This is cool as always, but in case anybody is seriously contemplating using it: this list is infamous for its complete uselessness for anybody actually trying to learn. It's mostly recommended because of 't Hooft's name, but it doesn't reflect how he actually learned physics himself, nor how anybody ever has, really.
It's been "under construction" (i.e. completely abandoned) for two decades. Half the links are broken, and the ones that aren't tend to be whatever the top Google hit was in the 90s, not what's pedagogically best. If you're serious about learning physics, there are many much better roadmaps, like Susan Fowler's list (https://www.susanjfowler.com/blog/2016/8/13/so-you-want-to-l...).
Even better is to look up the undergrad/grad curriculum from a university and then look at the course webpages (many universities still publish their course materials available to anyone who has the link, without needing to login through canvas or a university portal). Pretty often you can get access to homeworks/exams and solutions, lecture notes, etc. in addition to seeing whatever textbook they're using.
Plus, the added benefit helping limit "analysis paralysis" from having too many possible texts to choose from yourself, just pick whatever was standard for that particular class.
This is a great point. Out of all the ones I've looked into, I think MIT has by far the most complete public curriculum (because of MIT OCW), but Cambridge and Oxford are not far behind, with excellent lecture notes and problem sets.
Agreed, at some point I've used something from all three of those and they're all great! I've seen a surprising amount of great stuff from smaller universities too iirc, if you google around.
I'm sorry I can't take Susan Fowler seriously. She claims she went from zero math knowledge (besides sixth grade) and a philosophy major to studying quantum field theory in a span of something like a year and a half [0].
If this wasn't horsesh*t to begin with, she went on to work in non-physics areas after graduation, and never did any research work in physics (no grad school either).
How convenient.
(likely explanation: either her undergrad program was super lax, passing pretty much everyone who shows up in class and exams, hence useless for a serious career in physics, or she's misrepresenting her background)
Well, I've read almost all the books she lists and I've been a quantum field theory practitioner for years, and I can at least attest the list is good. People actually learn from these books.
I think your comment also directly illustrates what I was complaining about. You really shouldn't source learning recommendations from the highest ranking people, because these people know the least about what it's like to learn something anew. A Nobel prize doesn't automatically make somebody a good teacher.
Sure, he is admirable that way. But the comment says not necessarily, which is not a throwaway. Personally, it seems to me that being good at teaching is at the least independent of being a good researcher, if not perhaps negatively correlated. That very much does not rule out extraordinary exceptions (ones that deserve a great deal of attention, for sure).
I just think they are not correlated. Both require you to put effort into being good at it. They also require you to have a firm grasp of the source material.
It's believable to me that a smart+motivated person whose reason for not knowing much math is lack of formal education could catch up a lot faster than you might expect. Educational pacing is generally designed for people who aren't smart and aren't motivated, so if you're both, you can go much faster.
Additionally, she was doing this at around 22 years old, which is in the age range that your brain reaches its optimum performance at learning new things.
She also wasn't starting from sixth grade math knowledge, more like spotty knowledge: she says she had learned some logic, algebra, and set theory.
It's annoying that she characterizes herself as a person who isn't smart/mathy/etc., when her story implies she has plenty of talent for it and just lacked the formal education. The vast majority of people do get a public school education or equivalent, and if they consider themselves bad at math, it's because they were having trouble learning it. If anything the story just demonstrates the dominance of talent+motivation over amount of educational background.
Edit: To elaborate, she says she expected math to be difficult because "I had heard throughout my life that math and physics were really difficult", not because she wasn't able to do well in her math classes. She says "I had the most difficult time possible taking intro physics and the beginning calculus courses", and yeah it's going to be challenging and a lot of work, but she doesn't say her grades came out bad in the end. The takeaway _should_ be that you need to be careful with second-hand opinions about what's difficult, because people vary so much in their aptitudes and interests.
