The famed chessmaster Emanuel Lasker writes:
A table of simplest values in chess–that of the men themselves–was devised long ago. Leonard Euler, the mathematician, showed the way to calculate these values mathematically by the principle that the average utility of a man is proportionate to its average mobility. This assumption is correct, because accordingto the rules of chess the effect of a man on a point is 0 when the man cannot move to the point, and is 1 for any man who can move to the point. This reasoning does not apply to the promotion of a Pawn. The Pawn therefore gains in value at the End Game stage. Apart from this factor, Leonard Euler’s method is sound, and the values he thus found agreed with those based on experience…
From Lasker’s “How to Play Chess”.
That’s the Euler, of course. The Leonard Euler who is responsible for so much of mathematics, including the prime number theorem. I had no clue that he also developed the simple valuation system for chess as well.