**Help: examples of computer assisted mathematics needed.**

I'm in the middle of preparing a new course on computing/coding for mathematicians. I'm hoping to include a bunch of examples of computer assisted

*mathematics*.

I use the term mathematics in a loose sense to include 'things' that are not necessarily proofs:

- identifying conjectures;

- visualisations;

- etc

As such I'd love to hear any examples anyone might have and/or be able to point me towards.

I'm familiar with the

**'well known'**results that can be found on this +Wikipedia page: http://goo.gl/EjyKel

I can also recommend the book 'A=B' by Petkovsek, Wilf and Zeilberger which you can download here: http://www.math.upenn.edu/~wilf/AeqB.

#crowdsourcing

(if anyone is kind enough to share this and gets some good suggestions on their comments: please do ping me :))

Here's a link to an equivalent blog post I've just written in the hope of maximum exposure: http://goo.gl/w4Cviq

View 12 previous comments

- This crowd here does computer checked proofs in homotopy theory http://ncatlab.org/nlab/show/Homotopy+Type+Theory+--+Univalent+Foundations+of+MathematicsSep 9, 2013
- Chess endgame tablebases: http://en.wikipedia.org/wiki/Endgame_tablebaseSep 9, 2013
- Providing rigorous bounds for parameters occuring in some nonlinear system is often done by global optimisation methods. There are tons of papers on that out there: http://scholar.google.co.uk/scholar?q=global+optimization+parameter+estimation&btnG=&hl=en&as_sdt=0%2C5&as_vis=1

(And of course non-rigorous bounds can be obtained much quicker with local optimisation methods.)Sep 9, 2013 - This might be worth a listen although from memory +Marcus du Sautoy hardly got a word in edgeways. It is debate about discovering patterns in big data and making important decisions based on the findings without first having a mathematical model which might explain them or warn of the limitations.

https://plus.google.com/u/0/104765717987042844598/posts/eR6WirK3rcsSep 9, 2013 - Thanks so much for all your suggestions (I'll be looking through each and everyone in detail). Please keep them coming!Sep 9, 2013
- In this recent paper, we used hundreds of pages of Mathematica calculations (especially the "reduce" function) to prove things about absolutely monotonic rational functions:

http://arxiv.org/abs/1303.6651

Most of the heavy lifting was done by my Mathematica-whiz co-author, Lajos Loczi. He prefers to have human-readable proofs wherever possible, so he does the following:

1. Try to simplify the intermediate steps of the proof until each can be performed by Mathematica in a fraction of a second.

2. Look for a human-readable proof of each step.

The idea is that if it take Mathematica several seconds (or longer) to find a proof, then finding a human-readable version is unlikely. But if a step is nearly trivial for Mathematica, a persistent human can usually prove it too.

I should add that the conjectures (in Section 1) that motivated that work were all found through computation as well.Sep 10, 2013