/sci/ - Science & Math

was a wizard

Daily reminder that Grothendieck is a fucking wizard.

Is mathematics a science or a religion?

PROTIP: in what sense a point or muh cartesian coordinate system exist?

And if it is a religion should it be founded by the state? Or banned completely as a superstition?

RIP
;_;

HoTT : 500+ pages a fucking notations for at the end having <span class="math">\pi_{n}(\mathbb{S}^{n}) = \mathbf{Z}[\math].

WELL THANKS NIGGA[/spoiler]

>2015
>still not using Grothendieck universes
>still not moving problems into sheaf topoi
ishé diggé dú

This nigga. Sleep now, sweet prince.

>>7406934
I think I got rubber-ducked just by asking the question here. I have it now. I stopped when I got to characteristic maps before, because I didn't really see how he built up to it, but the characteristic maps made me see how the definition he gave in my screen shot their ends up defining the space we are CW-complex'ing by "realizing" every attaching map as a gluing of some disk.

Also, don't forget that /sci/ has some smart people. I'm going to start a /research/ thread, because people are always eager to share what they are passionate about! Have some Grothendieck and enjoy your day, anon.

>>7351049
>he thinks math is about numbers
Bask in the Great Wizard's disapproval.

>>7350711
Quite possibly the greatest mathematician in history. He doesn't get enough respect around here.

>>7304107
>Implying Grothendieck isn't literally a wizard

OP, you're retarded. What you are asking is akin to, "why work with graphic matroids when we could just work with the graph?" or, "why use a group's representation when we can just write down its presentation?" While C^n is homeomorphic, isometric, and diffeomorphic to R^2n, the fact that C is the algebraic closure of R gives it a tonne of extra value. That fact alone has led to all of the intrinsic connections between number theory and complex analysis; while we could work with R^2n, we would then have to take time out of our schedule to jump back over to C^n. We work with matroids because the give us connections between linear algebra, field extensions, and combinatorics (ignore please the crime I committed in not mentioning that many matroids cannot be represented with a graph). And if we didn't work with groups via their representations, we wouldn't have glorious things like the modular group and Conway's monstrous moonshine.

>Grothendieck is disappoint

>tfw you autistically very every step of proof in some area of mathematics
>tfw can reproduce most of the theory but have literally no idea what it means
>tfw years later, you come across a construction/application that makes all the theory you learned come to life beautifully

i'm looking at you, commutative algebra

>>7222310
no, but a wizard robe is.