Nathaniel Johnston

Associate Professor of Mathematics at Mount Allison University
I have moved over to BlueSky: @njohnston.ca

[Nathaniel Johnston @NathanielMath]

I know that my 17 non-bot followers will be devastated, but this site is officially so gross that I can't use it anymore. I've gone to BlueSky: @nathanielmath.bsky.social

[Nathaniel Johnston @NathanielMath]

@aryehazan p=4 comes up in quantum information and tensor optimization stuff: https://t.co/O2DOHWa9Et

[Nathaniel Johnston @NathanielMath]

@VinceVatter Had something like this happen when ordering a test copy of my Game of Life book. The book arrived with all of the correct content, plus an extra 30 or so pages from some other book.

[Nathaniel Johnston @NathanielMath]

Has anyone tried outsourcing their entire research program to MathOverflow? Seems a lot easier than actually doing research.

Anyway: https://t.co/IaR3xtVJwY

[Nathaniel Johnston @NathanielMath]

Hot take: squares are rectangles, which are parallelograms, which are trapezoids, and any textbooks saying otherwise should be burned.

[Nathaniel Johnston @NathanielMath]

There's an entire section on the Wikipedia "trapezoid" page (https://t.co/xvTtUkqwZA) that discusses the apparent disagreement in the mathematical community re: whether parallelograms should be considered trapezoids. Is this actually a thing?

[Nathaniel Johnston @NathanielMath]

Our paper about the new determinant formula is published! https://t.co/xu78WREKnL
Really fun to write a paper with @robinhouston and @apgox, and really neat to write a paper that stemmed from Twitter, of all places (https://t.co/9mMPcUmHKG).

[Robin Houston @robinhouston]

The trick is that you can traverse the hexagon in either direction, so it's okay that we're missing a piece.

We didn't define

I = i(d-e)

which would be the natural sixth thing.

We didn't need to because each of the six is the negation of the sum of the other five.

[Nathaniel Johnston @NathanielMath]

Over 15 years ago, I wrote a blog post with some formulas involving maximal self-avoiding walks (https://t.co/IwXzqVoCqj). At the end of last month, @jpantone et al posted a paper that improves upon those results in ridiculously impressive ways (https://t.co/UnV4LNInCw).

[Nathaniel Johnston @NathanielMath]

@BartoszRegula @LamiLudovico @Entanarchist Fantastic, thank you!

[Nathaniel Johnston @NathanielMath]

Fun fact for quantum information folks: if rho and sigma are separable density matrices (mixed quantum states) then their Hadamard product is separable as well. I somehow didn't notice this until today. Is this used anywhere?

[Nathaniel Johnston @NathanielMath]

@cbounya @DrEugeniaCheng Just arrange it in a 1x17 rectangle -- easy!

[Nathaniel Johnston @NathanielMath]

@JulietteBruce12 Singular value decomposition. So much of the rest of linear algebra (including rank-nullity) is a straightforward corollary of the SVD (as long as you’re OK with just working over R or C, and as long as you’re OK with “corollary” being logically backwards here).

[Nathaniel Johnston @NathanielMath]

Minimal superpermutations are too hard. Solution: generalize and a problem that is easier!... in all cases except for the case we actually care about. New video: https://t.co/2BGcOpSslW

[Nathaniel Johnston @NathanielMath]

@VivaLaVegaaaa Their take is basically "horror movies without tons of gore shouldn't exist". But many PG-13 horror movies like The Ring would be made exactly 0% better by the addition of R-rated elements.

[Nathaniel Johnston @NathanielMath]

@IAm_Not_APerson @no_earthquake It's honestly baffling to me that so many people contest the definition of 0^0, but then go on to use Taylor series or the binomial theorem without thinking twice about it.

0^0 = 1. If you need it to equal anything else or to be undefined, make that definition locally.

[Nathaniel Johnston @NathanielMath]

A 1993 math paper that I'm reading mysteriously has lots of "w"s missing. Anyone have any insight onto why this might have happened? Is there some software that was commonly used back then that could've led to this problem, or is it likely just a find-and-replace mistake?

[Nathaniel Johnston @NathanielMath]

@CmonMattTHINK We do. The “log identities” are the change of base formula and the facts that logs turn products into sums and exponents into products. The equation you posted follows from those.

[Nathaniel Johnston @NathanielMath]

Why does every single graph on Twitter say something like “Source: A questionnaire by The Washington Post” on it with no URL or further information? Half a step away from writing “Source: Internet” but people do it completely unironically.

[Nathaniel Johnston @NathanielMath]

It’s never too early to teach the kids about quantum computing.

[Nathaniel Johnston @NathanielMath]

Dave Greene is doing an Ask-Me-Anything about Conway's Game of Life and our book: https://t.co/15TL2ohtNF