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Comment by yakubin | Hacker News Reader

Nit: if it were top mathematicians of their age, then there wouldn’t be any ages without first-rate mathematicians, which is obviously wrong.

That said, the “of all time” version also doesn’t sound right.

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"First rank" is the phrase from OP's link, not "first-rate", but in both cases it is not obvious to me that it is wrong for there to be mathematicians with that descriptor in every age. They sound like relative adjectives; "first rank" undoubtedly so, "first-rate" to a lesser extent.

"Who are the first-rate/first rank musicians of $YEAR" does not seem to me like it could be answered with "there were none in that year".

I don’t know about “first-rank”. To me it sounds like an RPG term (“first-rank mage”). But in the case of “first-rate” I see nothing weird about the answer “there were none this year”. When quality is lower, that’s what I’d expect, since I think about this term a bit like the A1, A2, B1, B2, C1, C2 etc language proficiency certificates. They’re not assigned based on quantiles in current population, but based on a set of requirements applied to skill in absolute terms, not relative to skills of other people.

I think you'll find that if you set an absolute bar on most skills you'll end up with zero people above the bar in the past and a growing percentage of people above it in the future. The first person to run a four-minute mile was Roger Bannister in 1954. Now, that achievement is basically table stakes for college-level competitors. Similar effects can be observed in chess, piano performance, and just about any other activity you can measure. Making "first-rate" an absolute bar results in all sorts of crazy answers to the questions "who is first-rate now" and "who was first-rate 70 years ago". If you set the bar such that only the top 10 players of this year cut it, neither Bobby Fischer nor Michael Jordan would be first-rate.

In maths though there was some fluctuation. Mathematics in Roman times saw a decline, and in medieval times a complete breakdown (at least in Europe). If we take Euclid to be the bar for a first-rate mathematician, then there were none in medieval times, but later there appeared Gauss, Newton, Leibniz, Euler, Galois etc. I’m also not sure if today anyone clears the bar for Hilbert-level genius. So I don’t think the bar for “top 10 today” keeps going up. From time to time it goes down.

I don't think the fact that our 90th percentile capabilities have been known to decrease at times in history refutes the idea that the broader trend is dramatically upward, in such a way that any absolute measure of skill is very likely to give you ridiculous results if you pick it based on the standards of year X and then try to use it in year X + 1000 or X - 1000. Was Pythagoras a first-rate mathematician? By what measure that wouldn't also capture millions of people--most of them not even self-described mathematicians--alive today?

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