2529: Unsolved Math Problems

2021-10-16T07:43:59Z

Felisse: /* Explanation */

{{comic
| number = 2529
| date = October 15, 2021
| title = Unsolved Math Problems
| image = unsolved_math_problems.png
| titletext = After decades of studying the curve and the procedure that generates it, the consensus explanation is "it's just like that."
}}

==Explanation==
{{incomplete|Created by an Euler field Gödel-Escher-Klein strange curve walking randomly on a grid. Do NOT delete this tag too soon.}}

In mathematics, a concrete.problem is one that is very obviously connected to a real world process while an abstract problem is one which seems unconnected to actual problems. In modern math many problems tend to be very abstract requiring complicated notation to adequately state the problem in the first place like many of the millennium problems. On the other hand many unsolved problems are very concrete, for example there are very many problems related to packing objects into spaces which are very difficult to solve. Finally cursed problems are problems that have strange, seemingly random behavior such as, for example the collatz conjecture or the distribution of primes.

In the first panel, Ponytail describes a weird abstract problem. Her description seems to be a meaningless jumble of terms that are either mathematical or just ''sound'' mathematical. And the mathematical terms are from disparate branches of mathematics: group theory, topology, calculus. It's full of what seem to be [[Malamanteau|malamanteaus]]: "quasimonoid" combines the prefix "quasi" (meaning "partially" or "seemingly") and "monoid" (an object from category theory); "Gödel-Klein" combines {{w|Kurt Gödel}}, a 20th-century mathematician who studied logic and philophy (he's most well known for {{w|Gödel's incompleteness theorems}}) and {{w|Felix Klein}}, a 19th century mathematician who studied group theory and geometry, who probably never collaborated; "sondheim calculus" refers to {{w|Stephen Sondheim}}, one of the most successful composers and lyricists of American musical theatre -- the producer of his musical "Into the Woods" once [[https://www.indiewire.com/2015/01/watch-singing-sondheim-is-like-calculus-in-into-the-woods-behind-the-scenes-video-exclusive-189507/ remarked]] that “Singing Stephen Sondheim is like calculus for singers and actors.”; and "conjection" may combine conjecture and conjunction, or be a joke on pros and cons plus projection. Finally she asks whether the problem statement is ill-formed; considering that it's mostly gibberish, this may be true.

In the second panel, Cueball describes a concrete {{w|random walk}} problem, and then mentions that this somehow has applications in three unrelated fields. This is actually not uncommon. The Wikipedia article says "random walks have applications to engineering and many scientific fields including ecology, psychology, computer science, physics, chemistry, biology, economics, and sociology."

In the final panel, Megan is looking at a strange curve that seems to have no consistent pattern. At the bottom it's mostly straight, with a few little wobbles. In the middle it looks like a wild, high-frequency wave that suddenly bursts and then dies down. And the top is a helix that looks like a question mark. She wonders if this could even be mathematical. Considering the weird shapes that come from plotting some mathematical processes (e.g. the {{w|Mandelbrot set}}), it could well be.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

The Three Types Of Unsolved Math Problem

:First: Weirdly Abstract
:[Ponytail stands in front of an equation]
:Is the Euler Field Manifold Hypergroup Isomorphic to a Gödel-Klein Meta-Algebreic ε<0 Quasimonoid Conjection under Sondheim Calculus?
:Or is the question ill-formed?
:⬙ℝंℤ/Eℵ₅ The Z is raised and underneath it is a double-ended arrow bent at a right angle. One points toward the R the other toward the Z. The ₅ is double-struck like the ℝ and ℤ

:Second: Weirdly Concrete
:[Cueball stands in front of a grid with 6 columns and 7 rows]
:If I walk randomly on a grid, never visiting any square twice, placing a marble every ''N'' steps, on average how many marbles will be in the longest line after N*K steps?
:Somehow the answer is important in like three unrelated fields.
:[The path starts in the 3rd row and 3rd column, a small circle indicates the start. It takes the path: North, East, North, East (a black dot representing the 1st marble is placed here, so N=4), South, East, South, South (2nd marble), West, South, West, North (3rd marble), West, South, South, South (4th Marble), West, North, West, West (this goes offgrid to the West. There is no visible line or marble outside the grid). The 1st, 3rd, and 4th marbles are colinear and there is a dotted line connecting them. The line's slope is 3.]

:Third: Cursed
:[Megan stands next to a curve]
:What in god's name is going on with this curve?
:Is it even math?
:[The curve starts at the bottom of the screen, rises straight upward, begins to wobble left and right a little. It lists to the left and the left-right motion increases, then decreases. It begins a large counter-clockwise arc, spiraling inwards twice, then ends]

{{comic discussion}}

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2529: Unsolved Math Problems