Cantor's Conviction

You are a mathematician in the late 19th century and you receive a mysterious letter from your colleague Georg Cantor.

S   G   A S C O Q X
E G H D R H G D H L
D M   D K D R Z
H H   E Z D H   S
N R M E H B H S O
Q S E   E D M S M X
N N G   Z H Z H T F
R X Z L   M Q S Z
N R R S X E H   D
K S E H     N N S N

G. Cantor


What could he possibly be trying to tell you?

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I think the answer is:

because

If you shift every letter forward one place in the alphabet, the words appear diagonally from top left to bottom right:

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Well done! The cipher was supposed to be a sort of extension of Cantor's diagonal argument, using all the diagonals rather than only one. – Volatility Jan 14 at 21:55

Too long for a comment, so here goes what came to my mind.

A first (bad) try:

That's a 10x10 matrix of letters and spaces. Cantor is famous (among other things) for his diagonal argument for the existence of uncountable sets. In his proof he constructs a sequence of elements from an (infinitely large) "square" which feels like the same thing we are supposed to do here. The way he does it is he takes the diagonal and (in the case of 1s and 0s) inverts it, for decimals he adds 1 (modulo 10). A very naive approach would be to take the diagonal SGD EDZQ N and change it in some way it. However, I couldn't find a way that produces something that makes sense to me: A Caesar Cipher shift by any number doesn't yield anything. Switching letters like a<->z, b<->y, etc. is just as bad.

Another one:

Cantor's pairing function can also be used to produce a sequence of elements from a matrix. Starting at the top left corner, read diagonal lines: S, E, GG, etc. This does not produce anything I would call a message. Starting at another corner doesn't help either.

I'm not giving up just yet, but so far my best guess for his message to me is that I should have payed more attention in math classes.

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You're on the right track with the diagonal argument. The other characters are not random, however. – Volatility Jan 14 at 10:45