musgravepeter

Perhaps start with https://arxiv.org/abs/2605.21660

"It is certainly true that there are aspects of relativity that are counterintuitive, not only to retired engineers but also to many physicists."

Both these books are on my book shelf and are very good. Bate et. al. especially since it is a Dover book and very affordable.

The book that is always on my DESK is "Fundamentals of Astrodynamics and Applications" by Vallado. There is also a website with code from the book for Hohmann and Lambert transfers among other things. <self-promotion>This has been indispensable in creating my Unity Asset "Gravity Engine".</self-promotion>

Take a look at https://store.steampowered.com/app/882140/Reentry__An_Orbita...

The article mentions "few known exact solutions". There are actually quite a number. Most are from after 1950.

Cambridge University Press has two good books: Exact Spacetimes in Einstein's General Relativity (Griffith & Podolsky) - good readable (if you speak GR) account of the more common solutions Exact Solutions of Einstein's Feild Equations (Stephani, Kramer, MacCallum, Hoenstelaers, Herlt) - encyclopedic, authoritative and mathematical. In my case an aspirational purchase

L4 and L5 are stable when the smaller mass is less than about 0.0385 times the larger mass [1]. This means e.g. a typical binary star system would not have stable L4/L5 points. The reference [1] works through this in careful detail and is an excellent reference on this topic.

[1] Solar System Dynamics, Murray and Dermott, Cambridge University Press.

+1 for Artin's Algebra. I think is very under appreciated.

I've been on a Math journey since I retired a couple of years ago and I agree with all the books mentioned that I know and look forward to picking up some of the one I do not know. I agree baby Rudin is essential, but I find it tough going.

Some books I liked for self study because they have answers:

Introduction to Analysis, Mattock.

Elementary Differential Geometry, Pressley.

There is also recently Needham's Visual Differential Geometry and Forms, which is great.

Edit: I should also mention Topology without Tears (free, online, very good) https://www.topologywithouttears.net/

There is Geometric Algebra for Physicists by Doran and Lasenby (2003). It recasts mechanics, E&M up to gauge theories and GR into geometric algebra. I stalled out at mechanics but I've now taken it off the Tsundoku pile and may give it another chance.

I had a quick look and this seems like a solid, concise intro to GR.

The article https://people.carleton.edu/~nchriste/PTO000041.pdf gives an overview of the ways and books to learn GR. It does not cover some more recent intro books.

If you like "physics first" then I am a big fan of Hartle's book.

Snap. I am also a physicist trying to learn math. In my case it's:

- Introduction to Analysis (Mattuck)

- Elementary Differential Geometry (Pressley)

both chosen because they have solutions in the book, which I find important for self-study.

Also just got (hot off the presses)

Visual Differential Geometry and Forms (Needham)

Looks fantastic!

Topology is next on the list...

Steinhardt's book "The second kind of impossible" describes his involvement with quasi-crystals. It's very worthwhile.

Really looking forward to the "So you want to learn math" list!

Penrose's contribution is reviewed in https://arxiv.org/abs/1410.5226

"The discovery still leaves much of the universe undetected. About 85 per cent of its matter is thought to be "dark matter" — that which is undetectable using ordinary methods."

If I understand the abstract, it reports finding "Ωb=0.051+0.021−0.025h−170 (95 per cent confidence; h70 = H0/(70 km s−1 Mpc−1) " which I think means 5% of the total (mass+dark matter+dark energy), since cosmology assumes Omega total = 1.0

The BBC podcast "13 minutes to the moon" is very worth-while.

I am enjoying "The Moon, A history for the future" by Oliver Morton.

My perception (as a lapsed PhD physicist) is the community takes on a new formalism when it has to i.e. there are new results that can only be derived with the new formalism. A formalism that allows slightly better derivation of existing results does not attract attention. Twistors, Clifford algebras and other things seem to have not met this hurdle so far.

Feynman diagrams, Riemannian geometry (General Relativity) did.

I took that idea to its extreme and released "Geodesic Asteroids" on iOS (free) a couple of years ago. You can play on the 2D map or an embedded torus. There is also an old blog post I wrote at the time: http://nbodyphysics.com/blog/2015/03/06/asteroids-on-a-torus...

Depends on what the math re-learning covers. You'd need differential equations and 2nd year calculus.

A good choice for less math might be "Gravity from the ground up" by Schutz.

Physics from symmetry looks really fun. Another book for the pile! (see https://en.wikipedia.org/wiki/Tsundoku)

Mind reader!

Yeah, I'm keen to give that a go. Interestingly it is not a problem that is very easy to parallelize, since every mass will affect every other mass. There may still be some cool ways to use ECS though.

Some of the Unity asset work might fit that description e.g. provide a library of chaotic attractors packaged for use in a game.

My grad work had no connection to data/stats and I have not bumped into any low hanging fruit where Riemannian geometry might be the answer!

(PhD, 1996 in general relativity)

Embedded graphics drivers for real-time systems.

I keep the physics part of my brain alive by developing physics based Unity assets (nbodyphysics.com) and supporting a package for GR on github (grtensor).

I still buy WAY too many physics books. Current aspiration is to work through "Modern Classical Physics" Thorne/Blandford.

Three standouts for me this year:

Educated - Tara Westover: Perhaps the best memoir I have ever read.

Killing Commendatore - Haruki Murakami. Japanese mystical fiction.

An Absolutely Remarkable Thing - Hank Green. A really fun page-turner