Well, there's "learn" and then there's "Learn." One of my undergraduate QFT courses was taught by a nuclear physicist who wanted to spend the whole time talking about nuclear shells and mass gaps, so he crammed all the QFT in to the last half of the semester. In a blaze of glory, we ran though a bunch of linear algebra, got showed how to do Feynman diagrams and compute cross sections, and saw some vacuum solutions for the Dirac equation. After taking that class, I wouldn't say I knew QFT, but I could say I knew QFT without lying.
If you taught someone how to do derivatives in a half-semester blaze of glory like that, I bet you could combine it with the half-semester blaze of QFT glory to technically qualify as teaching a high school student QFT in half a year.
(I don't regret the professor's decision at all, by the way, I liked the nuclear stuff.)
I personally know the vast majority of the material in both roadmaps, so I know that 't Hooft's is far harder to learn from. Anybody can check this for themselves. There's plenty of broken links, extremely rough drafts of lecture notes, and wild fluctuations in sophistication. The ordering puts graduate-level stuff before its sophomore-level prerequisites.
My statement would only be controversial if you believed that arbitrary adversity in learning was necessary to be a good physicist -- and for my own sake I hope that isn't the case!
Yeah, well, t'Hooft's is harder to learn because it's actually a serious curriculum which is worth knowing rather than training wheels from someone who never did anything serious in physics. Title is how to be a good theoretical physicist; not "what someone might study as an undergraduate."
I mean sure but t' Hooft also denies every interpretation of QM other than superdeterminism, which is almost anti-science (no indepedence of experimenters).
Susan Fowler isn't and never was a physicist. t'Hooft won the Nobel Prize in physics. The title is "how to become a good theoretical physicist" -not "what they taught me as an undergraduate." The end.
Wtf are you talking about. All the recommendations here are look at what physics departments teach and do that. Instead of listening to some Jack ass who thinks the only real physics is theoretical physics.
I am working on something like this myself. I started by reading the Structure and Interpretation of Classical Mechanics, which uses Scheme to teach Hamiltonian and Lagrangian mechanics. And it's much more effective than an ordinary math/physics book. Normal math is a kind of code, except that the VM that executes it is your brain. You (or I, anyway) can only progress if you understand absolutely everything down to the last detail. Programming is much easier. If you don't understand something you can put together a little simulation to poke at the edge cases.
So I finished SICM and I thought, "wouldn't it be cool if I could keep learning physics like this?" And so now I've gotten in touch with some physics postdocs (who are paid shockingly little). I pay them to learn Scheme and encode quantum mechanics, general relativity, statistical mechanics as scheme programs. I work on this about 10 hours a week. In a year or two I'll have knowledge equivalent to an ABD physics grad student, plus information that can take other people from modest beginnings to the same level.
One thing this project has taught me is that students have shockingly little power in their relationships with teachers. I am a major source of income for my postdocs. Some of them may be prioritizing me over some of their other duties. And it really shows. I'm a good self-learner, but there is no substitute for having someone work really hard to anticipate all your questions.
Another thing I've noticed is that everyone (except, increasingly, my postdocs) is a terrible teacher in academia. I have a friend, a fellow grad student, who is scheduled to teach her first lab in her first semester. The lab meets Tuesday. The one-hour credit-only class that will supposedly teach her how to teach meets Wednesday. On day one she'll be going in completely unprepared. And she's not atypical. I suppose that, since students have no power, few people care whether they learn well or just adequately, so people (administrators, professors) prioritize other things. The glaring exception to all this proves the rule. The one person who has done the most to make me successful in graduate school has been my advisor -- and his name will be on every paper I publish. (I like the guy a lot, but self-interest plays a role)
Obviously to each their own, but I find almost all attempts to use anything other than mathematics a needless abstraction for the most part. Being able to poke and prod is useful, but if you do the exercises you shouldn't need to for the most part. Tensor Indices are a bit tricky at first but most notation has evolved for a fairly obvious reason.
Complaining about mathematical notation is quite common on HN, but realistically it's by far and away the easiest part of learning physics (and that's not including gasp actually doing experiments properly). If you aren't planning on doing research I guess it doesn't matter but it's worth keeping in mind that if you learn everything via Scheme or what have you, you may end up in Rome doing as the greeks do.
