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richard elwes - the grothendieck song lyrics

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when i was a young boy doing maths in cl-ss
i thought i knew it all
every test that i took, i was sure to p-ss
i felt pride, and there never came a fall

up at university, i found what life is for:
a world of mathematics, and all mine to explore
learning geometry and logic, i was having a ball
until i hit a wall…

for i adore euler and erdős
élie cartan and ramanujan
newton and noether
but not to sound churlish
there’s one man i cannot understand

no, i can’t get to grips with grothendieck
my palms feel sweaty and my knees go weak
i’m terrified that never will i master the technique
of les éments de géométrie algébrique

he’s a thoughtful and a thorough theory-builder, sans pareil
but can anybody help me find the secret, s’il vous plaît
of this awe-inspiring generality and abstraction?
i have to say it’s driving me to total distraction

for instance… a euclidean point is a location in sp-ce, and that we can all comprehend
rené descartes added coordinates for the power and the rigour they lend
later came zariski topology
where a point’s a type of algebraic set
of dimension nought
well, that’s not what i thought. but it’s ok
there’s hope for me yet!

but now and contra all prior belief
we hear a point’s a prime ideal
in a locally ringed sp-ce, overlaid with a sheaf
professor g, is truly this for real?

no, i can’t make head nor tail of grothendieck
or deligne, or serre, or any of that clique
i’ll have to learn not to care whenever people speak
of les fondements de la géométrie algébrique

but don’t take me for a geometrical fool
i can do much more than merely prove the cosine rule
i’ll calculate exotic spheres in dimension 29
and a variety of varieties, projective and affine

i’m comfortable with categories (though not if they’re derived)
i’ll tile hyperbolic sp-ce in dimension 25
i can compute curvature with the gauss-bonnet law
and just love the leech lattice in dimension 24

but algebro-geometric scheming
leaves me spluttering and screaming
and in logic too, you may call me absurd
but i wouldn’t know a topos, if trampled by a herd

i’ve tried pursuing stacks but they vanished out of sight
i’ve fought with étale coh0m-logy with all my might
and les dérivateurs. it’s 2000 pages long
i reach halfway through line 3, before it all goes badly wrong

no, i’ll never get to grips with grothendieck
and i’m frightened that i’m failing as a mathematics geek
all the same, i can’t deny the lure and the mystique
of le séminaire de géométrie algébrique

- richard elwes lyrics

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