I tend to be skeptical of the young cognitive peak hypothesis. Certain abilities peak at 14 while others peak at 65, and no one has managed to come up with a convincing case for knowing when people peak. It seems to be highly individual. Some people peak at 25, and others peak at 60.
What we do know is that some individuals peak early, while others come up late. The average seems to be in the late 30s, but there’s a lot of variance among people. You also have cases where people have multiple peaks, which is probably my profile (severe health issues from 22-27).
In the chess example, I’d guess that a number of people just get bored with the game after decades. It’s not that they become less intelligent at 36, but that their rate of improvement slows to the point where it no longer interests them. They’re still capable of growth, but the rate slows and the personal ceiling becomes more clear and, while it may be higher, it’s not at the absolute top of the field. And so they move on to do other things, and they get rusty. This isn’t hard biological decline; it’s the natural evolution of a person who, driven by a competitive spirit, becomes very good at something, realizes that he isn’t going to become the very best, and moves on to do other things, probably still playing but not as often.
Math does seem to confer an advantage to the young, but on closer inspection, this has more to do with how people allocate their time. 25-year-old mathematicians aren’t afraid to bet a few months on something that other mathematicians will judge to be trivial, pointless, arcane, or otherwise uninteresting. At 50, you’ve got a career to protect. Older mathematicians achieve a lot more than the popular narrative gives them credit for, but they tend to focus on refinements (often, within an existing specialty and on prior work) where the career risk is lower. Why invent a new field, when you can build on prior work and know that the results will be useful?
What does seem to happen is that stand-out precocious people tend to lose their relative prominence. Most people who test at 170 IQ in childhood will be around 145 in adulthood (which is about as high as we can reliably measure). They haven’t gotten dumber, but other people have caught up. Some people struggle with this, especially if high intelligence is a part of their identity.
Of course, there are a lot of cultural issues, and existing attitudes toward age. I also think that the existence of a business subordinate causes subclinical but detectable midlife depression that is mistaken for a hardware problem: a loss of “fluid intelligence” as opposed to a reversible (if chronic) condition that, while less severe than textbook clinical depression, causes a loss of cognitive “edge”. I’d guess that most corporates who peak in their mid-30s have this: the accumulated (and probably reversible, but not without a change of lifestyle and high risk to income) loss of energy, drive, and creativity that comes from long-term subordination, and that it’s severe enough to knock 10-20 points off their IQ, but not so severe that it would register as clinical depression.