How important is mathematical intuition in physics and other sciences?

Nightvision: How important is mathematical intuition in physics and other sciences?
I just feel like I don’t have that math “sense” that some people do, and I don’t just get math like some of the really smart people in my school.
However, I work really hard and I got top grades in Calculus AB and BC.
In classes like AP Physics C, I can also get top grades but I had to work really hard also.

I’m goin to UC Berkeley and I’m just worried that not having that math intuition will destroy me in universities and beyond. Please share some insights!

Thanks!

Answers and Views:

Answer by David N
Intuition is a no-no in the sciences!

Science is based on direct observation, constructing a theory to fit the facts and scientific proof.

All intuition is good for is coming up with a possible initial explanation…
If you can’t back it up, it isn’t science!

BIG difference between “intuition” and “aptitude.”

EDIT: I will concede the fact that intuition is necessary for theoretical science.
Most scientists are involved in applications, not theoretical postulations.

Answer by fizixx
I agree and disagree with the other response ahead of mine.

You absolutely must have that intuition. You have to be creative and imaginative. You cannot allow your mind to be mired down in dry, cold rules. Below is a famous Einstein quote which I believe totally.

Now….on the other hand, if you do not have the ability to weave together your knowledge and ideas into something concrete and formal with math, then forget it. You have to be skilled at the language of math.

You can possess the greatest and most profound discovery science has ever seen, but if you can’t formulate that into a mathematical framework that fits and weaves into existing theories and physical laws, it is pretty much useless.

So both of these talents and gifts are equally important, in my opinion.

Answer by Drostie
Probably the single greatest paper I have ever read on the difference between US high school maths and professional mathematics is called “A Mathematician’s Lament,” by Paul Lockhart. You can read a copy here if you’re so inclined:

Intuitions drive mathematical thought in the common case, but in US high schools, you are often coaxed to abandon your natural intuitions about a subject in favor of explicit proofs and rigorous details. For example: you’ve presumably seen the Fundamental Theorem of Calculus, and you’ve maybe even seen formal proofs of it. But the deep intuition behind the fundamental theorem of calculus is absolutely brainless: it occurs to anyone as an obvious fact of life:

The Fundamental Theorem of Calculus: “Sums undo differences, and vice versa.”

If you can pick up on those sorts of intuitions, you’re in good shape for mathematics and theoretical physics. Much of quantum mechanics is just linear algebra in funny hats: you just need to say, “oh, these vectors that went like v_i and these functions that went like f(x) were both the same thing — there’s some variable on the inside and I get some number on the outside. And dot products can be integrals etc. etc. There might even be other coordinate systems, other than the x-coordinate, in which we can express f — just as we can express v_i in rotated coordinate systems.” A senior course in transport phenomena can be generally performed by drawing boxes and saying “here’s the amount of stuff going into the box in a time dt. Here’s the amount leaving it. Therefore, the time rate of change of the amount inside the box is this minus that.”

Physical intuitions are similar, but they’re of a different character. Suppose I ask you, “air is full of these molecules bouncing around — presumably they hit each other every once in a while, yes? How far does a molecule go before it hits another one?”

That’s a physical question, and it has an elegant answer. “Well, it’s got to be less than one millimeter,” I say, “because sound is a phenomenon where molecules bump into each other, and sound passes through my ear, which — I’ve seen Q-tips — must be in the millimeter range or so. If the air were colliding into the walls of my ear much more than into other molecules, the pressure wave would probably have real trouble navigating my ear then.”

If you can have these sorts of insights on a topic — any topic — then that topic is where you should invest your academic interest. It doesn’t matter so much how good you are with moving symbols and equations around, and intuiting just what your teacher wants or doesn’t want you to do with the formulas in the textbook.