Lemma 2.1 in #165.2 of the OpenAI slop-nuke includes a clean inequality:
Suppose 𝑈₁,…,𝑈ₘ,𝑉₁,…,𝑉ₘ are subspaces of ℝᴺ such that 𝑈ᵢ∩𝑉ᵢ=0. Then we have the following inequality:
\[\sum_{i,j} \dim(U_i \cap V_j) \leq Nm^2/4\]
Seems fun, clean, and at least potentially clever. If the AI has done something toward theory building, I would expect to see several results like this. Thus the question: is this actually new (and interesting)?
The team produced the following artifact.
Great news! The cubes are now gender free. Remember that the dihedral group includes reflections, not just the cyclic group of rotations. That should clear up everything.
Don't panic. My team is removing gender from cubes as we speak.
I have just learned about the delightful mathematical research postcards! https://secure.math.ubc.ca/Links/mrp/
Recent interactions with the editing & styling at a journal (the folks in charge of the physical layout of the text and figures) has me very confused about their incentives. I guess they do not (or at least should not) read for the actual mathematics. So what incentives are they working under?
It seems like they also aren't incentivized to make the final product look... good? Aesthetically pleasing? They returned a submission to us with wildly variable figure sizes, some of the math in the figures was too small to read, and others were triple the size of surrounding text. Figures referenced only in a single example would appear 4 pages before, or 3 pages after the reference.
Latex was supposed to communicate author intent; I feel like it got lost in translation.
I am now allowed to use this mathstodon handle. Apologies for the last few months of fraud.
Thesis defended!
Historical question: why do we do an oral thesis/dissertation defense at the end of a PhD?
Similarly, I can't seem to find a claimed 'first' time a defense was given for a degree. What was the problem being solved?
Anyone know of good git tutorials for mathematics (or academic) use?
I'm aware of the Git for mathematicians by Najib Ideissi (idrissi.eu/post/git-1-preliminaries ), but it stops just short. The others I know of are targeted more to software.
Today I learned about https://landing.runestone.academy/
A nonprofit that's compiled, hosting, and creating modern open-source textbooks for math and CS (with interactive exercises!). While it is not a huge library of topics, the introductory college material all seems to be there? Very cool. Books available are listed here: https://runestone.academy/ns/books/index (click the blue title to go to the book; you don't need to register).
As this is easily missed news: At least 4 graduate students at the university of michigan have had their visa's revoked and been asked to leave the country. The dismissed students seem random, some phd and some masters, all from different departments. The university and students appear to be keeping quiet about it.