I will defer to others to write a general apology for mathematics. Here I will simply mention the reason Michael Spivak has given for writing books: namely, to learn the subject himself. Because of this, I would suggest that anything written by Spivak is worth reading.

So, why study physics? Answer: because Michael Spivak has written a book on the subject. Consequently, you now have available to you a map for understanding a subject with no less clarity than the mathematician who wrote it.

What? Spivak is alive!? That's great. I honestly never even considered looking him up on YouTube. I just assumed he was dead.

This is like finding out that Feynman is still alive and giving lectures that I haven't seen.

* I wanted to major in physics, but went into computer engineering instead.

* Physics always seemed glamorous. I know the reality is different, but studying physics makes me feel like a wizard (EDIT: in training).

* I want to be able to read pop-physics and actually be able to dissect it.

* I want to be able to simulate GR.

* I want to understand QFT

* I want to be able to simulate atoms and molecules from first-principles.

* I want to UNDERSTAND

   > * I want to be able to simulate GR.
   > * I want to understand QFT
   > * I want to be able to simulate atoms and molecules from first-principles.

With the current technology, assuming standard model of particle physics (which is QFT) is the first-principle, simulating atoms would take trillions of the age of the universe, let alone molecules, or any effect of GR.

If you haven't already, I highly recommend Feynman's Lectures on Physics: http://feynmanlectures.caltech.edu

While much more advanced than typical introductory texts, it does provide deeper insights than typical introductory texts, which makes it worth the investment.

I'm a beginner, thinking about returning to school for physics, but I'm dipping in with this tome I purchased recently. He's a great explainer for someone at my level.

And I have to brush up on all of the math (and learn calculus...) in order to fully understand. It's exciting that reading him isn't just a cold hard wall. It's proving to be a great guide into what to sort of triage my studies.

I strongly second this one! (Though I have to admit that I purchased a not-cheap edition of the first volume to get started -- though I prefer reading from paper, and don't yet own an eReader and have a bit of a burgeoning library anyway. But thanks for the link! it's nice to have the rest on hand).

I'm more at the level of Goldstein for Mechanics, and learning about the Lagrangian. Of course, there's still much to learn from Feynman.

For me it was that physics was about reality. In high school the key moment occurred when in a physics lab, after calculating and measuring and calculating more, we placed a cup on the floor, rolled a marble down the ramp and off the desk - and it landed in the cup! At that moment I realized that all the math I had been studying actually meant something in the real world, and was useful for explaining questions I had about the world.

A lot of contemporary mathematics have physical roots. Some things I like: Donaldson theory and Seiberg-Witten theory in differential topology, Gromov-Witten theory in sympletic/algebraic geometry. Knowing physics is not necessary to learn these things, but some rough idea of what QFT is doesn't hurt.