81–90 of 108 posts
I'm sorry, but who needs this? If the answer is "we will discover new math methods trying to solve that puzzle", isn't it better to discover new math methods trying to solve something useful?
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I do like to joke that I studied maths because I don't like numbers.
I pursued and achieved an EE degree plus a couple extra math courses largely because I was "not good at math" as a youth. Nothing like hearing "I don't think math is your subject" from a key adult to light a fire under ones fanny. In hindsight I could have had the same career path with a straight CS degree and much less stress during my college years. No regrets though, math really is fun! Even more so when the class…
At school, we had tests to show what we were good at. The guy who came to comment on our tests told me that I should definitely go for something like literature or history.
And here I am, an engineer with an extra PhD in physics who dreams about meeting these idiots and explaining to them that what they do is revolting. They are probably dead by now though (it was in the 80's)
Here's a fairly easily understood problem, which if you could solve it would make you famous in the mathematical world and win you a million dollar prize: For a positive integer n: Let H(n) = 1 + 1/2 + 1/3 + ... + 1/n Let D(n) = the sum of the positive integers that divide n. E.g., D(12) = 1 + 2 + 3 + 4 + 6 + 12 = 28. Prove or disprove that for any positive integer n > 1: D(n) That easy to understand problem turns ou…
The million dollar prize rules are surprisingly strict. They expect a "natural" proof, in that writing a one-page paper "my computer found counterexample 2^1729-1" may not get you the full prize, maybe instead a tiny acknowledgement prize, and they will wait for a proof of a generalization of the problem. https://www.claymath.org/wp-content/uploads/2022/03/millenni...
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>Here I was naively thinking that if no counter examples were found in the first, say, 10^10 numbers, no counter examples should exist why on earth would you ever think that
> naively I think that answers your question?
Here it is: https://www.emis.de/journals/EM/expmath/volumes/12/12.4/Guil...
The author of the paper actually notes that a slightly different series is suspected to converge to $32/\pi^3$. The good news is that that series is an alternating series, so it's guaranteed to converge to something. But, it converges so slowly that, although the second partial sum differs from $32/pi^3$ by about 0.0004328909249, the 5000th partial sum differs by about 0.0004330860787. Those two numbers only start to differ at the 6th digit beyond the decimal point.
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>Here I was naively thinking that if no counter examples were found in the first, say, 10^10 numbers, no counter examples should exist why on earth would you ever think that
Why do you assume the sun will rise tomorrow?
Here's a fairly easily understood problem, which if you could solve it would make you famous in the mathematical world and win you a million dollar prize: For a positive integer n: Let H(n) = 1 + 1/2 + 1/3 + ... + 1/n Let D(n) = the sum of the positive integers that divide n. E.g., D(12) = 1 + 2 + 3 + 4 + 6 + 12 = 28. Prove or disprove that for any positive integer n > 1: D(n) That easy to understand problem turns ou…
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This is absolutely my personal experience. I am absolutely awful at arithmetic, but I think pretty competent at decently advanced mathematics. It's like they say: the only numbers a mathematician needs are 0, 1, and 2 (and just because it's not 1).
In number theory, 2 is often a special case in a lot of theorems. There's something odd about the even prime.
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Why do you assume the sun will rise tomorrow?
this analogy illustrates the opposite of what I think you intend it to. if we could artificially iterate the sun rising infinite times, somewhere very high up, maybe after 10^10, it eventually would no longer rise
The point was more that any length of time greater than a few thousand years is as good as infinite for a human, so (for, you know, everyday purposes) we might as well assume that the sun will keep on rising forever.
Im in the middle of something but that doesn’t look that hard