/sci/ - Science & Math

[Anonymous No.9645595]

Post your /sci/ memes here

[Anonymous No.9645632]

>>9645595

[Anonymous No.9645642]

[Anonymous No.9645847]

[Anonymous No.9645972]

[Anonymous No.9645975]

[Anonymous No.9645978]

[Anonymous No.9646090]

[Anonymous No.9646465]

>>9645595

[Anonymous No.9646519]

>>9646465

For anyone who is curious, the full pdf of this article is available here:

https://arxiv.org/pdf/math/0511366v2.pdf

Lara Pudwell's little paper is actually part of an interesting exchange in the history of mathematics, which also investigates fairly simple subject matter so that the overall project is accessible to a wide audience. It goes like this.

Early in the 20th century, Hardy's skill is declining and so he instead writes a short popsci book, "A Mathematician's Apology", in which he describes, as well as he can, what being a mathematician is like and what he personally likes about his work. Typically, Hardy praises the cold, austere, abstract beauty of mathematics. I know that many here instinctively roll their eyes at this sort of thing, but just hang on a moment (and besides, the above disgust is not so much a disgust with the actual content of the aesthetic conceit, but rather an instinctive defense mechanism against pseuds who mouth platitudes without any understanding, "oh god this kid thinks he knows math because he watched a few youtube videos", that sort of thing). End digression: for Hardy, actual discovery (and thereby winning prestige, having your name attached) and the /competitive/ aspects of math are also at a premium. Hardy recalls with pleasure schoolboy days of being the first or only student who was able to prove such-and-such challenge problem.

Hardy's little book can still be defended: he gives examples of "trivial, non-deep" math which are to be distinguished from real, substantive math: little puzzles, curiosities, recreational math and so on. One example he cites, from a series of problems of Coxeter/Rouse Ball, is that 1089 and 2178 are the only two nontrivial four-digit numbers such that multiplication by some natural number gives their digit reversals. Hardy then dismisses the demonstration of this kind of thing as a tedium, and exactly what he has in mind as un-deep.

cont.

[Anonymous No.9646547]

Let Hardy's little book, and its own promulgation of the Coxeter/Rouse Ball problem percolate for a few decades. Now the truly advanced are free to legitimately roll their eyes if they're still bored.

Basically in the 1960s a handful of authors published in Mathematics Magazine get hold of the problem idea communicated by Hardy, and they decide to run with it for a few notes, generalizing the notions of digit reversal with different number bases, numbers of digits and so on. Not very serious stuff, but it's published on record. Kaczynski, then a newly-minted Ph.D., decides to join this exchange and pad his article count, producing a short note on same (which is three gears down from his own, more serious research work). Some further decades later, Kaczynski becomes the Unabomber, gets captured, and in the course of adding to this "60s" literature on the topic, Lara Pudwell herself contributes a new article, "Digit Reversal without Apology" (pun on Hardy's book), to the same journal, Mathematics Magazine-which of course is the source for the popular out-of-context meme, and humorous footnote. Pudwell's bibliography in the piece captures all the relevant lit to the above, including the Hardy book and the early MM 60s articles, including K's addition.

One of the other 60s articles does multiple variations on the themes of 2178 and 1089, appending various digits so that the whole business keeps working out in such-and-such circumstances. Something else I noticed, while playing with all this: 2178 is twice 1089. Per Hardy at least (though he'd spin in his grave), the invitation then is to check the multiples of 1089 through its own (highest in the limited sense) multple and digit-reversal, 9801. You get a small set of duals where the relevant factors become each others' reciprocals, and in the middle bit there's a few very simple rational terms. In the middle of this is the palindromic 5445.

[Anonymous No.9646551]

>>9645642
>this is what Stacy's learning
Interesting.