Amateur Mathematician Finds Smallest Universal Cover | Hacker News Reader

Amateur Mathematician Finds Smallest Universal Cover

quantamagazine.org

166 pointsPharmakon22 comments

Note: Smallest known universal cover. It isn't proved optimal (and probably isn't).

Also, the title here is a little confusing as this has nothing to do with universal covers in the usual (topological) sense; this is about Lebesgue's universal covering problem[0], a problem in plane geometry.

[0]https://en.wikipedia.org/wiki/Lebesgue%27s_universal_coverin...

Amateur Mathematician. Who has a degree in maths from Cambridge.

This shouldn't be surprising. You pretty much need formal training in mathematics of some sort to be able aspire to even be an amateur mathematician. There are many people with math degrees out there, it's just that most didn't pursue careers in mathematics.

Most people who get maths degrees from Oxbridge don't go on to be professional mathematics though. Out of the 7 I know only one did. The others basically don't do complex maths anymore.

In the sense that this person does not do maths as their full time job. Most folks writing papers and finding new proofs, etc, do.

An amateur is not a person that has no knowledge.

An amateur is a person who pursues an activity independently of their source of income.

It's kind of amusing that general understanding of the term has flipped in this way - basically it implies that if you're not doing something under a capitalistic structure, you're probably doing something wrong.

A bunch of software that you use on your computer on an everyday basis was produced by amateurs.

Hobbyist might be a better term.

I have a degree in Physics. I'm not even an amateur physicist - I don't really do anything in the field at all, my time is spent moving pixels about on screens. :P

Indeed, amateur means "lover".

An undergrad degree; his PhD was in a different field. So yes I'd call that "amateur".

Saying that Theoretical Physics isn't math is a little disingenuous don't you think?

This is nothing extraordinary, there are many people having a math Bachelor or Master. Also a famous university name on your BA/MA tells nothing about your level. University get their ranking through research publications not through undergrad math test . So what really matters is whereas you choose to dedicate (a part of) your life to Math or not, there is no secret magical course at Cambridge that will enlight you, courses are pretty much the same in all big universities

Fascinating that the methodology used to generate these covers is local optimisation. The shape is still fundamentally the one suggested 100 years ago, with "bits lopped off".

Which immediately suggests the possibility that they are iterating towards a local minimum. Is the space of solutions smooth enough to have any confidence that there aren't better places to start?

This form of problem reminds me a little of the Sofa Problem (although there you are maximising rather than minimising).

Yes, and it has the same kind of "decades of slow incremental improvements by shaving corners off" kind of vibe.

https://en.m.wikipedia.org/wiki/Moving_sofa_problem

If you check the wikipedia page, it seems that Philib Gibbs has contributed to this problem as well:

'''A computation by Philip Gibbs produced a shape indistinguishable from that of Gerver's sofa giving a value for the area equal to eight significant figures.[6] This is evidence that Gerver's sofa is indeed the best possible but it remains unproven. '''

I wonder if anyone sells an actual (Conjectured) Optimal Sofa.

I find it interesting that this problem has no real application and the resulting cover seems pretty ugly given how basic and fundamental the question seems.

> no real application

Yes, welcome to math.

Math has lots of applications. Computer science is basically just applied discrete maths.

It's interesting that the area he removed was asymmetric; my intuition would be that the optimal solution would be symmetric.

His methodology was to generate random shapes, fit them into the existing best known cover, and then shift them toward one of the corners; once you know that, it's unsurprising that he only removed area from the opposite corner.

I think the lack of left-right symmetry was the surprising bit.

It’s not as surprising when you realize that the problem allows reflections of the shape, removing the need for a symmetrical cover. There are lots of lopsided shapes that will barely fit on one side but leave room on the other. With an asymmetrical cover you can handle different classes of shapes with each side, while a symmetrical cover ends up overcompensating and being too “one size fits all.”

Reply on news.ycombinator.com