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That's just the first counterexample that was proven to exist. The smallest counter example is less than 10^10 (in fact smaller than 10^9). > The Pólya conject
by messe 3y ago
That's just the first counterexample that was proven to exist. The smallest counter example is less than 10^10 (in fact smaller than 10^9).
> The Pólya conjecture was disproved by C. Brian Haselgrove in 1958. He showed that the conjecture has a counterexample, which he estimated to be around 1.845 × 10^361.[3]
> An explicit counterexample, of n = 906,180,359 was given by R. Sherman Lehman in 1960;[4] the smallest counterexample is n = 906,150,257, found by Minoru Tanaka in 1980.[5]
EDIT: rephrased because despite having a maths degree I can't count.
- klysm 3y agoI believe inability to do arithmetic correctly is more common in folks with maths and other STEM degrees
- messe 3y agoI do like to joke that I studied maths because I don't like numbers.
- at_a_remove 3y agoI recall the end of a science fiction novel, wherein we finally meet aliens. It turns out that, as a trend, the species that are good at counting are bad at math and especially counting things at a glance. The species that is best at math have a hard time telling the difference between two things and three things just looking.
- hinkley 3y agoI know a young man with dyscalculia and we were hoping when he got to symbolic math that his problems would diminish. That has not born fruit so far.
- anthomtb 3y agoI 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 classroom setting is removed.
- BrandoElFollito 3y agoWhen I was about 12yo, I went to the eye doctor with my father (in France). The doctor realized that I had daltonism and told my father in front of me that I would never be an engineer because of that. 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)
- tocs3 3y agodaltonism : color blindness Had to look it up.
- DavidSJ 3y agoIt's one of the prerequisites in fact.
- susam 3y ago> I believe inability to do arithmetic correctly is more common in folks with maths and other STEM degrees Reminds me of a story from <https://www.ams.org/notices/200410/fea-grothendieck-part2.pdf https://www.ams.org/notices/200410/fea-grothendieck-part2.pd...>. Quoting it below: One striking characteristic of Grothendieck’s mode of thinking is that it seemed to rely so little on examples. This can be seen in the legend of the so-called “Grothendieck prime”. In a mathematical conversation, someone suggested to Grothendieck that they should consider a particular prime number. “You mean an actual number?” Grothendieck asked. The other person replied, yes, an actual prime number. Grothendieck suggested, “All right, take 57.”
- 1propionyl 3y agoThis 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).
- eru 3y agoIn number theory, 2 is often a special case in a lot of theorems. There's something odd about the even prime.
- xeonmc 3y agoi.e. the first information-encoding base.
- eru 3y agoI'm not sure. The Fibonacci numbering system has a smaller effective base. (And there's always unary.) See https://en.wikipedia.org/wiki/Fibonacci_coding https://en.wikipedia.org/wiki/Fibonacci_coding
- 1propionyl 3y agoIn analysis and its applications, the L^2 norm is also rather special.
- jl6 3y ago“I’m a mathematician, not an arithmetician!”
- keithalewis 3y agoThere are three kinds of mathematicians...
- globalnode 3y agojust looked that up, i like.
- cubefox 3y ago> He showed that the conjecture has a counterexample, which he estimated to be around 1.845 × 10361 1.845 × 10361 = 19116.045
- messe 3y agoThanks, it should be 10^361. I've fixed it.
- eru 3y ago> EDIT: rephrased because despite having a maths degree I can't count. You would probably enjoy Tom Körner's book 'The Pleasures of Counting'. See eg https://maa.org/press/maa-reviews/the-pleasures-of-counting https://maa.org/press/maa-reviews/the-pleasures-of-counting