Did I Just Solve An Unsolved Math Problem?

More detailed information and all the code and research I did for the neighborly polyhedron problem can be found on my GitHub.

Szilassi Polyhedron paper cutout:

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4D Golf OST - Neon Rebel

[Zosso-]

As sure as I am that you’ve been working on this for a good while, I still choose the believe the funnier option that you watched Vsauce’s short last night and obsessively solved the problem and edited this video in less than 24 hours.

[MrAdBounty]

Finding a list of number from a random email chain from 30 years ago that answer exactly a very niche math problem is peak internet

[Fedor-ny]

Hello! Last summer I explored this problem by myself, and (already known) results I got were published in the Crux Mathematicorum. The thing is that 12 faces is not the only possible case, because according to the formula i found, there could be 15, 16, 19, 24, 27.... faces with certain properties.

[crazzykai]

1:37 I seriously thought "why would you put light-blue and blue next to eachother its going to be so difficult to tell them apar- oh-"

[trinityy-]

i would have solved so many unsolved problems if i just lived in a time before all the problems were solved

[addiboi]

Very cool findings, but I would not be so quick to conclude that it is "very unlikely" that there isn't another solution out there. It's not too uncommon for us to make a conclusion about something because of overwhelming empirical evidence, only to later find a counterexample that disproves it. See Skewe's Number for an infamous example: (First counterexample was 10^316)

[happygimp]

You didn't solve a problem, but you made a, probably new, conjecture. If you can prove that conjecture or disprove it, then you solved a mathematical problem.

[_Epidemic_]

Lmao Vsauce just made a short that references this problem

[an_asp]

Seeing you struggle a little with that objective function makes me surprised you never looked into multiobjective optimization. It has a lot of advantages when you're trying to minimize or maximize multiple conflicting values, especially in maintaining diversity across your search landscape.

[goblinry]

Just started watching love the intro, cant wait until the twist where matt turk comes out of retirement and solves the problem right before you do.

[optozorax_en]

Try CMA-ES optimization algorithm, I tested it against differential evolution, nelder-mead, particle swarm, even gradient descend (of my non-differentiable simulation), and it worked better than anything.

Also, your loss is too discrete, it's hard to optimization algorithm to find anything good using it. Try to smoothining it, for example add some distance between something, that when minimized to zero, this removes one point from your discrete loss.

If you implement this smoothing, you should just add to your current loss, that is, when you find 1 less intersection, your loss gets -1. I found that to be most effective for 0-th order optimization methods. Because when you have such discrete steps after finding it, algorithm will not forget it and will not trade this for some minor improvements in another place. I found this perform dramatically well in my experiments too.

[veggiet]

Instead of the "pointy headed duck" you should call it the "gerrymander" 😂

[cipherjoe]

Love the Summoning Salt-inspired intro

[EDoyl]

Without a proof this is not at all solved, but you discovered a cool shape which is imo cooler than solving a little-known problem. Like you can show that 3D printed razorcross to people like this is the shape I discovered

[itisALWAYSR.A.]

Omg i got a handful of 3D-printed Szilassi polyhedra a few years ago at an event... and when I got home I forgot what they were for so i just had a bunch of mutated caltrops in my living room and i had no memory of their feature.

Thank you for allowing me to successfully pin it down without using a search engine - the universe provides!

[firefly]

Here's an idea: have you tried turning the problem into a differentiable one? Instead of assigning a value of 1 or 0 to each crossing or intersection, you could compute an "amount of intersection" where each pair of faces contributes a value of 0 if they are not intersecting; > 0 if they are, with an amount that tells how much they are intersecting, such as the length of the intersection segment. Something similar might be done with crossings. This way you could use automatic differentiation to compute the gradients of the entire construction, and then use one of the gradient-based optimization algorithms.

[Kknewkles]

"You friendly neighbour polyhedra, Szilassi"

[Bolpat]

14:50 Without a formal proof, it's not hard to say. Without a formal proof, the answer is: Absolutely not.

[MrCheeze]

Well, I'm definitely calling the theory that this shape is optimal "CodeParade's Conjecture".

[DrTrefor]

This was such a great video, had the feel of a @StuffMadeHere video but entirely for a math problem. Seeing first hand all the attempts and tweaks on it is cool and I wish we got to see more of the process behind coming up with ideas, so often in math we get the final polished paper and voila there it all is but not the process