It is very evidently known fact that, Mathematics is a language of Nature. Human Beings, as a marvelous fabrication of Nature, are very curious to decipher the philosophy behind the natural phenomenon. Therefore, in order to do that, we must understand the language of nature, i.e. ‘ Mathematics ‘, rigorously. That’s why I’m very passionate about Mathematics.
By reading mathematics stuff, much discussion about mathematical problems with my teachers, during class hours and other time, I think that mathematics research is an evaluation process towards an interpretation of mathematical intellect, which can begin with many ways. Here, I’m describing few, which I felt personally, the first, coming to my mind is, Hilbert’s famous 23 problems, some of them are still unsolved and their solutions may provide us a new path to understanding natural chaos. As, the abc-conjecture, which motivated the very new theory, called, “Inter-universal Teichmüller theory (IUT)” by, Shinichi Mochizuki. The Reimann Hypothesis, and Coltaz Problems, personally I like them.The second way is following the patterns, by observations and intuitions, and conjectured, and then prove them to theorems. As, the Fibonacci sequence, they are very rich in nature and lead us the Golden Ratio, giving us another way to observe the universe.
Some of the conjectures are not always gone to the theorems, as Goldbach Conjecture, and much more are still open.The third way of doing mathematics research is generalizing the known mathematical ideas, for example, Newton and Leibnitz gave us the differential calculus by using the concept of infinitesimal, but Cauchy, who gave the idea of Epsilon- Delta, have made the new way to generalize the concept of not only Differential Calculus but entire mathematics.I have just shared my experience, to the way of mathematics research, gained through discussions and specifically MTTS-2016, which reconstruct my viewpoint for mathematics, more thoroughly and enjoyable.