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I must be missing something. Why is this significant?
by rank0 7y ago
I must be missing something. Why is this significant?
- qrybam 7y agoI suppose it’s in reference to https://en.m.wikipedia.org/wiki/Phrases_from_The_Hitchhiker's_Guide_to_the_Galaxy https://en.m.wikipedia.org/wiki/Phrases_from_The_Hitchhiker'...
- JshWright 7y agoIt was the last (possible) number under 100 to be confirmed as the sum of three squares.
- tobr 7y agoI believe it’s the lowest number that did not have a known solution for x^3 + y^3 + z^3. Plus, it’s 42.
- timerol 7y agoLowest number that isn't 4 or 5 modulo 9. There are numbers that can't be expressed, the open question is whether all other numbers can be expressed
- inscionent 7y agoSo long and thanks for all the fish.
- mombul 7y agoSame question. People seem to be researching that kind of stuff (numbers that are sums of 3 cubes). Why?
- jerf 7y agoI only recently heard what I think is a pretty solid answer to this question [1] that put it this way: We've pretty much got addition nailed down. We're pretty solid on multiplication. However, we are surprisingly weak mathematically when we try to put the two together; you can write down some extremely small math statements that baffled mathematicians for centuries, and for such statements that we have solutions for, they often get into very, very complicated math. So you have things like Fermat's Last Theorum, or if you prefer, the Question: For a^n + b^n = c^n, are there any solutions with n > 2 for integers? Note how it's just multiplication and addition on the integers. There are simpler questions, but they don't get much simpler. There's no real analysis, transcendental numbers, imaginaries or higher-dimensional numbers, infinities, and so on, at least not in the question itself; it's literally so simple you can reasonably explain it to a middle schooler. It took mathematicians centuries, and the simplest version of the current proof is still PhD-level work to understand. (I suspect even a Master's student in math would have to carefully craft their entire post-doc education for the purpose of understanding this exact proof to be able to say they fully understood it, with no lemmas taken on faith, and I'm still not sure they could make it without a lot of independent study.) You have things like "Can all of the numbers of a certain form be created via 'a^3 + b^3 + c^3'?", which sounds like it really ought to be simple. It's not too hard to eliminate 4 or 5 mod 9, but proving that it can always be done for everything else is beyond all current known math. There's a lot of these sorts of questions in math right now. This is a particular single example of a family of very vexing problems. It's hard to know what the practical impact of mastery over this combination would be, but I expect there probably would be some. Mastery over addition and multiplication have practical consequences that would require a series of books to explore; you have to think that mastering them in combination couldn't help but be practically useful. [1]: I think it was a somewhat recent Numberphile video, but it may also have been a Terence Tao lecture. References solicited if you've got 'em. [2]: https://youtu.be/wymmCdLdPvM?t=209 https://youtu.be/wymmCdLdPvM?t=209
- ineedasername 7y agoBecause of the deep existential meaning of 42, which transcends any known religion or ideology. Its significant is only comparable, though not eclipsed, by the utility of a good towel. Never leave home with one.
- ocfnash 7y agoMathematicians are interested in which natural numbers k can be expressed as a sum of three cubes. Prior to this year, it had been established that this is possible for all k < 1000 except for the following thirteen values: 33, 42, 114, 165, 390, 579, 627, 633, 732, 795, 906, 921, 975. Earlier this year a solution for k=33 was found [1], so 42 was the next unknown value. [1] Brooker, A., "CRACKING THE PROBLEM WITH 33", https://people.maths.bris.ac.uk/~maarb/papers/cubesv1.pdf https://people.maths.bris.ac.uk/~maarb/papers/cubesv1.pdf
- tomd3v 7y ago> Mathematicians are interested in which natural numbers k can be expressed as a sum of three cubes. Why?
- intuitionist 7y agoThis isn’t quite right, it’s easy to show that if n is 4 or 5 (mod 9), then there are no integer solutions to a^3 + b^3 + c^3 = n. The conjecture is that the mod 9 obstruction is the only one and all other integers can be represented as the sum of 3 cubes.
- ocfnash 7y agoThanks, that was very sloppy of me!