digest its description of the problem as a layperson (with undergrad level math).

   [1] https://www.bbc.co.uk/programmes/p0038x8l

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2. jseligerDec 2016
   Yes. And Masha Gessen wrote an excellent book called Perfect Rigor about the proof and the man: https://jakeseliger.com/2016/11/29/perfect-rigor-a-genius-an.... Highly recommended.
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3. pm90Mar 2013
   The book "Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century[0]" which details the life of Giorgi Perelman (who solved the famous Poincare Conjecture) gives a detailed account of antisemitic policies extant in the USSR at the time.

   [0]:http://www.amazon.com/Perfect-Rigor-Mathematical-Breakthroug...

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4. rehackDec 2012
   Zen and the art of motorcycle maintenance - A book on philosophy, can go as deep as you like. Was written over 25 years ago, but feels very fresh. My key take away from this book was that you should be humble enough to appreciate various models of the world - e.g. Science or Religion. Favorite quote: "When you have a Chatuahaha in your head, you can't resist inflicting it on innocent people". Still makes me smile :-)

   Life of Pi - Bought it following the buzz of the movie. Read the book first, then saw the movie. A good simple read. Sort of reinforces, the 'various models' idea of the 'Zen...' book. Found the movie slightly better than the book, which was a surprise. Ang Lee has made subtle changes, which makes the story more peppy.

   Perfect Rigor - Captures the story (and math) behind, the turning down of a million dollar prize by Gregory Perelman. The genius Russian mathematician, who solved a 100 year old standing problem, of the missing proof of the Poincare Conjecture. It was perhaps my best technical read of the year.

   I am feeling Lucky (by Doug Edwards): Google's emplpyee number 59, writes about his experience at Google. I found it the best book on Google. Better than some of the others, which seem a bit like officially authorized versions.

   Below ones I read it in 2011. But haven't posted here, so here goes:

   Born to Run (By Chris Mcdougall): A health book. Has really helped my running. Highly recommended to all.

   A guide to a good life: The ancient art of Stoic Joy (By Joseph Irvine): A very good book on philosophy. Read it on the reco (http://sivers.org/book) of Derek Sivers.

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5. dsplittgerberMar 2010
   I recommend reading "Perfect Rigor - A genius & the mathematical breakthrough of the century" by Masha Gessen. It provides the best possible insights into Perelman's life and work and details why he most probably will not ever accept this prize.
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6. aws_lsAug 2016
   Grigori Perelman, who became famous because of turning down the Fields Medal, including a million dollar prize, for proving the Poincare conjecture, 100 year old standing problem, despite living in near-poverty. Stuff of legends.

   He also figure in sibling comment list. I read a book called Perfect Rigor, in that if I remember right, he could easily solve all the seven problems. Which happens rarely. Surely a living (and also tragic) genius. I get goose bumps just by typing this comment.

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