In defense of Euclid (was: Einstein's dream)

[purplie]

“In defence of Euclid” - what is the poet defending?
S1-3 say that the parallel lines postulate was thought so long to follow from Euclid’s axioms but it turned out it not to be so and logicians went insane trying to prove it till they found out they could not and so non Euclidean geometry was born in S4. 
So much so good. It’s a tale well told. 

I was in expecting the point in S5 to be that in leading maths astray for 2000 years Euclid did us a great service because he paradoxically laid the groundwork for non Euclidean geometry, as explained in S4. And so that would be the defence

But I don’t see S5 saying that. I’m not sure what it’s saying. The rhyme is tying up the poem in knots. The messaging is garbled.

Apologies.  I forgot the altered line that (I hope) answers both your points:

But for Beauty's sake Euclid held ground,
And he measured his room all around.
With its lengths so mismatched
A black hole should have hatched,
Proving Einstein's math wholly unsound!*

*And his own too, but that's left for the reader to catch.