@chzbrgr " A problem with doing a PhD after working for a few years is that in pure math at least, people’s ability to make serious new contributions to the field seems to decline rapidly with age. Even 25 is getting on a little, and by 35 pure mathematicians are over the hill. "
I have no idea where people get this foolishness. Literally nobody in my field did their best work before age 30, and the vast majority have done their best work after age 40. That includes two Fields medalists.
For every Terry Tao (who, incidentally, is as brilliant as ever and will surely continue to do outstanding work in his 60s), there are dozens of working mathematicians making “serious new contributions” and doing their best work well into their 40s and 50s.
Even if this were not the case, I find it irresponsible to give advice based on the few incredibly anomalous mathematicians you know anything about because they were famous enough to show up in the newspaper.
The idea that one’s “creativity” mysteriously disappears in one’s late 20’s, so that one can’t do research in pure math any longer is an inane hollywood fantasy. I have no idea why it continues to be perpetuated, but I suppose comfortable untruths die hard.
I feel no need to hunt for data on this but the explanations @QuantMech gives for this phenomenon, such as it is, seem far more plausible than the glamorous one.