Simplicity via complexity via simplicity? Sandboxes for simplicity
Andrés Villaveces, National University of Colombia, Bogotá
11:00-11:30 Thursday April 4
The one-way direction going from complicated proofs to their simplifications has been advocated by many [Rota, etc.], and seems to be addressed with some success in branches of mathematical logic. However, there is an interesting back-and-forth movement between the simple and the complex (and back to the simple) when one considers the question not just from the perspective of proofs but from the perspective of questions and proofs generating more questions and more proofs.
Some disciplines have generated what could be called "simplicity sandboxes": special conditions under which a simpler "answer" may be tested (in the absence of a proof) and then transferred (with luck) to situations without the special conditions. In this case, the first "proof" may seem much simpler than later proofs (apparently reversing the one-way direction), but is also only a proof under "rarefied" conditions.
I will present a couple of examples of the back-and-forth movement from simple to complex to simple and of the "simplicity sandboxes".