dxu comments on Innate Mathematical Ability - LessWrong
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Their father, Laszlo Polgar, was himself a fairly strong chess player, and it is well-known that intelligence is heritable. In addition, Judit Polgar at least (I don't know about the others) was a child prodigy, implying that she had a great deal of innate ability. Furthermore, chess requires very good working memory (due to something called the touch-move rule forcing players to calculate variations mentally), and it is theorized that working memory may actually be intelligence, further supporting the "innate ability" hypothesis.