
Mathematical software wish list - cosenal
http://mathoverflow.net/q/213266/7580
======
jacobolus
The coolest piece of mathematical software I’ve come across in the last few
years is Chebfun, [http://www.chebfun.org](http://www.chebfun.org)

Basic idea is to represent functions by high-degree polynomials which
approximate them to near machine precision. After each operation, any terms
which contribute at less than about 10^-15 are dropped, in the same way as
bits get dropped after a standard floating point operation. This keeps the
degree of the polynomial from growing exponentially.

The Chebfun team has found or invented a number of efficient algorithms for
interacting with such polynomials, which make it practical to find roots, take
integrals and derivatives, solve differential equations, combine multiple
functions in various ways, and so on.

I think it must be the largest Matlab library anyone has yet built, and while
I’m not the biggest fan of Matlab, they’ve done a great job integrating with
the environment. Turns out Matlab has a bunch of object oriented features with
operator and function overloading, so Chebfun can adopt most of the operators
and functions for operating on regular Matlab arrays and overload them to work
on their continuous function approximations. This makes for very clean and
readable code for their users, though the internals get pretty complex.

Also recommended is Trefethen’s book Approximation Theory and Approximation
Practice, which explains the mathematical ideas underlying the library. First
6 chapters are freely available online:
[http://www.chebfun.org/ATAP/](http://www.chebfun.org/ATAP/)

~~~
thisrod
I greatly admire Trefethen's writing. I worry that there must be some really
important aspects of numerical analysis that I ignore, simply because he
hasn't written about them and so I understand them less well.

~~~
jacobolus
+++

The clear exposition seems to have rubbed off on his whole Chebfun team at
Oxford; all their papers are very readable.
[http://www.chebfun.org/publications/](http://www.chebfun.org/publications/)

I’ve also been reading lots of other papers in the field recently, and there’s
at least a 2–3x slowdown and lots of extra mental effort when I try to read
some other papers (though to be fair many other researchers are not native
English speakers).

------
Jun8
This question and answers are gold! The answer with LaTex
([http://mathoverflow.net/a/213268/42557](http://mathoverflow.net/a/213268/42557))
and the diametrically opposed comments to it illustrate problems with Tex.

One thing I didn't see mentioned is better collaborative tools (true for any
research but doubly true here due to difficulties with notation, etc.). Note
the quick progression of results triggered by Tao's polymath blog
([http://polymathprojects.org/](http://polymathprojects.org/)) but I find the
current Wordpress format not very suitable for search and browsing.

~~~
williamstein
(I'm the founder of SageMath.) SageMathCloud
([https://cloud.sagemath.com](https://cloud.sagemath.com)) is a highly
collaborative online web application for working with Sage, R, Python,
IPython, LaTeX, etc that I've been working extremely hard on this for almost 3
years. We'll have a major new release this week with much new polish and
functionality (the testing server is at
[https://web0.sagemath.com](https://web0.sagemath.com)). Everything is 100%
open source.
[https://github.com/sagemathinc/smc](https://github.com/sagemathinc/smc)

~~~
iheartmemcache
Jim Simons, after retiring from Renaissance Technologies with a cool 15
billion, has spent the last 10 years giving grants to people in the pure
sciences. He's a true academic at heart -- a BS from MIT in Math, PhD from
Berkeley which yielded a whole new field (heh) of something to do with
Riemannian manifolds that's way beyond my ability to grok but apparently it's
on par with "oh yeah I invented abstract algebra (a la Emmy Noether)", worked
at Princeton for the NSA cracking Cold War codes during Vietnam but got fired
because he wanted to do his own recreational mathematics instead. Anyways,
he's very fond of academics and gives MacArthur-esque grants, especially to
people who want to change the way mathematics is taught. Approach his fund.
I'm 100% sure he'll give you a grant on the spot.

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noobie
I was surprised there weren't any "ambitious" wishes. Most, if not all, of the
answers seem in response to practicality issues. Nothing along the terms of ML
for math theorems or an accessible proof library for computers.

~~~
GFK_of_xmaspast
Scroll down: "I'd like to have on a usb key a user friendly software that
could parse a math article to check the proofs in it without having to learn
how to use stuff like Coq and highlight the possible gaps. But this may sound
unrealistic, at least for now."

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bitshiffed
This is great. I would love to see these kinds of discussions across different
communities/lines-of-work! I had hoped shouldexist, and similar attempts to
collect this kind of information, would get there; but none seem to survive.

------
hbt
Is there a similar thread for software development?

I'm not sure what keywords to google. Reply with links if you got any.

Thanks