As someone coming from the physics side of things, I was about to post a similar comment myself. However, what the commenter is trying to do actually provides value in a way most physicists haven't experienced. I agree it'll be hard to get far if you keep avoiding mathematics, but I also think that if a physicist can't program it in a way this person can, then that is indicating a deficiency in the physicist. And I don't mean that to emphasize the programming aspect, but more that it's easy to find physicists who become good at doing the math but not so good at the actual physics, and get by merely with mathematical manipulations.
I'm not avoiding mathematics. I used to be a mathematician. The math is the whole point.
In the mechanics library that comes with the book (which I'm building on in my own work), functions can take either numerical or symbolic values. If you have a computation involving symbolic values, you can manipulate it just like you would with pencil and paper (except you can operate at a higher level of abstraction, never get writer's cramp, and never have to laboriously recopy line after line of symbols to make sure you got the right number of minus signs). If, as so often happens, you find yourself up against an intractable integral, you pass the whole thing to a numerical solver and get a number back right away. With enough calculations you can build up a qualitative understanding of the system's behavior. My understanding is that this is what mechanics people do all day, but not how mechanics is taught to newcomers.
I taught Physics lab as a graduate student. I was surprised at how little formal guidance was provided by the University or department on how to teach effectively, how to engage with students, etc.
My guess about the level of engagement you are observing from the people you're paying: you are giving attention (measured in money) when few other people are demonstrating interest in their specialty.
Absolutely. The goal is to make ABD status available to anyone. Students learn better with programs than with lectures. Profs have more time because they don't have to lecture. Grad school becomes a more collaborative, research-based experience. It seems like a win-win to me.
The software side of it is tricky though. You often need a mental model before you can code. That's got to come by text, video, or whatever. So I have to develop something like a dynamic book with an embedded REPL. I've heard of small efforts in that direction (_why's tryruby.org was good but it's been taken down), but nothing built-out enough to support a multi-year reading project.
Amazing. I’m actually building this exact thing now at https://GitHub.com/sritchie/sicm for that book, and working on a port of https://github.com/littleredcomputer/sicmutils to Clojurescript to power this exact style of interactive textbook in the browser. I’d love to talk more if you’re interested in teaming up, or talking about any of this in more detail.
This sounds great. One hopes that in the years to come, all learning takes on such a multi-faceted structure.
I only wish there was a linear "wall" of learning, from baby arithmetic to algebraic cohomology, string theory, etc., with a clear(ish) path* of precedence for when you get stuck. (*generalized path, I suppose)
Maybe give latex a symbolic math system while we are at it, so that it may check our notes as we type them. ;)
The best way to learn something is incredibly subjective. I looked at SICM once, and I got nothing out of it. I learned classical mechanics from Arnold's "Mathematical Methods of Classical Mechanics". Now, I have total conviction that this is obviously the best way to learn it and I find it incomprehensible that anyone could disagree. And yet virtually nobody learns classical mechanics that way, so it's probably more of a idiosyncratic fact about me, and not a universal truth.
I studied physics as an undergrad and then went on to get a PhD from UW (Seattle), which has required courses for physics education that all graduate students must take. With ~10 years of physics study/practice/teaching, I think the one meta lesson I've carried with me is it's not about which book or which method, but rather the marathon process of ongoing exploration, which is often fueled by genuine interest and joy in exploring the subject. Exploration here applies to the subject itself in spirit, but in reality means exploring the resources to gather perspective and understanding.
The above probably sounds obvious (sorry!), but a lot of learning recommendation seems to focus on "the best" resource, which in my older years strikes me as kind of odd. In the grander scheme of studying something in earnest, time spent with any one book will not be the determiner of success. That's not to say there are no great books or resources, but rather if something is hard or not making sense you should try to approach the topic from another angle: read the chapter on the same topic from another text, or a few others, find some alternative lectures online, etc -- these days the resource list is near limitless... So, start somewhere, don't worry too much about how you start, and keep going!
