December 06, 2010

Christmas present of the year: mathematics!

Cubic surface with linesI think this is the first novelty gift that is described by a conference paper: The Theory behind TheoryMine. TheoryMine is a company that uses automatic theorem discovery and proof to generate new theorems, which customers can then buy the naming rights for.

This might sound similar to buying naming rights for stars which is a con, since real astronomers explicitly do not use or acknowledge the registries of star-naming companies. However, there is no formal system for naming theorems. There have also been real cases of theorems being sold, including the well-known L'H˘pital's rule which was likely due to Johann Bernoulli. In fact, a lot of named theorems are not due to the person who gave their name to them. Hence it is not that odd that one could buy the right to name a newly computer generated theorem. The real challenge is to get enough people to use it so that the name sticks. Given that the TheoryMine works in the domain of recursive theories generated to be deliberately obscure, this might prove to be hard. I suspect the recipients of a nice theorem ought to prove a few other theorems in the theory, and then write a paper about them. Sounds like a good activity for the after-Christmas holidays.

In related news the bloggosphere is a-twitter with excitement of the discovery how this paper rediscovers the trapezoidal rule of numerical integration, with the author naming it after himself. The paper even has a good amount of citations.

Most commenters have laughed at how Diabetes Care appears to have failed peer review, and how medical people clearly don't know elementary numerical calculus. I'm not entirely convinced: the paper itself is inaccessible (even from my Oxford University account), so we might be reading too much into the abstract. Second, several of the citing papers correctly calls the method the trapezoidal rule and not "Tai's rule", so maybe the paper is not as bad or self-serving as it looks. A lot of ridicule might have been avoided if it had been open publishing.

However, sometimes bringing a method that is well-known in one field into another field has very positive effects. Neural networks benefited greatly in the 1980's by being able to borrow methods from spin glass theory in physics. Physics benefited a lot from group theory once the link between particle symmetries and mathematical symmetries became clear. A friend of mine boasts that he got a paper out of the cross product, which neatly solved a problem in chemistry. So maybe telling diabetes researchers about the trapezoidal rule is worth a well-cited publication.

A final idea: Christmas present of the year: home-made theorems! Sure, you can buy a machine-made theorem. But why not try your hand at proving something nice for your loved one's? A neat geometrical construction for the kids to ponder, some topology for your aunt, some category theory about symmetric relations for your partner...

[Update: I have an extended version of this post here, on Practical Ethics: Is mathematics the Christmas present of the year? ]

Posted by Anders3 at December 6, 2010 02:00 PM
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