In my opinion, it is much harder for mathematicians than for other scientists to explain to a layman what basic mathematical research means, why can it be loved since most people look at mathematics with horror. Naturally, I can try to explain how important mathematics is in informatics, physics, and in other science areas, but frankly speaking, my own daily research has nothing to do with either informatics, or physics. It is said that “sometime in the future, it will be applied…”
However, it is also beside the point: indeed, it would be a very shallow motivation for me to hope that the problem I am working on, what I want to prove, might be useful for someone, sometime. I had better admit: I love mathematics for its own sake. I would like to understand and describe relations between abstract mathematical concepts which are also interesting for other mathematicians. Mathematicians, who are curious about those relations too, and make efforts to reveal them.
Though, I must admit that my work is not led alone by my love for mathematics. My real happiness, my biggest inspiration, my deepest driving force to endure constant struggling, sleepless nights, recurring failures is my ultimate goal: being the first who finds the answer. Yes, it is the same motive power that forces a sculptor, a painter, or a composer to create the most beautiful, the best piece of art which cannot be excelled. It is pure luck that there is a non-mathematical benefit of my work which, though it is not a defining reason, but is enough for me: it simply delights me. Of course, I know, there are fewer people who can feel this mathematics related satisfaction than those who are delighted by the aesthetic of arts. However, a creative mathematician does not think about it this way: it makes him very happy if there is even a small group, or one mental partner with whom one can share what one found, and who likes that idea without any personal interest.
Mathematics is a form of art. Deep mathematical results are sources of aesthetic satisfaction, they are the “fuel” needed to continue the research, the fuel that cannot be substituted by financial means. The one who tastes it, needs no explanation, he will understand without words. The one who immerses himself into it, will become its eternal, voluntary prisoner.