> Or take a look at any undergraduate text in mathematics. How many of them will mention recent research in mathematics from the last couple decades? I’ve never seen it. Now take an undergraduate text in biology and you’ll still find quite a few citations to modern research.

That’s because, in the natural sciences, a lot of what was considered knowledge long ago has been found out to be incorrect.

If you study Galen (https://en.wikipedia.org/wiki/Galen) or Hippocrates (https://en.wikipedia.org/wiki/Hippocrates), or Newton’s works on alchemy, you aren’t studying medicine or chemistry, but the history thereof.

On the other hand, look at the Pythagorean theorem. There has been a bit of chipping at its corners when non-Euclidean geometry was discovered/invented, but it remains true in large branches of mathematics.

And this isn’t a matter of centuries. A lot of genetics work that predates the discovery of the structure of DNA isn’t worth studying anymore.

> At what point can we still say with a straight face that it makes sense to pour millions of dollars into mathematics research when its only objective seems reaching the next highest peak of hyper-specialization?

Luckily, lots of mathematics research is fairly cheap. As Alfréd Rényi said (https://en.wikipedia.org/wiki/Alfréd_Rényi#Quotations) it runs on coffee.