> 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.
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...