[suyash]

The articles mentions a criteria that to be a PolyMath one has to make to make at least a major contribution in three different fields. For someone to make a major contribution, by definition they are an expert in that field, therefore there are a fewer people number of Polymaths vs those who are considered as "Jack of all trades".

[ackbar03]

I don't think even Einstein fits by that definition. An instrument as a hobby hardly is a contribution. Da Vinci is probably one of the closest I can think of by that definition and even he said something like "tell me if anything ever was done" since he felt like he never managed to finish anything properly

[morelisp]

There are plenty of uncontroversial polymaths in the 20th century alone - von Neumann (hopefully no need to list here), Chomsky (political science, linguistics, computer science), and Nabokov (literature, chess, entomology) come to mind quickly.

In retrospect, many polymaths look like an expert in only one field because they more or less invented it. (Chomsky synthesized computation and lingustics into computational linguistics; Helmhotz synthesized physics, medicine, psychology, and philosophy to help found modern psychophysics; Frege, Russell, and Whitehead synthesized logic and mathematics into, uh, mathematics.)

Another issue seems to be assuming that all or at least one of the fields is a science (or even a hard science), but this isn't the case. Paul Robeson has been cited as a polymath due to his contribution across several dramatic arts, law degree, his political activism, and football career.

[tux1968]

I like the one Bill Burr made a point of highlighting: Arnold Schwarzenegger. Body building champion, movie star, and governor of California.

[copperx]

The definition also fits Von Neumann perfectly.

[yabadabadoes]

The question is really how common each base group is and then how many single field experts each accounts for..

I.e. on one extreme every Expert is a jack of all trades that hasn't reached acknowledgement in more fields. A little absurd, but not as absurd as the other extreme: that all jack of all trades that reach expertise in a field simultaneously get acknowledgement in enough fields to be a Polymath.

The only evidence I see in the article towards that question is the analysis of arts hobbies in Nobel prize winners vs average scientists.