survival bias skews IQ in certain fields. taken to the extreme, you're essentially saying that the IQ of field's medalists are not skewed.

I misread the point they were trying to make, I took the 5 std to be a sign they were pulling from general population IQ. On second reading it’s clear that is not their intended point.

In any case the resulting intermediate distribution from selection criteria bias would be a Chi distribution (I think - it has been a while.) 5 standard deviations on a normal distribution is 175 IQ or top 1/700K which is insane.

A few additional biases, Physics majors have higher average IQs, and not everyone smart enough to do the math has the desire or the opportunity.

The point I was making is that IQ score has been normalized, when imagining the intermediate distribution of IQ it would make more sense to look at composite probabilities of factors that led to the IQ score and consider the probability that those same factors lead to a sufficient innate ability in math.

Does intermediate distribution here correspond to a Sampling distribution? If so I think you got it right.

Is it? I would indeed hypothesize that within the population of Fields medalists, IQ distribution is roughly normally distributed.

Are you arguing that it is actually skewed towards some cutoff point of "just smart enough to get the medal"?

Let's say every mathematician draws an IQ from the IQ distribution and a luck score from the luck distribution. Then, the highest sum of numbers wins a Fields medal.

That would be distributed according to the distribution of the maximum of N Gaussian-distributed random variables, and according to this[0] stack overflow answer, it's skewed downwards, below its mean. (Its mean, of course, is much higher than the mean IQ+Luck).

[0] https://math.stackexchange.com/questions/2105921/pdf-for-min...

> Let's say every mathematician draws an IQ from the IQ distribution and a luck score from the luck distribution.

That's a huge assumption. I could easily propose a half dozen other models each with a different conclusion. You would need to look at the data.

He just proves there exists models that gives a skewed distribution by providing an example. So having a skewed model is a possibility.

The more selection criteria depends on cut-off (which it is in the university setting), the more likely selection from normal distribution is going to be skewed. Then Fields medalists are selected from long tail of already skewed population, all bets are off.

>IQ has no skew by definition.

There isn't a skew per se but possible inflation that gp intended to account for. See Flynn Effect.