Guest comic: Foundations of Forcing

Jul 28 2020, 13:29

I recently posted an answer on MathOverflow where I explained a bit about the approaches to forcing in the literature, at least as I experienced them.

Hanul Jeon took some of these words, and made them into a real nice comic. Originally appearing on his Twitter account. He was kind enough to let me post it here with his permission.

What can you learn about writing papers from cooking pasta?

May 25 2020, 21:40

Those who know me in real life will know that I enjoy cooking. I particularly enjoy cooking pasta. Most authentic Italian recipes are so simple (algio e olio anyone?) that it's just wonderful.

I was cooking dinner today, bucatini alla matriciana if you must know, and I realised that cooking pasta and writing papers have nothing in common. Exactly one of those things is enjoyable, and it is not the writing part of papers (I do love the research part, of course).

Five Star Theorems

Aug 24 2018, 16:35

Talks. Giving talks. We usually don't give talks about past research. Talks are meant to present recent research, things you've just finished, that you're finishing right now, that you've found out!

So often times, it seems, it is very tempting to talk about theorems that you haven't finished writing their proofs in full. Usaully, we put "work in progress" to indicate that this is something not fully verified, not fully vetted (at the very least by ourselves).

Constructive proof that large cardinals are consistent

Jul 06 2016, 13:30

I am not a Platonist, as I keep pointing out. Existence, even not in mathematics, is relative and confusing to begin with, so I don't pretend to try and understand it in a meaningful way.

However, we have a proof, a constructive proof that large cardinals are consistent. And they exist in an inner model of our universe.

Syntactic T-Rex: Irregularized

Jun 20 2016, 20:39

One of my huge pet peeves is with people who think that writing \(1+2+3+\ldots=-\frac1{12}\) is a reasonable thing without context. Convention dictates that when no context is set, we interpret infinite summation as the usual convergence of a series, namely the limit of the partial sums, if it exists (and of course that \(1+2+3+\ldots\) does not converge to any real number). However, a lot of people who are [probably] not mathematicians per se, insist that just because you can set up a context in which the above equality holds, e.g., Ramanujan summation or zeta regularization, then it is automatically perfectly fine to write this out of nowhere without context and being treated as wrong.

But those people forget that \(0=1\) is also very true in the ring with a single element; or you know, just in any structure for a language including the two constant symbols \(0\) and \(1\), where both constants are interpreted to be the same object. And hey, who even said that \(0\) and \(1\) have to denote constants? Why not ternary relations, or some other thing?

Banach-Tarski Banach-T-Rex

Oct 21 2015, 01:10

I had already written about anti-anti-Banach-Tarski arguments. But now the Mathematical T-Rex has something to say too.

Mathematical T-Rex

Aug 28 2015, 22:53

Ever explained to a "working mathematician" about the undecidability of the continuum hypothesis? I bet you too had felt like this T-Rex.