The "fundamental theorem of symmetric polynomials" states that any symmetric polynomial can be expressed as a polynomial in the elementary symmetric polynomials. This, or at least variants on it or corollaries of it, was definitely known to Lagrange in the 18th century (probably many others) and possibly even to Newton.

I don't see anything "elementary" about the elementary symmetric polynomials - in the sense that I don't see anything about them that immedaitely suggests that all symmetric polynomials should be expressible by them. What do we know about how and when such an obscure yet powerful fact was discovered?


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