The AAA algorithm computes rational approximations with amazing speed and reliability. Things are now easy that would have required major effort before, and in practice were not done at all.

We have no proof that the method works. So it is perhaps not surprising that rather often, mathematicians attending my talks express incredulity that I spend my time working on a method that has no theorem to justify it.

The incredulity sounds reasonable enough until you dig deeper. Suppose those people had the theorem they say is so important. Reassured, would they then use AAA to compute rational approximations? I think not. Their talks (which are awfully unlike mine) reveal an implicit view that the purpose of mathematics is not (A) to do things, but (B) to prove one could do things in principle. (A) may be important, but it is not mathematics. More like engineering.

I yearn for a world where mathematicians recognize both (A) and (B) as their business.

[21 May 2025]

When I’m trying to recall a name, sometimes I take notes of my guesses along the way so I can enjoy following the trail again once I’ve reached the destination. This morning my guesses were Baratchart, D’Alembert, Constable and Dalrymple on the way to Perlmutter. The other day it was Studebaker on the way to Spiegelhalter.

[22 May 2025]