Could someone please explain to me, a pleb tier undergrad, what

>>8137131
He had a really big dick so we could say that he really grew a dick but because good grammar was not invented back then people did not know how to do past tense correctly so preople said he growed-a-dick so much that it became his nickname.

As time passed and most people forgot the origin people just pronounced the base of it like grouthadick and then it degenerated further into Grothendieck.

If you are talking with mathematicians then you might want to use Grothendieck but if you are talking with historians then growed-a-dick will be the only acceptable choice. But if you are talking with english majors then Grew a dick will be better.

>>8137131
He went into hiding because his dick grew too big. He then donned the robes and beard of a wizard with a large dick, shunning society and it's average sized penises.

>>8137155
>>8137152
bad answers

>>8137131
Do you know what a manifold is?
Do you know what a ring is?

>>8139252
Manifold: something that looks smooth when you zoom in
Ring: like a field but with crappier multiplication

Hm?

>>8137131
Algebraic geometry had some foundational problems. He took care of all of that by introducing a change in the way we think about the subject which has proven to be very fruitful.

>>8139261
A n-manifold is a topological space that locally looks like an open subset of [math]{\mathbb{R}^n}[/math].

i.e. Suppose that [math]X[/math] is a manifold. Then there exists a cover of [math]X[/math] by open sets [math]{{U_i}}[/math] such that each [math]{U_i} \cong B \subset {\mathbb{R}^n}[/math].

So what we have is a way of constructing complicated objects by gluing together a lot of patches that look like open subsets of [math]{\mathbb{R}^n}[/math].


A commutative ring is a ring whose multiplication is commutative.

Let [math] R [/math] be a commutative ring. An ideal of [math] R [/math] is a subgroup under addition [math]I \subset R[/math] closed under multiplication by elements of [math] R [/math].

An ideal [math] I\triangleleft R [/math] is called prime if [math]a \cdot b \in I[/math] implies [math]a \in I[/math] or [math]b \in I[/math].

We denote the set of prime ideals as [math] \operatorname{Spec} R = \left\{ {I \triangleleft R|I\;{\text{is}}\;{\text{prime}}} \right\} [/math].


Grothendieck created something called a Scheme.

It is possible to give the set [math]\operatorname{Spec} R[/math] a topology. It is defined by thinking of elements of [math] R [/math] as "functions" on the set [math]\operatorname{Spec} R[/math], that way you define the closed sets of the topology as follows:

[math]S \subset R[/math] a subset, then define [math]V\left( S \right) = \left\{ {x \in \operatorname{Spec} R\;|\;f\left( x \right) = 0\;\;\forall \;\;f \in S} \right\}[/math] to be a closed set.


The topological spaces [math]{\operatorname{Spec} R}[/math] are called affine schemes.

A scheme is a topological space that locally looks like affine schemes. In the same way a manifold locally looks like open subsets of euclidean space.

A scheme also is given structure by something called its structure sheaf. The definition of a sheaf is complicated, so think of it as something that has an analogous behavior to the set of smooth functions on a manifold.

>>8139299
So what Grothendieck did was give us a whole new way of looking at geometry, from a very abstracted and generalized point of view by inventing these Schemes.

>>8139299
I'm studying schemes right now and I didn't know they were invented by Grothendieck.

>>8137152
>>8137155
The only correct answers in this thread.

The rest of you trolls should be ashamed of yourselves. Growed-a-dick must be rolling in his grave right now.