The Aperiodical

There is also Guesstimation 2.0 by the same authors which is a sequel to Guesstimation and is just as good.

Also see Maths on the Back of an Envelope: Clever ways to (roughly) calculate anything. by Rob Eastaway - https://aperiodical.com/2019/11/review-maths-on-the-back-of-an-envelope-by-rob-eastaway/

Related is How to Read Numbers: A Guide to Statistics in the News (and Knowing When to Trust Them) by Tom Chivers and David Chivers - https://en.wikipedia.org/wiki/How_to_Read_Numbers

Finally, the old Soviet books by Yakov Perelman (https://mirtitles.org/?s=Yakov+Perelman) named Physics for Entertainment, Mathematics for Fun etc. also fall under the same category and are a good read.

Bonus: https://en.wikipedia.org/wiki/Back-of-the-envelope_calculation Follow other links like "Guesstimate" from the "See also" section.

Some context: the Invariant Subspace Problem is an important open problem in functional analysis [1]. There is a MathOverflow thread discussing its significance [2].

For those not familiar with functional analysis, it is basically a generalization of basic linear algebra fact that, in complex finite-dimensional vector spaces, every matrix (or to be more precise, every linear operator) has at least one eigenvector.

Cowen and Gallardo announced [3] that they proved the theorem in December, but apparently the proof is wrong, so the problem is still open.

[1] http://en.wikipedia.org/wiki/Invariant_subspace_problem

[2] http://mathoverflow.net/questions/48908/is-the-invariant-subspace-problem-interesting

[3] http://aperiodical.com/2013/01/the-invariant-subspace-problem-solved-for-hilbert-space/

You can fold a paper to get a torus [1]. With those foldings, the distances on the torus embedded in 3D are the same as the distances on the flat paper.

It is even theoretically possible to embed the flat paper as a torus in 3D with a C^1 surface, without polyhedral edges [2,3]. However, this surface has a fractal structure.

Finally, any torus surface embedded in 3D that is at least C^2 (with a continuous second derivative) will nessecarily stretch some distances [4].

[1]: https://www.imaginary.org/hands-on/diplotori-flat-polyhedral-tori

[2]: https://aperiodical.com/2012/05/torus/

[3]: https://www.pnas.org/doi/full/10.1073/pnas.1118478109

[4]: https://math.stackexchange.com/questions/2291382/c2-isometric-embedding-of-the-flat-torus-into-mathbbr3

At timestamp 30:00 he talks about hyperlinked drill down proofs, as the format of textbooks of the future.

Leslie Lamport begged everyone to do this 7 years ago (paper and video linked from blog post [1]), based on his TLA-backed speech on a similar topic 30 years ago [2]

and I'm sure it goes back further. Proof wiki also does this, in part.

[1] https://aperiodical.com/2017/09/hlf-blogs-leslie-lamport-thinks-your-proofs-are-bad/

[2] https://www.microsoft.com/en-us/research/publication/how-to-write-a-proof/

Aside, it's encouraging to see that someone with poor public speaking ability can still become a top mathematician and mathematical writer.

Perhaps it was the example you were thinking of, but Christopher Danielson really brings home the extreme ambiguity of terms using vehicles and children.

I keep coming back to that every time I'm trying to have one of these conversations with people, especially when the question is deeper than whether a salad is a vehicle(as if that were possible).

https://talkingmathwithkids.com/blog/vehicle-chat-invitation/

or discussed in audio form

https://aperiodical.com/2020/08/mathematical-objects-a-vehicle-with-christopher-danielson/

Maybe they tested both and found one more aesthetically pleasing?

Maybe Game of Life simply doesn't produce patterns as interesting as Rule 30? With GoL you can only show one generation.

Maybe they were going for the randomness that rule 30 provides (you can build a PRNG from it) but Game of Life doesn't?

http://aperiodical.com/2017/05/right-answer-for-the-wrong-reason-cellular-automaton-on-the-new-cambridge-north-station/#comment-780944

They're professionals like you. Give them some credit.