True Logick is Neohermetic Pythagoreanism for the the modern mathematician.

vixra.org/abs/1905.0086

I want to use the phrase “fire up the Rips machine” in my thesis.

How to threaten a mathematician: "This is some nice Hagoromo Fulltouch chalk you have here. It would be a shame if you came into your office one day and found it broken to pieces on the floor."

New entry!
Computational complexity and 3-manifolds and zombies
Article by Greg Kuperberg and Eric Samperton
In collections: Attention-grabbing titles, Basically computer science
We show the problem of counting homomorphisms from the fundamental group of a homology $$3$$-sphere $$M$$ to a finite, non-abelian simple...
URL: arxiv.org/abs/1707.03811v1
PDF: arxiv.org/pdf/1707.03811v1

Like, doing this just feels weird: $$\bigcirc_{i=1}^nf_i := f_1 \circ f_2 \circ \dots \circ f_n$$

Idle thought: with the exception of $$\sum$$ and $$\prod$$, transforming an associative binary operation into an agglomerative "summation notation" is just making the symbol big and adding sub/superscripts. E.g., $$\bigotimes_{i=0}^n v_i$$. It's strange to me that this applies to non-commutative operators ( $$\wedge$$ ), but also that there are many binary operations where this rule can't be applied due to limitations of the syntax (bracket operators, function composition, modulo).

I recently learned about Ologs, which are basically "category theory for normal people". These are very useful for knowledge representation. I am now in the making of a blog post about how to make them and how to translate ologs to Haskell code.

en.wikipedia.org/wiki/Olog

I recently found some hilariously-named software that cuts PDFs scanned as two pages side-by-side into single pages.
briss.sourceforge.net/

Let $$Y$$ be a subspace of $$X$$. The wizard hat space $$W$$ is constructed by attaching the base of the cone $$CY$$ over $$Y$$ to $$X$$ along $$Y$$.

(This showed up in a topology class I took once. We needed to use the fact that $$W$$ deformation retracts onto $$X$$, but I don't remember what it was used for. The name is mine.)

Math genealogy visualizer now supports finding the closest common ancestor of two mathematicians.

j2kun.github.io/math-genealogy/index.html

Working on my thesis project. Given two torsion-free groups $$\Gamma_1,\Gamma_2$$ which are elementarily equivalent and both hyperbolic relative to their abelian subgroups, I'm currently trying to determine what sorts of constraints I can put on how homomorphisms $$\Gamma_1\to\Gamma_2$$ behave on the abelian subgroups.

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