Like many other mathematicians I use mathematical software like SAGE, GAP, Polymake, and of course $\LaTeX$ extensively. When I chat with colleagues about such software tools, very often someone has an idea of how to extend an existing tool, what (non-existent) tool would be useful, or which piece of documentation should be (re)written. Due to lack of time & energy and often also programming expertise, these ideas rarely materialize.
On the other hand, every now and then I meet programmers with a strong interest in mathematics (who are often actually trained mathematicians), and who are looking for a software project to work on. However, normally they don't really know what's needed and end up doing a non-mathematical project.
This gave me the idea to ask the mathematical community to compile a wish list for mathematical software. Wishes can be very small or or something bigger. Just try to make sure that it's realistic and maybe also give an explanation why you consider your project as interesting.
And if you happen to be a programmer fulfilling one of the wishes, please leave a comment.
It would be great if you could also include an estimate on how complex your project and what the math/coding ratio is — but this is optional.
tl;dr
- What software tool would you like to see created?
- What existent software tool would you like to see extended by what feature?
- What piece of documentation is missing or should be updated/extended?
One suggestion per answer, please.
Best Answer
I think some aspects of math would be revolutionized by having a good math search engine. Recently, a question was asked on Meta.MathStackExchange about what they perceived as the greatest problems facing the site. The biggest response was that there was no search engine that indexed mathematics.
This is partly reasonable, since math is stored and documented in $\TeX$ and this can be taken as a standard. But this is also problematic, as there are multiple noncanonical ways to do things in $\TeX$. I would be remiss if I didn't say there are very many other challenging aspects of this.
As an example use case, I often have to look things up in the Gradshteyn and Ryzhik Table of Integrals and Series. It would be remarkable if there were a reasonable way to search for my expressions within the book. Even if I had to attempt multiple searches, it would almost certainly be faster. Taking it up a step, it would be great to search through TeX on the arXiv for certain expressions as well.
I think that even a relatively mediocre math search engine would be a handy start.⠀⠀⠀⠀⠀