algeom

Academic mathematician here. I’ve been stuck on something for the last 20 years.

Can you explain what you mean when you compare Gmail and Facebook to the moon landing? On its face that comment looks way out of whack to someone who is outside the tech industry.

I bought a 20 year supply of that chalk when the demise of Hagoromo was announced, but it turns out that production of that particular product was turned over to a Korean company. I’m still using my legacy supply, so I can’t comment first-hand on old/new comparisons, but I haven’t heard any complaints.

This is actually not true in pure mathematics. Students usually do not publish with their advisors, there are no labs churning out publications, advisors do not apply their names to all the products of their groups, etc. In fact, the vast majority of math PhDs from almost all institutions end up leaving academia.

The small number of families seems more likely attributable to the small size of the enterprise and the difficulty of the subject matter. It's very hard to have a good idea and equally hard to publish it. I don't know of anyone in pure math who decides about the value of a piece of work based upon pedigree.

Most academics do not get funding or tenure. Most funded academic mathematicians lose funding at some point. The funding rate for NSF grants in mathematics is certainly less than 33%, and one can only submit a standard proposal once per year. The competition is FIERCE. (I've been on panels: it is terrifying to see who doesn't get funded.) Ask any mathematician -- theorem prover or software writer -- about excellent people she knows who have lost their grants. You will instantly get multiple examples.

Mathematicians who write software are no more likely to be "truly making the world better" than those who prove theorems and teach hundreds or thousands of students every year.

I'm not saying anything about Stein here. He's a rare mathematician: strong on theory and practice, a passionate advocate for his causes, and a respected teacher. But there is a danger of missing the real point here -- most good things don't get funded or recognized. This has gone on for centuries. The funding situation now in the US (for both theory and practice) is better than it has been almost everywhere for almost all time.

When you've won a Fields Medal and then made fundamental contributions to an entirely different area of mathematics, you might have earned the right to make such comments on Mumford's thoughts. Until then, at least follow the HN site and comment guidelines!