/sci/ - Science & Math

Was he the most based and redpilled of them all?
>Tragic background: dad deported by the nazis, raised in the countryside.
>Enters random uni, discovers by himself the entirety of Lebesgue integration theory.
>Gets skyrocketted to the ENS math departments, solves a whole bunch of their problems.
>Revolutionize algebraic geometry and category theory forever.
>Get Fields Medal.
>Refuses to go to the USSR to get it to protest their political system and the invasion of Czechoslovakia.
>Ends up selling it to North Vietnam and teaching maths to Vietnamese kids to protest against the Vietnam War.
>Stops doing math as it serves only the military-industrial complex, protests against military funding of science.
>Engages in ecological activism and writes about it (being visionary about climate change and environmental destruction), quits the prestigious math departments he was for them being inert to social and political matters.
>Goes back to teach at the random uni he started in.
>Disappears from society and goes back to the countryside, converts to New Age and weird theological thoughts, writes about the "18 mutants" of history.
>Dies in the 2010s, orders all of his previous works to be burned.
Weirdly inspiring and tragic at the same time. Kaczynski but without the pointless murders.

57

In Grothendieck's retrospective Récoltes et Semailles, he identified twelve of his contributions that he believed qualified as "great ideas". In chronological order, they are:
>Topological tensor products and nuclear spaces
>"Continuous" and "discrete" duality (derived categories, "six operations")
>Yoga of the Grothendieck–Riemann–Roch theorem K-theory relation with intersection theory
>Schemes
>Topoi
>Étale cohomology and l-adic cohomology
>Motives and the motivic Galois group (Grothendieck ⊗-categories)
>Crystals and crystalline cohomology, yoga of "de Rham coefficients", "Hodge coefficients"...
>"Topological algebra": ∞-stacks, derivators; cohomological formalism of topoi as inspiration for a new homotopical algebra
>Tame topology
>Yoga of anabelian algebraic geometry, Galois–Teichmüller theory
>"Schematic" or "arithmetic" point of view for regular polyhedra and regular configurations of all kinds

Today is Fields medal.

Post Alex G and post your predictions.

>>12517451
Smol

Yo, can someone give me an example of a scheme that isn't fucking dumb? Worst case I'm willing to chug 200 pages of categorical bullshit to get to real examples, but dear god something besides affine schemes, varieties, Proj bullshit and the line with 2 points (or any nonsense that is just impossible to apprehend without reducing to one of those) would be great for my intuition.

Also, I'm willing to accept the fibered product, especially in light of the notion of S-valued points, but intuition for what it actually is which is given in a way that doesn't reduce to handwaving about it being the appropriate patching of information given by the pullback of spectra / tensor products of modules in constructing sheaves of the same (i.e., as an object which purports to be "geometric") would be great.

Inb4 EGA didn't have any pictures

>>11901807
>publish one (1) paper in the tohoku math journal
>when people now refer to "the tohoku", they mean his article
how did he do it? He literally cucked the biggest japanese math journal...

>sheaf
>stalk
>germ
why are they called like that?

Required prerequisite for reading Grothendieck's Éléments de géométrie algébrique?

>>10537081
BEGOME GADOLIC

https://www.wikiwand.com/en/Alexander_Grothendieck
"He is considered by many to be the greatest mathematician of the 20th century."
Any citations on this? I'm a mathematician and never heard of him, until recently. Looks like the article is written from category theorists' POV, who assume their theory is the most important thing in mathematics, when it clearly isn't. It is pure POV. His list of achievements doesn't look all that significant, if you consider that most of them are in some obscure part of mathematics. Half of his "major archievements" don't even have a Wikipedia article. The more I look at it, the more it looks like some sort of fraud, or an instance of extreme fanboyism.

How smart was he? How do I get on his level?

Well Grothendiecks work was revolutionary but it's importance isn't really explainable for people other than mathematicians. You can't really do non-technical books or five minute youtube video explaining homological algebra or sheaf theory to public.

>>8428024
>not even the best mathematician from the 20th century

>>8094774
This man rejected it.

https://en.wikipedia.org/wiki/Alexander_Grothendieck

LET'S START A RIOT, A RIOT.

>>7740279
Not exactly a scientist but this man was pretty great.

>pour out massive amounts of work in a few decades, fundamentally building and rebuilding algebraic geometry
>move up into the mountains and tell all your former colleagues to go fuck themselves

>>7111838
I agree.
I also think this works the other way, and that more artists (including musicians and writers) should learn about mathematics in some detail (obviously less detail than a mathematician would). This is particularly true of pure maths, which is just a form of art like any other; there is no reason for any artist to ignore maths.
Likewise, there is no reason for a mathematician, scientist or engineer to ignore art.

step the fuck up

I'm surprised there isn't much discussion about defense research.

It's pretty obvious to me that engineering/physics have been taken over by nuclear power, energy and military contracting. That's like 90% of jobs.

I would have majored in physics were it not for my Marxist tendencies.

Sagan's "Demon Haunted World" had a statistic from the 90s about how many scientists (not just physicists/engineers) were employed in defense. It was over 50% if I recall correctly.

Pic related. Humanity is not ready for more science and math until it overthrows oppressive systems of power like statehood and violent religious views.

Until then, science will be intimately intertwined with the research grant system that runs the show on universities.

>>6549785