What is algebraic geometry?

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Straight forward question for someone who’s upper most math class was calc 1 a long time ago. Also bonus points if someone can explain why Grothendieck is the “Einstein of math”

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Anonymous 0 Comments

I can’t say I’m any more qualified than you to explain this. But I dipped my toe in and Grothendieck won the Fields medal in 1966.

The Wikipedia article on [algebraic geometry](https://en.wikipedia.org/wiki/Algebraic_geometry) starts off by saying:

>Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros.

So, it sounds like it started out by solving simple things like 7x+5=0 and then gets a lot more complex.

The Wikipedia on [Grothendieck](https://en.wikipedia.org/wiki/Alexander_Grothendieck) says

><He> was a stateless and then French mathematician who became the leading figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory and category theory to its foundations, while his so-called “relative” perspective led to revolutionary advances in many areas of pure mathematics. He is considered by many to be the greatest mathematician of the 20th century.

The reference in Wikipedia led me to [this obit](https://www.dam.brown.edu/people/mumford/blog/2014/Grothendieck.html), which was interesting, but the math was over my head. But it sounds like he laid the foundation for algebraic geometry and his ideas are still being used today.

I think using Einstein is a way to try and communicate his genius.

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