Nathaniel Johnston @NathanielMath

Associate Professor of Mathematics at Mount Allison University I have moved over to BlueSky: @njohnston.ca njohnston.ca New Brunswick, Canada Joined November 2021

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Nathaniel Johnston @NathanielMath

2 years ago

@aryehazan p=4 comes up in quantum information and tensor optimization stuff: arxiv.org/abs/1205.4484

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Nathaniel Johnston @NathanielMath

2 years ago

@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.

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Nathaniel Johnston @NathanielMath

2 years ago

Has anyone tried outsourcing their entire research program to MathOverflow? Seems a lot easier than actually doing research. Anyway: mathoverflow.net/questions/4795…

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Nathaniel Johnston @NathanielMath

2 years ago

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

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Nathaniel Johnston @NathanielMath

2 years ago

There's an entire section on the Wikipedia "trapezoid" page (en.wikipedia.org/wiki/Trapezoid…) that discusses the apparent disagreement in the mathematical community re: whether parallelograms should be considered trapezoids. Is this actually a thing?

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Nathaniel Johnston @NathanielMath

2 years ago

Our paper about the new determinant formula is published! cambridge.org/core/journals/… Really fun to write a paper with @robinhouston and @apgox, and really neat to write a paper that stemmed from Twitter, of all places ().

Robin Houston @robinhouston

4 years ago

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.

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Nathaniel Johnston @NathanielMath

2 years ago

Over 15 years ago, I wrote a blog post with some formulas involving maximal self-avoiding walks (njohnston.ca/2009/05/on-max…). At the end of last month, @jpantone et al posted a paper that improves upon those results in ridiculously impressive ways (arxiv.org/abs/2407.18205).

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Nathaniel Johnston @NathanielMath

2 years ago

@BartoszRegula @LamiLudovico @Entanarchist Fantastic, thank you!

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Nathaniel Johnston @NathanielMath

2 years ago

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?

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Nathaniel Johnston @NathanielMath

2 years ago

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

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Nathaniel Johnston @NathanielMath

2 years ago

@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).

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Nathaniel Johnston @NathanielMath

2 years ago

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: youtu.be/Uds_fgle37c

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Nathaniel Johnston @NathanielMath

2 years ago

@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.

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Nathaniel Johnston @NathanielMath

2 years ago

@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.

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Nathaniel Johnston @NathanielMath

2 years ago

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?

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Nathaniel Johnston @NathanielMath

2 years ago

@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.

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Nathaniel Johnston @NathanielMath

2 years ago

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.