Encountering some new courses like quantum mechanics, theoretical solid state physics and some other courses made me feel dumber than I ever felt. 

Basically, I'm that kind of students who hate to take the pure approach towards the science, that's why I hate my pure mathematics class. However, that's why I kept looking for physical intuition behind  every single concept I encounter.

I asked my professor about my approach because it was taking me too long to figure these concepts out, from an intuitive stand point, beside the fact that the whole semester in nothing bust 2.5 months, and he literally told me:

" Intuition doesn't really matter in the beginning, take a pure approach, and you shall figure the intuitive  point behind these concepts during the course of the process! "

Just wanted to know different thoughts on this point?  


closed as primarily opinion-based by ACuriousMind Jan 20 at 9:54

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ I'm closing this question as primarily opinion-based because it is not evident that there is a clear, objective idea of what "intuition" means or what its importance is in physics $\endgroup$ – ACuriousMind Jan 20 at 9:56
  • $\begingroup$ Yes, and I also think this is off topic for this site. $\endgroup$ – David Z Jan 20 at 13:18

In my experience both matters.

Take for example something that I've learned recently. The theory of characteristic classes and vector bundles. An intuitive interpretation of characteristic classes is that they measure how a bundle twists. Twisting is like curvature, an intuitive geometric concept. But whereas the name curvature intuitively helps is to understand what the Riemann curvature tensor measures, the term characteristic class has a name that is of no help in determining what is useful about it.

Here's another example. Homological algebra is well known for being rather heavy going mathematically. It's essentially to do with an operator whose square vanishes $d^2=0$; it took me a while to realise that I'd seen this before somewhere and this somewhere was in the calculus where generally we say infinitesimals like vanish when squaring, $\delta^2=0$; and it turns out that in the smooth context, homological algebra is essentially the De Rham complex which just encodes the generalisations of the derivative to the vector context, ie $grad$, $curl$ and $div$; except here it's not just for 3d vector spaces but for any manifold of any dimension!

A final example is more physical. Consider quantum spin, it was first introduced into QM on a suggestion from Pauli that there was a 'hidden' rotational symmetry in QM which inspired Uhlenbeck and Goudsmit to revive the model of a spinning electron, despite the fact physically, if made no sense. The problem of course, was to make sense of it, and this means we have to begin somewhere with a good first approximation and that relies on physical intuition as to what is most appropriate under the circumstances. Later, it becomes more formalised and further removed from that accessible first intuition, sometimes to the point where that first intuition is not visible and then it's something of a chore to learn how physicists think about physics. The best thing is to ask.

Good luck in fixing that 'dumb' feeling, we've all been through it at some point, I'd say, rather than feeling comfortable with that dumb feeling, learn to hate it, and then, fix it (though I'd question whether theoretical physics is your forte if you find yourself 'hating' pure mathematics - there's a lot of it there, and it's something you might want to spend some time thinking about, particularly when there are so many equally interesting and enticing things in the world).


Not the answer you're looking for? Browse other questions tagged or ask your own question.