A lot of the above opinion was motivated by a kind of serendipitous conversation I had with a physics professor. I returned to that convo often enough that I finally decided to write it down last year. Pardon the self plug, but intent was to help share a learning perspective: https://medium.com/@kevinconnolly/effort-neglect-and-the-sec...
'The Second Textbook' is a nice perspective which resonates with me. In my experience I've found the need for as many textbooks as I can get my paws on - each book usually handles one or other topic better than others, or gives me that extra angle that helps my understanding.
Yeah, and there is path dependence in learning, too! The Feynman lectures are quite deep and insightful, but because of that probably good to circle back to at different times, as an example.
But the real kicker for me was just breaking through the impression that “understanding” is a function of rereading, getting stuck, and focusing on one explanation as if parsing the syntax of some author’s statement was how you got information and understanding of a subject. My general rule now is to simply read different explanations. That, imo, is how you develop pedagogical awareness, too, as you then begin to see what authors are not saying in their attempt to convey a subject.
Gerard 't Hooft knows a thing or two about being a GOOD theoretical physicist. But I do have one general complaint about what he is saying. It is apparently common for people, especially ex-physicists like myself, to think they have figured it out (whatever "it" is). In reality, they just forgot (or never knew) enough to realize how bad their idea is. He pretty much agrees with this and his solution is for people to learn it all. In _general_ I don't think it's fair to say you have to be an expert to contribute. We wouldn't make any progress if nobody was allowed to make a suggestion unless they were an expert. This would pretty much silence me (in things not related physics, such as software, or if I was so inclined, in physics too).
Now, I am being a little unfair. I think it is great what he is doing. AND, if anyone does think they have solved the secrets of the universe, don't take it to one of the top physicists in the world before checking it out a little more humbly.
But in any oher case, just throw caution to the wind and don't worry if you don't know everything.
I had a professor who was fond of saying "you have to jump in and do it" ("it" being whatever calculation, or problem, or whatever)
If you are timid and stay on the sidelines, you will never do anything. Of course in physics there is the small further problem where you are up against the smartest people who have ever lived, ...sans the math folk... and double points if you have been jailed in France, doing math during a war, or similar. eh... Really though, can't we all contribute if we work hard enough?
He pretty much agrees with this and his solution is for people to learn it all.
I thought 't Hooft was saying you have to learn all of this stuff. But it sounds like you're saying you can do good work in physics without some of this information. Is that true? What can you dispense with?
No. I wasn't trying to say that. He is right that there is a lot to know to make any contribution to physics. I was trying to make a more general comment that people shouldn't be afraid to try something even if they don't know all the background. Make mistakes and learn as you go. That applies more to "easy" things like software.
I think the author is missing a couple of important points:
1) How would one approach this task having a day job?
2) How do you compensate for not having a chance to work
in a suitable environment doing good research?
2a)Knowing and
understanding everything that has been done in the past
doesn't by itself make you a researcher. This (being a scientist) must be
taught by actual theoretical physicists. There are many
supervisors, but very few that can teach you to do research.
2b) Serious and worthwhile research is seldom done by one person. You need to collaborate or at least communicate with
other scientists in the field (and sometimes even out of the field). You have to be in the right
environment. Just reading arxiv won't quite cut it.
Generality and technical ability, proper mathematical awareness, historical understanding and appreciation of our forerunners. Mainly read the damned texts and task good teachers when confused. Go hard, go long, never give up. Seek elegance. Don't be afraid to disagree but always be rigorous. Play well with others.
Ask the ancient questions and think better.
I don't have a Noble prize for Physics I just study the work of those who do
This list is barely updated. New texts and standards have emerged, and gives no insight as to how to develop the analytical skills. Just a list of books won't do.
It's been "under construction" (i.e. completely abandoned) for two decades. Half the links are broken, and the ones that aren't tend to be whatever the top Google hit was in the 90s, not what's pedagogically best. If you're serious about learning physics, there are many much better roadmaps, like Susan Fowler's list (https://www.susanjfowler.com/blog/2016/8/13/so-you-want-to-l...).