Read Yuri Manin's book on Mathematical Logic, it's pretty based. Except for the part where he talks about von Neumann's proof of the impossibility of hidden variables in QM, which is correct mathematically, it just turns out that it doesn't really do what it is advertised to do. I think Manin may be a little bit of a chud (after all he was somewhat close to Safarevich) but he's a great mathematician and his books own. He takes some boring subject like advanced proof based linear and homological algebra and he makes it about quantum mechanics and 20 dimensional watermelons (which turn out to be about 2/3 skin so they're not really worth buying) without losing anything in rigor. Pretty advanced book though. Not a first course.
Also Godel, Escher Bach is a cool semi-pop math book on the subject of logic.
Love GEB. Also Penrose's road to reality if you want to step by step learn the real math behind physics rather than the "lies to children" in Pop Sci (and have enough math to solve a simple quadratic/differentiate X^2)
I don't know Road to Reality but I know Leonard Susskind's Theoretical Minimum series and the associated lectures are simple enough that someone who literally doesn't know calculus yet can follow them (he teaches you calculus) and eventually he actually gives you the real deal, actual physics that you learn in uni. It's not easy though, it's easily above pop Sci level.
From what I can see Road to reality basically covers the same stuff, with a few differences in the progression of the math and some of the wilder areas of GUT/TOE research like Loop Quantum Gravity, Spinnors, Twistors etc. I suspect Susskind is more up to date, so it comes down to if you prefer lectures or a book to guide you.
Neither work is for the faint of heart. It took me three attempts and maybe 7-8 months regular work to get through road properly
It's not a matter of up to date. It's just that Susskind literally teaches you almost undergrad level physics. You can actually calculate stuff. Again, haven't read Road to Reality but it definitely doesn't do that especially if it touches on GUT adjacent research, teaching that even on the level of detail of Susskind would be way too advanced. Like, the quantum mechanics you learn from Susskind is almost good enough for an introductory course at uni, if you earned it well enough, mayyybe you would have a chance to pass an exam in said introductory course. It wouldn't be guaranteed, but you'd have a chance. The classical mechanics he teaches you are actually pretty "complete", it almost covers all the big ideas of classical mechanics you will encounter in undergrad, and you'd have a pretty good chance to pass an exam. Same with special relativity, he teaches more or less all the relativity you would expect in an intro class on the subject, and you could definitely pass an exam based on what he teaches. I haven't watched the entirety of the other lectures (and I think the books only cover QM and classical mechanics), but I think maybe the statistical mechanics stuff wouldn't be enough, but the general relativity would be good for a very basic intro class.
So basically the strength of Theoretical Minimum is that he gives you something that's actually really close to what people learn in introductory classes in uni. The drawback is that the stuff he teaches is probably not as "exciting" as what I imagine Penrose gets into. On the other hand, I see Penrose spent lots of pages on math, so maybe he does give you enough to go beyond qualitative understanding of some concepts. Looking at the wiki page, I saw something very interesting:
From there it moves on to fields in spacetime, deriving the classical electrical and magnetic forces from first principles; that is, if one lives in spacetime of a particular sort, these fields develop naturally as a consequence.
I don't know how you might do that. Never heard it before. Sounds really interesting.
Penrose goes beyond undergrad by some way, heck beyond some grad school, but you couldn't pass undergrad physics with it. (I did quantum mechanics and modelling but I was a materials science/ Molecular Biology major so the courses had an applied focus, and there was no General Relativity of course.)
His goal is more "be able to read a current paper on Calabi-Yau manifolds and understand at a very general quantitative level what the equations mean and what is being talked about" rather than "become a physics undergrad/grad school equivalent in knowledge". With textbooks it would be a good roadmap for a coursework masters level education though.
Read Yuri Manin's book on Mathematical Logic, it's pretty based. Except for the part where he talks about von Neumann's proof of the impossibility of hidden variables in QM, which is correct mathematically, it just turns out that it doesn't really do what it is advertised to do. I think Manin may be a little bit of a chud (after all he was somewhat close to Safarevich) but he's a great mathematician and his books own. He takes some boring subject like advanced proof based linear and homological algebra and he makes it about quantum mechanics and 20 dimensional watermelons (which turn out to be about 2/3 skin so they're not really worth buying) without losing anything in rigor. Pretty advanced book though. Not a first course.
Also Godel, Escher Bach is a cool semi-pop math book on the subject of logic.
Love GEB. Also Penrose's road to reality if you want to step by step learn the real math behind physics rather than the "lies to children" in Pop Sci (and have enough math to solve a simple quadratic/differentiate X^2)
I don't know Road to Reality but I know Leonard Susskind's Theoretical Minimum series and the associated lectures are simple enough that someone who literally doesn't know calculus yet can follow them (he teaches you calculus) and eventually he actually gives you the real deal, actual physics that you learn in uni. It's not easy though, it's easily above pop Sci level.
From what I can see Road to reality basically covers the same stuff, with a few differences in the progression of the math and some of the wilder areas of GUT/TOE research like Loop Quantum Gravity, Spinnors, Twistors etc. I suspect Susskind is more up to date, so it comes down to if you prefer lectures or a book to guide you.
Neither work is for the faint of heart. It took me three attempts and maybe 7-8 months regular work to get through road properly
It's not a matter of up to date. It's just that Susskind literally teaches you almost undergrad level physics. You can actually calculate stuff. Again, haven't read Road to Reality but it definitely doesn't do that especially if it touches on GUT adjacent research, teaching that even on the level of detail of Susskind would be way too advanced. Like, the quantum mechanics you learn from Susskind is almost good enough for an introductory course at uni, if you earned it well enough, mayyybe you would have a chance to pass an exam in said introductory course. It wouldn't be guaranteed, but you'd have a chance. The classical mechanics he teaches you are actually pretty "complete", it almost covers all the big ideas of classical mechanics you will encounter in undergrad, and you'd have a pretty good chance to pass an exam. Same with special relativity, he teaches more or less all the relativity you would expect in an intro class on the subject, and you could definitely pass an exam based on what he teaches. I haven't watched the entirety of the other lectures (and I think the books only cover QM and classical mechanics), but I think maybe the statistical mechanics stuff wouldn't be enough, but the general relativity would be good for a very basic intro class.
So basically the strength of Theoretical Minimum is that he gives you something that's actually really close to what people learn in introductory classes in uni. The drawback is that the stuff he teaches is probably not as "exciting" as what I imagine Penrose gets into. On the other hand, I see Penrose spent lots of pages on math, so maybe he does give you enough to go beyond qualitative understanding of some concepts. Looking at the wiki page, I saw something very interesting:
I don't know how you might do that. Never heard it before. Sounds really interesting.
Penrose goes beyond undergrad by some way, heck beyond some grad school, but you couldn't pass undergrad physics with it. (I did quantum mechanics and modelling but I was a materials science/ Molecular Biology major so the courses had an applied focus, and there was no General Relativity of course.)
His goal is more "be able to read a current paper on Calabi-Yau manifolds and understand at a very general quantitative level what the equations mean and what is being talked about" rather than "become a physics undergrad/grad school equivalent in knowledge". With textbooks it would be a good roadmap for a coursework masters level education though.