RE: https://mathstodon.xyz/@zbMATH/116160822401206741
Grete Hermann also proved a doubly exponential degree bound on the coefficient polynomials when writing a polynomial as member of an ideal. People in the 1920s thought of this to be a 'first bound' that is far from the truth.
Only in the 1980s it was understood that the bound is sharp, via the Mayr-Meyer construction from computer science:
https://zbmath.org/0506.03007
