One of the SDMB’s more gifted posters–okay, I’m talking about our muscle-bound friend, Ultrafilter–made this surprising declaration some two months ago. I’ve always considered Ultra’s mathematical prowess rather remarkable and have always assumed that mathematical acumen neatly translates into physics aptitude. After all, weren’t some of the 20th century’s great physicists exceptionally strong mathematicians and isn’t physics essentially the application of left-brained, mathematics-heavy principles?
How can it be that someone gifted in math is only so-so in physics? BTW, I’m not talking high-end abstract physics that entails substantial creativity.
In short, I had always assumed a very strong correlation between mathematics aptitude and physics aptitude, believing mathematics the master key to all scientific disciplines.
One can be gifted in a certain area of mathematics and be completely weak in some other. Same with physics. Broad, sweeping statements is just a personal opinion of a perceived average of how you perform in a subject.
For example, I’m ok when it comes to higher algebra, field theory, galois, etc. I can easily do formal languages, graph theory or advanced linear algebra. I can grasp relativistic physics fairly quickly. Give me a high school level combinatorics problem or a differential equation and I’ll start whining and it will take me forever. In physics I’d always resort to hand waving “and we integrate the flux over this area” rather than writing out the integral, because vector calculus is just not something that comes to me easily.
It’s probably a lot easier than the other way around.
Certainly one possibility is simply that one has spent far more time and effort studying math than studying physics.
Then there’s the experimental aspect to physics and other sciences. Personally, I did much better in, and enjoyed more, the math classes I took in college than the science classes, and part of the reason is that I hated labs. (Or, as my philosophy professor remarked once when discussing Descartes, “Incidentally the one reason for doing mathematics and philosophy is you can do them in bed. For history you have to go down to the library, for physics you have to go down to the lab… But don’t let me make you give up all your other subjects so you can lie in bed and think.”)
Actually, it’s possible to be gifted in some areas of math but not in others. (e.g. one could be a good algebraist but a lousy geometer.)
Physics is about what happens in the “real world”. Mathematics is about being logically correct. Being good at the one doesn’t often translate into the other.
Nope. Most physicists I know can’t write a decent proof to save their lives. And the leaps of logic in their books make me want to put my forehead through theirs. Even Ed Witten does a lot more conjecturing about what the math “should” work out to be than actually doing it himself.
To expand on this a little, the cutting edge of physics often lack mathematics and not the other way around. Usually, you discover a phenom in nature and then attempt to find mathematics to fit, instead of fitting physics to a mathematical discovery of nature. There are many physicists who simply just search for the phenoms and describe them, instead of further developing existing theories. For example – and I am a bit rusty, so I apologize for any wrong information – multi-dimensional super string theory has mathematics that sort of explains the situation, since the actual math is way beyond human comprehension at this point in time. In essence, it’s merely a rounded “best guess.”
It’s funny, I came into this thread ready to say that the title described me to a ‘t’. I guess I’m not the only one who’s aware of that.
At the level I’ve taken it, physics is much more strongly oriented towards calculus and really basic algebra. Those are the areas of math that I’m weakest at, and so physics was tough for me.
I’ve no doubt that some of the more algebraic areas (e.g. quantum mechanics, string theory) would come more easily to me, but I’m not interested enough to make it through the mechanics and whatnot.
What’s odd is that while I do struggle and make stupid mistakes doing the algebra, I can handle the notations of model and computation theories just fine. Is it a question of interest? Or do they involve different skills?
When you look at a math problem, the symbols represent well-defined concepts. When you look at a physics problem, the symbols represent some theoretical gobbledegook, and that confuses us pure mathematicians.
I had a friend in my undergrad days that could be described by the OP’s statement. We were both math/physics majors, and he was excellent at our pure math courses, but when we sat down to do our physics problems, he would extract a few equations from the problem and go off doing tons of manipulations on them, totally loosing track of the physical systems that the equations were describing. As a result he’d often miss easy simplifications or become so entranced by the mathematics that he wouldn’t have any idea how to apply it back to the original problem.
Yep.
I had a horrible time applying mathematics when it was used in certain (most) areas of physics. I could do whatever I needed to do with the equation or theory or proof or idea. But then when it was time to do something with it, I’d have huge brain farts. (Frequently, I’d end up saying things like “I don’t need you to show me how to get 17. I know the answer is 17. Don’t solve it again. What does ‘17’ mean? 17 what?”)
