3

Several days ago, I found the following quote by Emmy Noether:

If one proves the equality of two numbers $a$ and $b$ by showing first that $a \leqq b$ and then that $a \geqq b$, it is unfair; one should instead show that they are really equal by disclosing the inner ground for their equality.

It seems this comes from Weyl's Levels of Infinity. I own a copy of the book and puzzled by the meaning of the quote, I tried to read trying to obtain more context:

enter image description here

enter image description here

But I'm still puzzled by what it may mean, I must also admit I know a very limited amount of algebra (supposing such is needed). I know what are groups, fields, rings, isomorphisms, automorphisms. But I can't give meaning to the quote only with that. I am also assuming that the content of the quote is not too vague to be interpreted.

Community
  • 1
Red Banana
  • 23,956
  • 20
  • 91
  • 192
  • 5
    Sounds to me as if she was saying that to show $a\le b$ and $b\le a$ is a purely "technical" [my word not hers] proof which establishes the result without giving any deep insight into why $a=b$. – David Feb 15 '18 at 23:18
  • The words read like a poor translation: "unfair" and "ground" don't work properly in this context in English. – Rob Arthan Feb 16 '18 at 00:06
  • I think you should re-ask this question at the english language stackexchange (and delete it here.) It looks like "the inner ground" is just an out-of-use expression in English, more commonly used in Noether's lifetime, with no mathematical significance. Or maybe the real significance is epistemological, in which case it might survive here or maybe in a philosophy stackexchange. – rschwieb Feb 16 '18 at 14:34

0 Answers0