The root terms histor and math have similar meanings in their etymological antecedents (to learn, learned, knowledge), though with some initial and ancillarily added differing qualities.
Innate in historíā (Greek and Latin) is that the learning takes place via inquiry and narrative. Hístōr also implies that the polyhistor displays erudition and wisdom. From Proto-Indo-European it shares a root with the word "wit". Inquiry and narrative are specific sets of pedagogical and research heuristics.
Here are two conceivable definitions of polymath. Firstly, the overt 'greatly learned,' which would be inclusive of polyhistor (though not all polymaths would be polyhistors, all polyhistors would be polymaths). Another definition would include the adjunct of science, with the Greek mathēmatikè téchnē implying that the knowledge and learning are specifically about sciences or have been gained through scientific inquiry or, more broadly, are based in mathematical logic. Science is a somewhat different set of specific research heuristics.
The artist as polyhistor; "The intellectual superstructure", in the work of Per Kirkeby.(Brief Article)(Book Review)
Aug 01, 2006; 8779341543 The artist as polyhistor; "The intellectual superstructure", in the work of Per Kirkeby. Morell, Lars. Aarhus...