  We study empirically how the fame of WWI fighter-pilot aces, measured in
numbers of web pages mentioning them, is related to their achievement, measured
in numbers of opponent aircraft destroyed. We find that on the average fame
grows exponentially with achievement; the correlation coefficient between
achievement and the logarithm of fame is 0.72. The number of people with a
particular level of achievement decreases exponentially with the level, leading
to a power-law distribution of fame. We propose a stochastic model that can
explain the exponential growth of fame with achievement. Next, we hypothesize
that the same functional relation between achievement and fame that we found
for the aces holds for other professions. This allows us to estimate
achievement for professions where an unquestionable and universally accepted
measure of achievement does not exist. We apply the method to Nobel Prize
winners in Physics. For example, we obtain that Paul Dirac, who is a hundred
times less famous than Einstein contributed to physics only two times less. We
compare our results with Landau's ranking.
