[nileshtrivedi]

Can you recommend a book/resource that explains this from first principles and introduces the math involved as well? The books I've read either exclude math altogether or if they don't, they assume that reader already knows and understands all the math that is required for this.

[raattgift]

Just about any standard textbook on General Relativity will cover the content of my comment in the first chapter or so.

I like Carroll's [ https://www.preposterousuniverse.com/spacetimeandgeometry/ ] and indeed, you get to deal with intervals and worldlines in chapter 1.

It assumes you know or are ready to learn some differential calculus and how to read a formula with an integral but it (maybe a bit steeply) teaches tensors (and some aspects of vectors and scalars) across the first couple of chapters. Carroll provides some (quasi-)samples under the "Lecture Notes" tab, but the book itself has benefited from editing. He also supplies links to alternatives that can be had for free-as-in-beer.

[SAI_Peregrinus]

The classic text is "Grativation" by Misner, Thorne, and Wheeler. It's very dense, but very thorough. The other classic is "General Relativity" by Wald. They don't really include the math background though, for that you need texts on multivariable calculus.

[spaceseaman]

You would be interested in this book

https://en.wikipedia.org/wiki/The_Road_to_Reality

It is quite long and dense but explains the math from first princples like you want.

[reubenswartz]

Check out "Why Does E=MC^2". (I wish I understood it better. I think some of what raattgift was saying is related to the deeper issues, which the book does raise, and which I paraphrased at a very high level.)

https://smile.amazon.com/dp/B002TJLF7W/