How I Learned to Love Algebraic Geometry • Hacker News Board

Re: How I Learned to Love Algebraic Geometry

#21

Post by dhimes » Sat, Mar 16, 2019, 1:07 PM UTC

chmaynard wrote: post #17

melling wrote: post #12

Joan Baez’s dad, his uncle, gave him the physics book that he wrote. Hopefully, someday when we see Joan Baez represented in movies, we’ll see her physicist father, perhaps giving a physics book to his 8 year old nephew.

In 1968, I enjoyed taking a physics course at Harvard Summer School that was taught by Dr. Albert Baez. He had a home in Cambridge and graciously invited the entire class over for a party after the course ended. The highlight of the evening was an impromptu performance by his daughter Joan.

He was also the crew-cut guy running demos in film loops I saw in school when I was a kid in the '60s and '70s.

Re: How I Learned to Love Algebraic Geometry

#22

Post by agumonkey » Sat, Mar 16, 2019, 1:23 PM UTC

melling wrote: post #12

Joan Baez’s dad, his uncle, gave him the physics book that he wrote. Hopefully, someday when we see Joan Baez represented in movies, we’ll see her physicist father, perhaps giving a physics book to his 8 year old nephew.

oh I never realized they were siblings .. https://ncatlab.org/johnbaez/show/HomePage

Re: How I Learned to Love Algebraic Geometry

#23

Post by eggy » Sat, Mar 16, 2019, 1:24 PM UTC

Can geometric algebra be used in algebraic geometry? I understand geometric algebra is useful in physics involving differential geometry and calculus, and that algebraic geometry is heavy on the algebra of polynomials and a complete field of study in mathematics, whereas geometric algebra is more like an object (Clifford algebra, etc.).

Re: How I Learned to Love Algebraic Geometry

#24

Post by NiftyWalrus » Sat, Mar 16, 2019, 1:28 PM UTC

throwawaymath wrote: post #20

maaaats wrote: post #11

What are some good resources for grasping or learning more about algebraic geometry?

This isn't a fun answer, but you basically can't without substantial background in undergrad mathematics. The subject has some of the highest prerequisites of any upper undergrad/lower grad level math course, as it touches on (and uses) just about everything you'd learn through an undergrad math degree. I don't want to discourage you, I'm just being realistic. If you want to work towards algebraic geometry, you can c…

Could you describe what Grothendieck was doing in algerbiac geometry? Would studying the above get you up to the point of his work? If not, what are concrete suggestions that would get you there?

Re: How I Learned to Love Algebraic Geometry

#25

Post by mcslearner » Sat, Mar 16, 2019, 1:30 PM UTC

maaaats wrote: post #11

What are some good resources for grasping or learning more about algebraic geometry?

Depends how much math you know, but Chapter 15 (Commutative Rings and Algebraic Geometry) of Dummit and Foote may be a good starting place.

Re: How I Learned to Love Algebraic Geometry

#26

Post by nikofeyn » Sat, Mar 16, 2019, 2:16 PM UTC

agumonkey wrote: post #22

melling wrote: post #12

Joan Baez’s dad, his uncle, gave him the physics book that he wrote. Hopefully, someday when we see Joan Baez represented in movies, we’ll see her physicist father, perhaps giving a physics book to his 8 year old nephew.

oh I never realized they were siblings .. https://ncatlab.org/johnbaez/show/HomePage

they aren’t. joan and john are cousins.

Re: How I Learned to Love Algebraic Geometry

#27

Post by obastani » Sat, Mar 16, 2019, 2:21 PM UTC

NiftyWalrus wrote: post #24

throwawaymath wrote: post #20

Earlier quoted context omitted.

This isn't a fun answer, but you basically can't without substantial background in undergrad mathematics. The subject has some of the highest prerequisites of any upper undergrad/lower grad level math course, as it touches on (and uses) just about everything you'd learn through an undergrad math degree. I don't want to discourage you, I'm just being realistic. If you want to work towards algebraic geometry, you can c…

Could you describe what Grothendieck was doing in algerbiac geometry? Would studying the above get you up to the point of his work? If not, what are concrete suggestions that would get you there?

The "Background and history" section of the following article gives a very high-level idea of Grothendieck's contribution:

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

Re: How I Learned to Love Algebraic Geometry

#28

Post by phkahler » Sat, Mar 16, 2019, 2:33 PM UTC

joppy wrote: post #18

aaaaaaaaaaab wrote: post #14

Earlier quoted context omitted.

But aren’t we missing out on something important by glossing over these “pathological” cases? Like how we kept ignoring nonlinear differential equations, because they aren’t that well-behaving as their linear counterparts... And then when we eventually looked into it, we found a completely new paradigm: chaos theory.

For sure we are missing something. But what hope do we have of understanding the more complicated case, before we figure out what we can know in simpler cases? The eventual goal is to move back to the more complicated cases.

What if the approach to the simpler cases is not applicable to the harder ones. Studying the simple may shape ones thoughts in a way that prevents seeing the way to harder problems. Maybe? Sometimes new things are discovered because someone didn't know any better and tried something they were not ready for. Innovation sometimes comes from the self taught.

Re: How I Learned to Love Algebraic Geometry

#29

Post by agumonkey » Sat, Mar 16, 2019, 2:37 PM UTC

nikofeyn wrote: post #26

agumonkey wrote: post #22

Earlier quoted context omitted.

oh I never realized they were siblings .. https://ncatlab.org/johnbaez/show/HomePage

they aren’t. joan and john are cousins.

vocabulary fail on my part, I thought siblings was a larger class

Re: How I Learned to Love Algebraic Geometry

#30

Post by NiftyWalrus » Sat, Mar 16, 2019, 2:37 PM UTC

obastani wrote: post #27

NiftyWalrus wrote: post #24

Earlier quoted context omitted.

Could you describe what Grothendieck was doing in algerbiac geometry? Would studying the above get you up to the point of his work? If not, what are concrete suggestions that would get you there?

The "Background and history" section of the following article gives a very high-level idea of Grothendieck's contribution: https://en.wikipedia.org/wiki/Weil_conjectures

What is the modern path to study this area now? I’m sure it’s better understood now and one wouldn’t have to follow the historical approach to study the same concepts.