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Grokking Grothendieck
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Sadly, there probably isn't an answer to your question that you will like: one simply has to have at least a graduate-level mathematics education to properly understand Grothendieck's mathematics.
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I did my undergrad in math and I'm finishing my masters in math, soon to start a Phd in math. Much like you I have also heard that Alexander Grothendieck revolutionized math. I have taken some courses in commutative algebra but I never managed to learn anything, all of my exercises where completely hackable through noob methods so that's what I did.

The only thing I have been able to do similar to Grothendieck have been a couple of times I fasted with chamomille tea.
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> I'm thinking of a presentation of Grothendieck's legendary revolution that goes deeper into the actual mathematics

Do you even cohomology , bruh?
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I believe Colin McLarty, quoted in that article, has some good expository papers about Grothendieck. I always thought it was funny their thesis was "I think Grothendieck is pretty neat and here's why you should too."

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