Magos Logis Logan @jmw150@qoto.org

When reading a math proof

I am pretty fond of the math sorcerer. So much optimism.

https://youtu.be/xTqx8qEx3PA

Pretty nice intro to algebraic number theory

https://youtu.be/4m_EaWA08H0

Good mathematics art is so underrated.

Credit to the K-theory YouTube channel.
https://www.youtube.com/channel/UCRXC6M65qiFlHaXGDNC--VA

Platonism, Formalism -> mathematical theism

Structuralism -> mathematical agnosticism

Constructivism, Logicism, Finitism -> mathematical atheism

Update link

https://cocoa.dima.unige.it/cocoa/cocoalib/

People seem to be adding professional models though.

Model theory types are pretty clear. Composites of types are pretty easy to think about like:

const int a = 1;

It is possible to even extend them to Ada like:

subtype Capital_Letter is Character range 'A' .. 'Z';

https://modeltheory.fandom.com/wiki/Type

The Model Theory wiki is great. Its definitions so far have been really clear.

https://modeltheory.fandom.com/wiki/O-minimality

I like polynomial and power series set notation.

K[X] (polynomial set)

K[[X]] (commutative formal power series set)
So, a super polynomial
"This is not even my final form."

K⟨⟨X⟩⟩ (formal power series set)
Even less limited
"And this... is to go even further beyond!"

philosophy of mathematics and logic book

https://link.springer.com/book/10.1007/978-3-030-84706-7

I am just so busy this week. I might pass the thousand page mark for math literature read this month.

First we do the math. Then we make the math do the math.

https://www.microsoft.com/en-us/research/wp-content/uploads/2016/12/popl10_synthesis.pdf

Yeah, you can make a whole ideology out of algebra. Whitehead was great.

https://plato.stanford.edu/entries/process-philosophy/

@freeschool

Convex algebraic geometry is both pretty, and really easy.

Also it is one of those areas that is a mix of algorithm analysis and optimization. So, super useful.

https://math.berkeley.edu/~bernd/feb19.pdf

I do not get why Noam Chomsky dislikes structural linguistics. It seems to work just as well.

I wonder how analysis made it into mathematics. Now there is just a schism in the doctrine in a lot of places.

I think it is a "does it 'solve' problems I care about?” kind of thing. I think it is the foundation for validating inferences in math. The choice axiom went from, being considered problematic, to being mostly accepted because new problems from it did not hurt old problems.

No idea why, but a lot of scientific books and journals are free to download right now through Springer.

Algorithms in Real Algebraic Geometry
https://link.springer.com/book/10.1007/3-540-33099-2

CoCoAlib (Computations in Commutative Algebra library)

This thing is actually nice. My tired-brain can understand C/C++. It is well documented and has tests and debugging procedures. Is that a Hilbert Algebra? I can has type PolyRing?

http://cocoa.dima.unige.it/cocoalib/index.shtml

Generic distractions and initial ideals (We played with CoCoA, got paid)

https://arxiv.org/abs/math/0308004