FourEyedRaven said:
And if you have a screw loose, read Grothendieck's EGA.
Back on topic. I'm wondering, can Roger Penrose's 'The Road To Reality' (2001) be considered as a Bible? Apart from its 1100 page format, it is definitely the "broadest" single book I have ever read on physics, spanning and unifying perspectives and ideas in mathematics and physics from the point of view of a mathematical physicist. The only other book I can even think of coming anywhere close is 'The Foundation of Science' (1912) by Henri Poincaré, which by contemporary standards is woefully outdated for physics per se and nowhere near as explicitly mathematical, but extremely useful as a historical and philosophy of science text.
For those not in the know, The Road to Reality literally starts off from elementary mathematics, building its way up to graduate level mathematics in the course of 400 pages. Penrose then introduces classical physics and modern physics in the next 400 pages using the mathematics from the earlier chapters. The remaining pages are devoted to a few important topics in mathematical and theoretical physics, which again build on the earlier mathematical basis. During the entire book he leaves many exercises for the reader to complete, ranging from simple to arcane.
Both the depth and comprehensiveness are considerable, though the book obviously does not contain literally everything one needs to know in a single particular subject which it treats (it would need to be way over 10000 pages in order to do that). On the contrary, I would say that it illuminates both mathematical intuition and directly applicable and procedural physics knowledge along with their interconnections to other fields in mathematics and physics; these are all separate things one expects that a good physicist should know.
It is also somewhat difficult to judge the book in this day and age, seeing practically all physicists today are specialists, while the book very much has the approach of a generalist; this also explains why we don't see any books like this summarizing all of physics anymore, certainly not written by one person and certainly not including as much mathematics as is done here. A few of my old physics professors actually said large sections of the mathematical chapters are beyond them, while the physics sections are mostly good, yet not always treated in depth enough for them or necessarily aligned with their own perspectives on matters.
I believe Penrose has mainly written the book for multiple audiences, namely:
1) (physics) students, in order to lure them into mathematical and/or theoretical physics.
2) practicing physicists who have already chosen a career path outside theoretical physics, but remain interested in it.
3) mathematicians wanting to learn more physics.
4) physicists, who went on to become philosophers of physics/science, who need a quick introduction or refresher into any of these topics for their work.
5) interested 'layman', i.e. (retired) engineers and scientists from other fields who are unafraid of mathematics.
If nothing else, for the amount of typos in those volumes, especially the SGA, I assume. There are intermediary texts between Hartshorne and basic algebraic geometry that can make it easier to understand. But if you want to read EGA, and the material in the SGA that was supposed to go into later volumes of EGA, then start here. I'd say they're the ultimate Algebraic Geometry Bible.
