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 m

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-minimum-and-maximum-of-n-independent-gaussian-random-variables https://math.stackexchange.com/questions/2105921/pdf-for-min...