I think I’m a Platonist when it comes to mathematics. Some scholars feel very strongly that mathematical truths are “out there,” waiting to be discovered. Platonism takes its name from the ancient Greek thinker Plato, who imagined that mathematical truths inhabit a world of their own—not a physical world, but rather a non-physical realm of unchanging perfection; a realm that exists outside of space and time. We reach out there and make discoveries – at least when it comes to the kind of mathematics, I studied in my three Ph.D. years. There were no applied math courses offered in the Ph.D. program. We used to joke that “if a course could be applied it wasn’t offered.” So, I never had the opportunity to take Probability and Statistics, for example. Instead Measure Theory, an abstraction, was offered in its place. Later when I worked at a think tank solving weapons systems problems, I needed probability and statistics. So, I got a job at Northeastern University teaching a graduate course in the subject. It was a struggle trying to learn it faster than my class.
Anyway, I got comfortable starting with axioms, employing lemmas and stringing theorems together and finally finished (in 1962) a thesis that was called Topologically Induced Generalized Proximity Relations. There weren’t many people in the world interested in it at the time – about five of us, including two Russians and a Pole. But something happened that I didn’t discover until 2010. My work became looked at as a significant breakthrough in the field of Proximity Spaces (a branch of Topology) and my findings have been referenced in hundreds of research papers and led to the adoption of new mathematics terms (Lodato Proximity and Lodato Space.). If you Google Lodato Proximity, as I just did, you’ll find many examples of those references. And I have been included in the Encyclopedia of Mathematics.
So, I’ve grown to regard mathematics as a framework within which creative work of the highest caliber is possible. To me. It’s art. Other artists have chosen a different framework, and it is mainly this choice that distinguishes them from the mathematician. Both access their work on the basis of its beauty, its elegance, and its symmetry. The mathematician adds the demand of logical consistency.