Tyler Bryson

[Tyler Bryson @tyler_a_bryson]

@MStoudenmire @MathMatize Contrast with real analysis where continuity is a weaker condition and you can easily have "nice" functions with quite different singularities e.g. 1/x versus 1/x^2

[Tyler Bryson @tyler_a_bryson]

@MStoudenmire @MathMatize Mult. achieves rotation ⇒ strong constraints on continuity & that all values are achieved in balls around essential singularities ≈ there's only one way for good functions to fail being good & that failure is captured by the modulus ⇒ Riemann sphere is the correct extension.

[Tyler Bryson @tyler_a_bryson]

@MStoudenmire @MathMatize You really want to twist your noodle: why is that a good idea for complex and a bad idea in real analysis?

[Tyler Bryson @tyler_a_bryson]

@TimHenke9 Of course...this only works if you know all the things that could happen

[Tyler Bryson @tyler_a_bryson]

@littmath Vibes

[Tyler Bryson @tyler_a_bryson]

@pulpy_fiction There's a tendency to tie up one's whole personality in the PhD. Coupled with the low pay, you get a psychologically distressing cocktail, "if I fail, my glorious poverty was as pointless as my life will have turned out".

[Tyler Bryson @tyler_a_bryson]

@RodeoProfessor I don't know...just seems like a defense pic. We can't all always wear our bow ties, suspenders, and government issue spats. PhD people are people, *shrugs*

[Tyler Bryson @tyler_a_bryson]

@Anthony_Bonato Or contractible...

[Tyler Bryson @tyler_a_bryson]

@Anthony_Bonato Sure...but it shouldn't be connected

[Tyler Bryson @tyler_a_bryson]

@beyondreasdoubt Zero is a natural number.

[Tyler Bryson @tyler_a_bryson]

@MStoudenmire @QuantaMagazine As long as you've a bias against choosing a basis and a good idea when you might accidentally find yourself in infinite dimensional settings and and and
I don't actually have a problem w/ that view.

[Tyler Bryson @tyler_a_bryson]

@Aron_Adler It does skip all the hard stuff to do with using periodic functions as a basis... but I see your point, love a good illustration to highlight parts of an idea

[Tyler Bryson @tyler_a_bryson]

@aryehazan Of if you like computation, you might like proofs in sheaf theory that do stuff by components/ in generators. Extra credit: computations that rely on existence of a set of generators for something who's Kan extension solves your problem

[Tyler Bryson @tyler_a_bryson]

@aryehazan e.g. here is part of a proof to do with Kan Extensions showing that there's a natural map from a certain coproduct to a product

[Tyler Bryson @tyler_a_bryson]

@JDHamkins Stokes' theorem might be a candidate. Both by misattribution and the drift toward generalization.

[Tyler Bryson @tyler_a_bryson]

@Anthony_Bonato "whence" is my ride or die

[Tyler Bryson @tyler_a_bryson]

@miniapeur Sum of first n odd numbers = nth square. First mathematical memory and it eventually connects up to 2x is derivative of x^2

[Tyler Bryson @tyler_a_bryson]

@miniapeur \empyset is nearly as disappointing \phi. Though my all time is":" v \colon