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WoahNoun

For those interested in reproducible research, the authors have made their Sage notebooks available.

Arxiv link to the paper: https://arxiv.org/abs/1811.04131

Sage notebooks: http://userhome.brooklyn.cuny.edu/aulicino/dodecahedron/

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> reproducible research

This has not been a concern in mathematics up to relatively recently, mostly because computers were generally too puny to be of much use. By "recently," I mean from the birth of the computer up through probably 15-20 years ago. Since then, there's been a real convergence of tools and computing power that's going to send mathematics in new and interesting directions over the next decades.

Unfortunately, the mathematics curriculum doesn't seem to have caught up. (Please correct me if I'm wrong here -- and I'd be happy to be wrong.) If you wanted to learn these skills as a grad student even 10 years ago, you would have to go to the CS department, most likely, unless you were at one of the handful of departments doing formalized mathematics. I believe that's still the case.

When I got my undergrad about a decade ago, one of the core freshman classes was a lab course on Mathematica. Not CS style programming, but it was immensely helpful in the rest of my classes for tedious calculations, eg calculating a Groebner basis or Taylor expansions of a Lie group.

Unfortunately, the mathematics curriculum doesn't seem to have caught up. (Please correct me if I'm wrong here -- and I'd be happy to be wrong.) If you wanted to learn these skills as a grad student even 10 years ago, you would have to go to the CS department, most likely, unless you were at one of the handful of departments doing formalized mathematics. I believe that's still the case.

I would guess that by "these skills" you mean something beyond just programming in the general sense, or even numerical computation, as there shouldn't be any harm in leaning on the C.S department for that. No?

Are you instead proposing that a new course be added to the mathematics curriculum, that might be titled something like "Computational Mathematics" or "Experimental Mathematics" or something along those lines? If so, what kinds of things would go in such a class in your eyes?

Since then, there's been a real convergence of tools and computing power that's going to send mathematics in new and interesting directions over the next decades.

Indeed. One of the things I'm interested in is learning more about Interactive Theorem Provers. I just bought a book on Coq and intend to start diving down that rabbit-hole. Interestingly, I'm only just now starting to learn to do proofs based math at all, so I'm especially (but not exclusively) curious about whether or not there's an pedagogical value in starting to learn to use these proof assistant type tools right alongside learning to do proofs. It may well turn out that the answer is "no", but it should be fun to explore all of this in either case.

There could be more courses that teach the necessary programming techniques but also case studies of problems that have been solved this way. For example, the course "Experimental Mathematics" given by Doron Zeilberger.

For example, the course "Experimental Mathematics" given by Doron Zeilberger.

Interesting stuff.

Link, for anybody else who's curious:

https://sites.math.rutgers.edu/~zeilberg/teaching.html

I love his blogging and writing even if I don’t agree with most of his opinions.

This is more or less what I was thinking of: "these skills," as in "these skills, which are necessary to construct a proof like this."

Counterexample here, I started working with William Stein in 2006, contributing to Sage Math. As a math student, I actually learned these skills (including source control, unit testing, peer review, etc in addition to high-performance algorithms) as an undergrad and continued to sharpen them through my grad career. True, I was seen as an oddity, but my skills were valued by colleagues and I took every opportunity I could to teach in computational summer programs.

You raise an important point. These skills are very important, but they are barely raised when we teach scientists how to copy and paste python snippets. In a British university it's even harder to acquire these skills because the course is often set in stone (e.g. I wrote my first - not very good! - compiler several years ago now but I still have to take Introduction to Python in effect twice)

When I was 15/16, I was very lucky to have a computing teacher who - although he didn't teach us much actual programming - absolutely drilled into us the importance of a program's quality and aims. The absolute basics go a very long way: Should this function be smaller, is this logic simple etc.

Is Fortran still a thing these days in a mathematics curriculum?

More or less no, in my experience, unless you're specializing in such a way that it would be useful. And, in that case, you're probably better off doing your degree in a CS department, anyway.

yes, it is, in Physics, astronomy, chemistry, petroleum, climate and space sciences and the engineering fields.

Alternate link to paper: http://userhome.brooklyn.cuny.edu/aulicino/dodecahedron/join...

Will this be archived the same way the paper is archived? Or will it be lost in 200 years like Fermat's proof of his last theorem?

Well, Github archived it's 2020 snapshot in Svalbard. This probably won't be a one off thing, so if you're concerned; upload it to a github repo and they'll probably do it again.

https://archiveprogram.github.com/

There's no evidence Fermat had anything close to a proof.

We have the word of a world known mathematician (Fermat). But yeah if he had written down the proof somewhere that he had in mind, maybe it would have turned out to have had mistakes in it, and it wouldn't have ever become such a large story/theme that it is now.

Anyways, it's important to archive the knowledge in a way that it can be understood by future humans as well. Some random website under an .edu can disappear at any moment.

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