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0 pointsSomeone4y ago0 comments

> It’s amazing how different the subjects of mathematics are. It’s like the difference between a drum and flute.

I think it’s amazing how connected the fields are. It’s almost like “pick any two of analysis, algebra, geometry, number theory, topology, turn one into a adjective and you’ve got a new subject area”.

Topological algebra? Check (https://en.wikipedia.org/wiki/Topological_algebra)

Algebraic topology? Check (https://en.wikipedia.org/wiki/Algebraic_topology).

Geometric topology? Check (https://en.wikipedia.org/wiki/Geometric_topology).

Geometric algebra? Check (https://en.wikipedia.org/wiki/Geometric_algebra)

Algebraic geometry? Check (https://en.wikipedia.org/wiki/Algebraic_geometry)

Geometric number theory? Close (https://en.wikipedia.org/wiki/Geometry_of_numbers)

Mix algebra, number theory, and topology, and you may end up with arithmetic topology (https://en.wikipedia.org/wiki/Arithmetic_topology)

And don’t confuse that with arithmetic geometry (https://en.wikipedia.org/wiki/Arithmetic_geometry)

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travisjungroth4y ago

Isomorphs abound!

I think they’re both true. To the musician, the drum and the flute have a sameness. “You make notes in time with them”, the unconscious mastery. To the beginner (me) it’s worthwhile to see their separateness. I shouldn’t think “I don’t like playing instruments.” because of my experience with recorders in the third grade. Don’t let the trauma of high school trig keep you out of graph theory. They certainly feel different.

This is not hollow advice. Yesterday I bought a flute!

sdenton44y ago

You can add 'combinatorics' to the list of primitives.

Algebraic combinatorics (imo) encompasses related structures in all three of combinatorics, algebra, and geometry, though.

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