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:
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.