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Comment by varelse | Hacker News Reader

And I admitted it's a cool pure math problem. The challenge in the tech industry is balancing the rigor of a pure but nearly intractable solution with using the theory to pump up an O(n) imperfect solution to acceptable reliability. I find the latter more interesting, YMMV.

But if that isn't as interesting as the original problem, maybe stay in academia? AI itself is an example of tailoring activation and pooling functions to deliver imperfect solutions that are "good enough" to ship. It's unfortunate these two viewpoints are seen as contradictory rather than complementary, but that does echo our political balkanization so I guess I shouldn't be surprised.

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Making things hard sometimes leads to insights down the line. For instance, the formula for solving cubic equations seems kind of silly from a numerical point of view -- you can just use a general-purpose numerical algorithm to solve cubics. But the research into solving cubics using restricted operations led to the discovery of the complex numbers, group theory, and the theory of fields, etc. So it was worth doing things the hard way and sticking to the letter of the problem.

Likewise, the ideas people use to solve the problem in the article may have applications elsewhere.

I do sometimes have doubts about whether this is the most efficient way of discovering scientific ideas: Posing puzzles and seeing what tools people throw at them. So I can see the criticisms coming...

Not going to criticize you, I think it's a cool math problem, but I've experienced people throwing problems like this at me at job interviews in the past so it echoed. And in those cases, they weren't looking for an answer, they were looking for the answer they knew about and no other answer would do. I once ended an interview early over one of these questions.

I am relentlessly production focused but that doesn't mean I don't like math. But by the time you get to FP64 with this thing, the probability of finding a fail case seems insanely low and in fact for the most part you can provably bound the error of the sum and therefore likely prove you have found the solution. Anything beyond that is a corner case as the mathematicians love to say. And now I see the criticisms coming.

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