Beautiful Mathematics

I met a person recently who told me that he was doing a PhD in Mathematics. I always have had awe for people who are researching in Math or Physics. Having read stories of physicists and mathematicians who were glorified by war efforts to build "The bomb" and all the frenetic activity that went with it, I always have wondered if the people of the present generation have much to offer that will take the whole world by storm like Einstein and others did in their time. Does anyone today, have the opportunity to capture the imagination of the entire world, with theories that would destroy the theories that we have held to be true for a few hundred years?
What does this Math PhD guy do really? I regretted asking the question after I saw how uncomfortable it made him. He mumbled a few words about how "research in Mathematics is never really with an application in mind. You know, you have some math... and... you work around with it you know... and see what you get from it.." he trails off. I am still listening expectantly. "You know, you can work with it for years and never really get anywhere..". Then he goes on, "You know, math is full of axioms, so we never can say if we are getting anywhere by accepting them". His voice trails off again. Then I got his point. He thought I was too stupid to get it in technical terms.
"So it is more like free thinking? You turn axioms out of your mind and try looking at things differently?", I asked. At my mention of 'free thinking' he jumped. He excitedly says that is so and that it was free thinking without being bothered about applications. "More like art for art's sake?" Yes he says, beautiful Mathematics. They have trouble getting funds for their work. No one can explain why beautiful Mathematics is important. That is if you can explain to someone (especially people who are in charge of supplying funds) how math can be beautiful in the first place.
Then again, isn't Mathematics our feeble attempt to understand a universe that has so many mysteries? We take pleasure in knowing that there are some numbers that seem to resonate with the universe and occur everywhere - like pi. There are others that we will never understand, never feel and never be able to imagine like infinity. Yet Mathematics is our only tool aiding us in hope of understanding the universe - a means to find order in chaos, an attempt to structure and organize life. Almost like religion that is based on strong beliefs, passed down from generation to generation, and little else.