A couple of months ago,

**fimmtiu** and I were talking about mathematicians. Why was it, we speculated, that so many mathematicians are (or are perceived to be) over the hill by age 30?

And suddenly the answer -- or at least

*an* answer -- occurred to me. "You know, that's always bugged me," I said, which was a stark lie, because I'd never thought of it until an instant beforehand, but which was also quite true, because what

*has* always bugged me is when people make up additional causes for something that's already perfectly naturally explained by sheer statistics.

**( For example, evolution vs. intelligent design. )****( For another example: bisexuality. )**So to return to mathematicians: Let P

_{m}% be the chance of experiencing some genuine mathematical insight, of a level of brilliance that even some mathematicians will never achieve, in any given year that you're practising mathematics. Of necessity this will be quite low. Now let P

_{0}% be the chance of experiencing the same insight in a year that you

*don't* practise mathematics. I believe it's safe to assume that P

_{0} is significantly less than P

_{m}.

Now let Q

_{0}% be the chance that any given mathematician will quit practising mathematics in any given year, if she

*has never* experienced such an insight -- and let Q

_{m}% be the equivalent chance for a mathematician who has experienced at least one. This time, I believe it's safe to assume that Q

_{0} is rather greater than Q

_{m}. (For simplicity, I'm going to assume that the odds of returning to mathematics is uniformly 0% among people who experience no insight that year, and 100% among people who do, but again the important part is only that the latter probability exceeds the former.)

So take an initial population of 20-year-old mathematicians. In year one, Q

_{0} of them will quit, and P

_{m} of them will experience an insight. In year two, Q

_{0}(1-Q

_{0}-P

_{m})+Q

_{m}P

_{m} of them will quit; P

_{m}(1-Q

_{0}) will experience an insight; and Q

_{0}P

_{0} former mathematicians will return to the fold. The formulae get more complex as you iterate, but the upshot is that if all mathematicians stayed mathematicians for life, then flashes of insight would still occur just once in a lifetime, but when viewed over the entire population of mathematicians, they'd be evenly distributed throughout that lifetime. However, mathematicians who reach the age of 25 without an insight are much more likely to quit mathematics (and lose their chance to experience an insight at age 50) than those who've already had one. Over enough iterations, the average age of each insight will tend to skew quite low.

Once again, there's no need to invent bizarre explanations about loss of mathematical creativity when raw statistics already predict the same outcome.

I'm honestly surprised that more mathematicians haven't figured this out.

^{1}Yes, I know there are people who would really prefer to pretend that sexual reproduction doesn't exist either, but I believe that deep in their hearts they know it's real.^{2}One word: broccoli.