I gave a talk the other day based on our recent work on graded bundles in the category of Lie groupoids. Anyway, as part of the motivation I drew the audiences attention to two quotes…

“Mathematics is written for mathematicians.” Copernicus

“For the things of this world cannot be made known without a knowledge of mathematics.” Roger Bacon

They show the two different sides of mathematics; mathematics motivated by mathematics and mathematics motivated by applications. I think one should to some extent sit in the middle here, but ultimately it is nice when mathematics has something to to with the real world, even if that connection is somewhat loose.

My real motivation for these two specific quotes was that Copernicus was Polish and Bacon English!

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“Everything is number.” – Pythagoras