I've just read "The Music of the Primes" by Marcus du Sautoy, it is worth a read. I'm not from a maths background, but I'd like to develop a deeper understanding of the concepts. The poetry of math is something I'd like to experience and I feel like I didn't find as much joy in math as there is in the world of numbers.

Elliptical curve crypto-systems sounds like a direction I might want to head towards. I have no concept of where to start, or how in depth I would need to go to understand elliptical curves. Geometry was the most interesting math to me, but I am willing to move in different directions based on advice and materials.

In sum, I want to sit down with math again to give myself the chance at something I haven't experienced, the music of mathematics. There is no timeline or test on the horizon. What captivates you about math? What are the most interesting questions? Where would you recommend I start?

Thank you for any thoughts ahead of time.

  • $\begingroup$ You should make your question more precise. State your mathematical background and aim more precisely. If you only want fiction math, request for such list. If you actually want to do math at research level in future, state so. $\endgroup$
    – user45099
    Apr 16, 2013 at 11:20
  • 1
    $\begingroup$ Elliptical curve cryptography definitely isn't for the faint of heart... $\endgroup$
    – vonbrand
    Apr 16, 2013 at 12:06
  • $\begingroup$ Nothing to do with elliptic curves, but you might be interested in Poetry of the Universe by Robert Osserman, goodreads.com/book/show/282508.Poetry_of_the_Universe $\endgroup$ Apr 16, 2013 at 12:42
  • $\begingroup$ The prerequisites for understanding and appreciating the beauty of the theory of elliptic curves encompass pretty much an entire undergraduate degree. Just to expose yourself to some beautiful mathematics, you could have a look at "Proofs from THE BOOK" by Aigner and Ziegler. If you are serious about elliptic curve cryptography and want to start learning mathematics in depth, pick up an undergraduate Calculus book and see how you get on. $\endgroup$
    – Alex B.
    Apr 18, 2013 at 9:45
  • $\begingroup$ You are completely correct, sorry for the delay. I took Statistics, Pre-Cal, Algebra, and Geometry in high school and almost nothing in college. And thank you for the suggested reading. I was afraid that elliptical curves might be beyond my reach. Do you think the best thing to do is to just pick up any Calc book and start working the problems? $\endgroup$ Apr 18, 2013 at 14:00

2 Answers 2


A very nice book is Paul Nahim's "An imaginary tale: The story of $\sqrt{-1}$". The books by William Dunham ("When Euler met l'Hôpital", "Journey through Genius", and others) give a historical perspective.

Free for personal use are several nice textbooks by The Trillia Group.


That book is really inspiring. I have a background in physical chemistry but this book made me studying mathematics just because I found it pleasurable. I've started from basic undergraduate mathematics books and currently I'm studying G.C.Smith's "Introductory mathematics algebra and analysis" book.


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