John Baez, a mathematical physicist, writes expository pages on math and physics, including relativity, topology, and the Crackpot Index.
Commenters value his explanations, citing the Relativistic Rocket page and his root-plot pictures, and say they love his blogs.
> I do know quite a bit about physics. But if I just said the EmDrive is nonsense due to conservation of momentum (which is the 100% correct answer with no caveats), people would shut me down because "NASA scientists know what they're doing".
I wouldn't. However, I would ask why you think violation of conservation of momentum is completely dispositive, rather than just a strong reason for great skepticism?
From Noether's Theorem [1] we know that conservation of momentum is a consequence of physics being invariant under space translation. As far as I've been able to find, we don't know that a universe that results from a big bang must be isotropic. Observationally, ours appears to be, but there are some hints that it might not be, and scientists are taking those seriously.
[1] http://math.ucr.edu/home/baez/noether.html
Maybe. Another possibility for a "Rosetta Stone", or perhaps the Lovecraftian perversion of said stone, comes from the ADE situation [0][1]. Even category theory, that great unifier with its own "Rosetta" tables [2][3], cannot escape; quivers have an ADE property.
Either way, we still don't know what's up with 1728. That will truly unlock everything, I think. Understanding 2, 3, or 5 would be nice; understanding 8 or 12 or 24 would be groundbreaking; but I think understanding 1728 will also be understanding Langlands' programme entire.
[0] https://en.wikipedia.org/wiki/ADE_classification
[1] http://www-groups.mcs.st-andrews.ac.uk/~pjc/talks/boundaries/ade2.pdf
[2] http://math.ucr.edu/home/baez/rosetta.pdf
[3] https://ncatlab.org/nlab/show/computational+trinitarianism
I prefer that point of view if you want to understand Euler's identity, and I find John Baez does it even better:
http://math.ucr.edu/home/baez/trig.html
The Baez article does leave it to the reader to convince himself that exp(i*theta) is good notation for a point on a unit circle.
I have problems with the attitude of the article you linked, though. Especially
"Therefore, I’d like to complain to the thousands of people who find Euler’s identity stunning and beautiful."
followed by a snide list of reasons why someone might find it beautiful. It's very common when doing math that something amazing is obvious an hour later. I believe that we are better served by reminding ourselves that (a) nobody knows everything, and (b) the basics facts are actually very beautiful.
Mass is energy, energy is mass. What's the difference? They are at different points in a curve that relates space to time.
If you trade away all the time, you get a maximum velocity: c. So the things moving at c don't experience time, and have momentum but not mass.
http://www.math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html
In the same direction, if you take a mass and accelerate it, it experiences less time. There you have relativistic time dilation, as beloved by science fiction stories.
https://en.wikipedia.org/wiki/Time_dilation
And you simultaneously get length contraction in the direction of each velocity:
https://en.wikipedia.org/wiki/Length_contraction
These are all aspects of the same thing.
Really not a dumb question at all.
John Baez's Prehistory of n-Categorial Physics [1] has some interesting nuggets about Feynman diagrams, in the "Feynman (1947)" section.
In particular, "The mathematics necessary for [interesting Feynman diagrams] was formalized later, in Mac Lane's 1963 paper on monoidal categories (see below) and Joyal and Street's 1980s work on 'string diagrams.'"
In other words, Feynman diagrams were (or at least can be taken as) an early precursor of diagrammatic approaches in category-theoretic mathematical physics.
The paper is really great for getting some context around these diagrams and a sense of the underlying mathematics, even for a category-theory ignoramus like myself, with a little "suspension of comprehension."
1: http://math.ucr.edu/home/baez/history.pdf
This is a pleasant but intentionally very elementary summary of the relevant concepts. If you're interested in much more on this, one place to start is MO (https://mathoverflow.net/questions/4841/what-precisely-is-categorification), or the n-Category Café (https://golem.ph.utexas.edu/category/2008/10/what_is_categorification.html), or Baez's TWF 121 (http://math.ucr.edu/home/baez/week121.html).
Warning: all are much math-ier than Riehl's very nice slides, although the first one has enough content that you may find an answer that you like. If your math itch still isn't scratched, there's Baez and Dolan's paper "Categorification" (https://arxiv.org/abs/math/9802029). I don't know a programmer-focussed view on categorification; can anyone recommend one?