While I agree with the author broadly, he is definitely overselling his thesis. Going from 'fewer grad students now care about problems in Journal of Algebra' to 'Math is running out of problems' is quite a stretch.
Take any period of time - some subfields will run hot & others will be fallow. Doesn't mean we have run out of problems.Trace formula for theta groups will appeal to only fifteen people - ok so what's the issue ? Math isn't some popularity contest. We have a ballroom at the university which is reserved for talks from visiting professors. When we have an economics lecture, usually it is jampacked. All 100 seats are taken, not even standing room. Then the next talk is by some topologist. The room practically empties out in real time. If you watched it live, you would be shocked at how fast people are rushing out of the room - you would think some stinkbomb was thrown. Finally, nobody is left other than the topologist himself & 5 grad students, 4 of whom look like they literally jumped out of bed & grabbed a coffee mug on the way. That's math for you. That's how its always been.
Take any period of time - some subfields will run hot & others will be fallow. Doesn't mean we have run out of problems.Trace formula for theta groups will appeal to only fifteen people - ok so what's the issue ? Math isn't some popularity contest. We have a ballroom at the university which is reserved for talks from visiting professors. When we have an economics lecture, usually it is jampacked. All 100 seats are taken, not even standing room. Then the next talk is by some topologist. The room practically empties out in real time. If you watched it live, you would be shocked at how fast people are rushing out of the room - you would think some stinkbomb was thrown. Finally, nobody is left other than the topologist himself & 5 grad students, 4 of whom look like they literally jumped out of bed & grabbed a coffee mug on the way. That's math for you. That's how its always been.