Keeping track of different mathematical works

[Akash Pratap Singh]

I just like to read and know, and still, I realize that there have been so many works in mathematics and so much to study which I don't even know of.
Is there any way I can keep a track of different mathematical works so that I can read them. For example, it was not very late when I came to know about the existence of hyperbolic functions and pedal curves and Hamiltonian Mathematics. If I just have the hint about the existence of such things, I can dig up and read.

 

[fresh_42]

I just like to read and know, and still, I realize that there have been so many works in mathematics and so much to study which I don't even know of.
Is there any way I can keep a track of different mathematical works so that I can read them. For example, it was not very late when I came to know about the existence of hyperbolic functions and pedal curves and Hamiltonian Mathematics. If I just have the hint about the existence of such things, I can dig up and read.

You can start with Wikipdia articles, at least it gives you the hint where to look and sometimes also links to sources which are available online, although often just textbooks. Of course this assumes that you already know what to look up. Unfortunately "the existence of such things" covers more than can be studied during a lifetime. So without any specifications, the answer to this question is simply too long to even write it down, not to mention to look it up. You tell me an area, and I will tell you ten technical terms, which alone require months of study.

 

[FactChecker]

Is there any way I can keep a track of different mathematical works so that I can read them.

That is an admirable goal. Unfortunately it is completely impossible. Mathematics is the "language of science" and its range is huge. You would be in danger of spending much time on things that you will not be interested in. I recommend that you get a book (article?) on the history of math and see what subjects interest you; then follow those leads.

 

[jedishrfu]

I got an eye opening experience with the Prof Elwes book that covered many areas of math with brief paragraph discussions. It was enough to get me to research them further.

https://www.amazon.com/dp/1554077192/?tag=pfamazon01-20

There’s also the Princeton Mathematics compendium that covers a lot of areas but is much harder to read.

https://www.amazon.com/dp/0691118809/?tag=pfamazon01-20

 

[fresh_42]

That is an admirable goal. Unfortunately it is completely impossible.

So true. I've gone through some books of mine just yesterday on the hunt for good problems. I haven't found any, yet, but it became obvious, that even to state a problem from, say page 50 onward, it sometimes would take me weeks to even explain the terminology and in many cases learn them myself. Additionally the language changed throughout the years, e.g. what we now call Lie algebra has been called infinitesimal ring. The times of universal scientists are definitely gone.