That can’t be the only answer, because both algebra and calculus are so easy to me they’re second-nature, but I struggled to maked Cs in physics, and couldn’t even pass statics.
Good question. Your description fits me except I’d call myself OK, not weak, in physics. There was a point in my education where I was studying both subjects into the advanced material. But there came a point when I had to decide and I chose math. My best friend at the time had to make the same decision and chose physics. Academically, we both went as far as we could in our respective fields. So he would be strong in physics and OK in math. He always defer to me in math-related questions, and I do likewise in physics queries. I should add that I don’t consider myself strong in all areas of math, just those areas where I’ve devoted a lot of study and work experience. When someone says “I’m strong in math, but weak in physics”, the person is just saying that he/she knows a lot more math than physics, that’s all. As others have pointed out, the subjects are not synonymous.
Maybe I should note that this also apparently “afflicted” at least one genius of legendary renown: J. Robert Oppenheimer. Even his lifelong friends and future Nobel laureate-winning associates in the Manhattan Project made statements that Oppenheimer’s intellect far exceeded there’s–and he was said to have strong aptitude in both advanced mathematics and physics–but when it came to breaking ground in theoretical physics, he just couldn’t do the original thinking. Some accounts recall him quickly grasping the most abstract concepts thrown his way, but when it came to making his own theoretical insights, he would just stand there at a blackboard for hours, unable to connect dots. That said, he later did work re: black holes/quasars (can’t recall) that some believe might have won him a Nobel prize, if not for his having played footsies with the Reds decades earlier.
After running into theoretical roadblocks, physicist Edward Teller (father of the hydrogen bomb, aka “Dr. Strangelove”) apparently had to seek the computational talents of Polish mathematician Stanislav Ulaam, later explaining he simply couldn’t bulldoze his way through the complex mathematics. After the 1949 detonation, both men signed the patent application for the bomb.
This is how things seem to me, coming from the math side of things.
It’s true that being good at math means that the main thing that makes physics hard for the general population won’t be a problem. However, physics is it’s own highly advanced field distinct from mathematics, and it will require years of study even when you are well-versed in math. Somewhat analogously, even if you are fluent in Spanish, you are still going to have to invest a lot of work before Italian completely makes sense. Until you have reached that point, there is nothing strange about saying “I’m strong in Spanish, but weak in Italian.”
So, part if the phenomenon that the OP describes is nothing more than that. However, Mathocist and others are right that physicist think in a way that can seem quite strange to mathematicians. From my perspective, they seem to grok some ideas in a way that completely by-passes the left brain. Some physics people seem to be able to use mathematical concepts and notation with fluency, but when I ask for a definition of a concept they use, they are as adrift as I would be if someone had asked me to rigorously define “happiness”.
For example, when I was an undergrad, I had a friend who was studying General Relativity. I had taken a linear algebra course, so I knew what a vector was, but he would mention something called a covector. Yet when I asked him what this was, he could provide nothing more than that it was “something like a vector, but different.” Yet he was working with vector, covectors, and tensors everyday. This became more mysterious when I later learned the very simple definition of “covector” (and, as a matter of fact, covectors are just vectors, at least as mathematicians understand them; what makes some vectors “co-” has to do with their relationships to other vectors). That my friend could reason correctly while doing physics problems involving covectors when he didn’t know this definition almost seems magical to me. In this example, I suppose that there is a lot of learning computations by rote, but it’s hard to believe that that accounts for all of it. I can only conclude that physicists learn to use mathematics correctly in the same way that I have learned to use prepositions correctly in English. I can do it, but I can’t explain how I do it.
Mathematics involves two very different skill sets:
Arithmetic, algebra, and related stuff that 90+% of people think of when you say “mathematics”.
Proofs.
Being good at the first doesn’t mean you’ll be good at the second. A lot of math majors at my school left the major when they came to the first class that really taught proofs- they’d thought #1 was what math was, and they were good at that, but not good at proofs.
I got a degree in math, did well in the proofs courses- but if I do a lengthy algebra problem, I’m probably going to make a mistake in there, and doing arithmetic in my head- fuhgeddaboutit.
