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Elliptic curves I: Why?
What motivates studying a mathematical concept
“All highly competent people continually search for ways to keep learning, growing, and improving. They do that by asking WHY. After all, the person who knows HOW will always have a job, but the person who knows WHY will always be the boss” — John C. Maxwell
The sequel to this article can be found here.
It’s surprising how many people think of frontier research mathematics as being little more than ‘doing bigger and bigger sums’; indeed, university management holding precisely this misguided view has led to the demise of more than one mathematics department. Some people take the even stranger view that mathematicians just make up a random concept and study that for the sake of it, making the whole thing seem rather pointless.
Yet if you actually read a serious research paper, most of the opening section contains some form of motivation, an explanation as to why the concept they’re considering is a natural one and why what they’re doing is worth it. For example, sometimes, particularly in applied mathematics, the work in question comes from a real-world problem. Sometimes the work directly addresses a question or conjecture made elsewhere. Sometimes it’s an attempt to adapt something from an analogous situation elsewhere in mathematics that seemed…
