
Alexander Grothendieck, a genius of mathematics (2015) - ar7hur
https://al3x.svbtle.com/alexander-grothendieck
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savanaly
If anyone's curious about the actual math Grothendieck was doing but is (like
me) a layman when it comes to mathematics, there's a useful summary of one of
his major areas of work in parts II and III of this blog post [0].

The essence, I believe, is

>Bottom line: To study the Weil conjectures, you have to think very hard about
the subtle properties of curves, surfaces and higher-dimensional objects. When
you do this, you find yourself mentally “moving around” the curve, trying to
hop from point to point. And — in a sense that I cannot hope to make precise
here — you sometimes find that your mental exploration is hampered by the fact
that there somehow aren’t enough points to hop to.

>So life would be easier if these curves (and other objects) had more points.
A normal person might say “Well, life’s not always easy. We’ll just have to
get by somehow with the points we’ve got”. But Grothendieck lived by the
conviction that everything is easy if you look at it right — which means there
have got to be enough points. And if we think there aren’t, it must be because
we haven’t yet figured out what a point is.

I don't think I'm closer to understanding what it is he was working on after
reading it, at least not in a meaningful sense, but it is fascinating to me to
read about.

[0] [http://www.thebigquestions.com/2014/11/17/the-
generalist/](http://www.thebigquestions.com/2014/11/17/the-generalist/)

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agumonkey
> Grothendieck lived by the conviction that everything is easy if you look at
> it right

so I can measure my arrogance in nanoGrothendiecks, cute.

~~~
Jtsummers
This seems to be an unfair reading of that sentence. A fairer interpretation
might be closer to "right tool for the right job". Certain topics or materials
can be more easily understood when viewed with the right framework. In
physics, for instance, calculus yields results that mere algebra and
trigonometry cannot easily provide. It's not that calculus is easy, but that
with it (the framework, point of view), the physics becomes easy.

EDIT: After reading more, I stand by this. And Grothendieck seemed to
specialize in creating those frameworks.

~~~
HiroshiSan
Aside from frameworks looking at it right might have to come from years of
study which may necessarily not be easy but once you find something easy you
are looking at it right.

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sireat
Grothendieck is also famous for discovering a new prime:
[https://en.wikipedia.org/wiki/57_(number)](https://en.wikipedia.org/wiki/57_\(number\))

He was a very abstract genius.

More on his life: [http://www.ams.org/notices/200410/fea-grothendieck-
part2.pdf](http://www.ams.org/notices/200410/fea-grothendieck-part2.pdf)

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aratno
> He ignores the silent and flawless consensus that is part of the air we
> breathe – the consensus of all the people who are, or are reputed to be,
> reasonable.

Very well put, especially considering this is from a personal journal.

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javiramos
A friend of mine, Carlos Fonseca, wrote a fantastic Spanish novel (also
translated to English) inspired by Grothendieck's life. [0]

[0] [https://www.amazon.com/Coronel-Lagrimas-Spanish-
Narrativas-H...](https://www.amazon.com/Coronel-Lagrimas-Spanish-Narrativas-
Hispanicas/dp/8433997912/ref=sr_1_1)

