### Philosophy of Real Mathematics

#### Posted by Urs Schreiber

While I am struggling to understand elliptic cohomolohy, David Corfield, over on his weblog, has taken a look at the literature from the perspective of a philosopher of *real* mathematics.

“Real” here is meant in the sense of “what active mathematicians are *really* concerned with”, as opposed to an eternal occupation with Russel’s paradox and Gödel’s incompleteness. Have a look at his book for more.

To me, the interesting point to be addressed here is how we actually go about identifying the structures that we feel should be out there. As in: “How should we really think about elliptic cohomology?”, or the outworn but still curiously elusive “What *is* string theory?”. And maybe this one: “Is there a relation between these two questions?”

## Re: Philosophy of Real Mathematics

What would interest me about your questions is not so much their ultimate answers, but what kinds of answer would satisfy you. E.g., would characterising elliptic cohomology in terms of some 2-categorical universal property be the right kind of thing. Similarly, would you be happy with ‘String theory is a 2-functor…’?