An answer to a question on Quora: Is pure math hard? What type of people would study pure math?
Any mathematics is hard, not only pure mathematics, but pure mathematics is special, and is perhaps is hardest of all. I love this motto coined by my colleague Rob Wilson:
Mathematics: solving tomorrow’s problems yesterday.
Of course, it is about pure mathematics — applied mathematics solves today’s problems, and solves today. But it was pure mathematics which had ready mathematical methods for physicists when they started to develop the general relativity theory and quantum mechanics, and for cryptographers when they needed computer based methods for signing and authenticating electronic documents, including financial documents and money transactions — the very existence of the global financial system now depends on this tools based on mathematics of yesteryear.
So, what type of people would study pure math? People who love precise, concise, very abstract thinking, people who value clarity of thought. Serious study of pure mathematics means choosing a specific lifestyle: first of all, you have to love the process of thinking, deep systematic thinking with full concentration of all your attention on it. Also, you have to have a sufficiently long attention span, ability to think, and do nothing else, for long periods of time.
So, the shortest answer to your question:
People who love to think.