Talk:2529: Unsolved Math Problems

Does anyone have any clue whether the writing on the board in the weirdly abstract panel means anything? Maybe add an explanation about it?162.158.227.91 13:23, 17 October 2021 (UTC)

Center panel possibly related to "The drunkards walk" and theories on randomised motion. https://www.quantamagazine.org/random-walk-puzzle-solution-20160907/ More references https://mathworld.wolfram.com/RandomWalk.html

Someone's gotta point out that "walking randomly on a grid, never visiting the same square twice" would rapidly trap you in a corner (even the example has a 50/50 chance of that happening on the next move) 172.70.130.125 04:29, 16 October 2021 (UTC)

Not if it's an infinite grid.

I think there's two different ways to interpret the question - as a uniform random element of the set of all non-self-intersection NxK length paths, in which case it's fine, or as a path defined by a random walk in which moves onto your own path are not allowed, which doesn't seem well defined, since you might end up in a situation where you are surrounded by your own path and cannot continue for all NxK steps.

An early example of a cursed problem is the Cantor Function. https://en.wikipedia.org/wiki/Cantor_function

I admire whoever wrote the description of the curve in the "cursed" panel. Barmar (talk) 05:36, 16 October 2021 (UTC)

"Algebreic" is a misspelling of "algebraic". Could Randall really have made this mistake, or is it another malamanteu? What does "breic" come from? Barmar (talk) 06:10, 16 October 2021 (UTC)

I wonder if Randall was actually referring to that quote about "Into the Woods", or he just thought "Sondheim calculus" sounded cool and it was a total coincidence. I found it when I googled "sondheim calculus" to make sure it wasn't a real thing. Barmar (talk) 06:29, 16 October 2021 (UTC)

In panel 2, what would 'k' be? 172.69.35.108 08:00, 16 October 2021 (UTC)

'k' would represent the number of marbles placed on the ground. 162.158.88.127 08:09, 16 October 2021 (UTC)

Though probably correct, I think the implied state is that an integer multiple (k) of N steps is made (s=N*k), with that number of marbles dropped, not s=(N*k)+c steps (for N>c) which would have the same result (uselessly) for all values of s where c ranges 0..N-1. It just introduces inflections into the graph (with s as an axis) that needn't be there (with just a k-based one). Or, in other words, selectively poll all s-values that are exactly divisible by N, and forget all the rest. (That divisor is k, and hence k is the number of marbles. Or perhaps k+1 if you leave one on the starting spot too.) 162.158.159.25 21:59, 16 October 2021 (UTC)

To me, the cursed curve looks a bit like a crosier https://commons.m.wikimedia.org/wiki/File:Crosiere_of_arcbishop_Heinrich_of_Finstingen.jpg

--> I had the same impression and added it. --162.158.94.219 11:40, 16 October 2021 (UTC)

No explanation of the "Euler Field Manifold Hypergroup (Isomorphic to a)..." part?

The cursed curve looks almost like someone took a graph of the Binet formula in the complex plane, stretched it out a bit, and rotated it onto the i axis.

This was my first thought too when I saw it. 172.69.34.87 17:16, 16 October 2021 (UTC)

It looks like Vulcan script to me. LtPowers (talk) 13:51, 16 October 2021 (UTC)

That's what it looks like to me too; recognized it from that Numberphile video on Fibonacci numbers in the complex plane 108.162.245.245 07:36, 17 October 2021 (UTC)

Could the cursed curve be a reference to the logistic map?

Can someone produce a high resolution image of the Cursed Curve? It needs to be on a T-shirt Avimimus (talk) 21:39, 16 October 2021 (UTC)

Is someone going to mention the title text?

I swear I've seen that third plot, I thought it was in XKCD, but a quick run through tagged entries didn't find anything... unfortunately I consume a lot of math media so I can't place it. It's bugging me so I hope this note will serve as encourgement to someone that DOES remember 162.158.106.221 21:29, 16 October 2021 (UTC)

I'm sure I've seen components of the cursed-curve, not sure if they fit together like that, easily, though. The differentiation of dy/dt (which is odd in itself) of the first (lower) bit looks discontinuous, followed by a chaotic oscilation (may just be the culmination of the less frenetic chaos that created the first set of x=f(y) - again, an unusual way round) that then settles into a pattern where regardless of the 'prime axis', you have multiple real roots on the other, towards some great-attractor value.

In more standard x/y (or y=f'(x)?) notation, it is clear that there are multiple real roots for various values of x within a range, and possible none at all beyond that (or it's a plotting error insofar as x tendsvto ±infinity it has a very narrow range of y that is never sampled properly, but should connect to that pulse 'randomness'). If it's a plot of real vs imaginary components of a complex function to a different continuous value, I suspect someone is playing silly-buggers with multiple (perhaps nested?) trigonometric fuctions, polynomials and variable-shifted powers. But it's nearly thirty years since I did mathematics at the level needed to disentangle this neatly (back when Mandelbrots and Julias were still a staple wall-poster for any student not more into the likes of Iron Maiden skull-motifs or <insert your favourite classic film here>, and even then it might be) so don't ask me where to start. 162.158.89.140 16:48, 17 October 2021 (UTC)

Are there any examples of "cursed" math problems? I've seen "weirdly abstract" and "weirdly concrete" ones, but not "cursed" ones. 162.158.63.117 01:03, 17 October 2021 (UTC)

The symbol in the third panel looks like an unalome, which is not a mathematical symbol but a Buddhist or mystical one https://en.m.wikipedia.org/wiki/Yantra_tattooing#Types_and_designs

There is at least one paper on arxiv defining quasimonoid, 1401.7748. It's from 2014 so it existed long before the comic. --162.158.88.253 14:04, 17 October 2021 (UTC)

Links, **please**! Not all of us are mathematicians. If you mention something that you think the cursed curve might represent, please provide a link to something describing that something so the rest of us can read it and attempt to learn more. Shamino (talk) 17:44, 17 October 2021 (UTC)