Every once in a while, I enjoy finding particularly important news about mathematics, and yesterday I came across a story that is worthy of discussion, even if my ability to explain it is somewhat hampered by difficulties in typing mathematical notation. In 1985, two mathematicians independently made an important conjecture (which they did not prove) involving square free numbers. Despite the fact that their conjecture was elegant, and nowhere near as complicated as many of the other unsolved problems of mathematics, it happened that this particular conjecture was at the middle of a great deal of other mathematical issues .
In fact, it is the fact that so many problems in number theory are all basically related to the ABC conjecture that makes proving the conjecture a matter of great importance, as it represents a grand unified theorem of a large branch of mathematics. Solving this problem, for example, makes Fermat’s Last Theorem a corollary of a much larger truth, and the solving of Fermat’s Last Theorem was a matter of extreme joy within the mathematical community because of its results. The ABC theorem, as a much larger grand unified theorem, would present mathematicians with logical proofs of a great many conjectures in a short way , making its proof a matter of great and intense interest in showing the logical and deeply unified nature of the universe of mathematics.
While many people tend to be daunted by mathematics, and others like myself only have modest abilities in math that do not quite reach the level of our ambitions, there is a beauty and an elegance in the world of numbers and sets and proofs that helps make a complicated and messy world more easy to understand. The beauty of mathematics (and modeling in general) is the ability to take jagged and messy reality and to divine the deeper unity and beauty and wholeness that lies underneath the corruption and complexity of our fallen world. Mathematics is one of the ways to see the design and purpose of the world beneath the accretions of sin and evil. Everything is so much simpler in an equation than it is in the push and pull of feelings and urges. Perhaps in some ways the interest in math is a longing for an orderly life free from complications and entirely rational.
Let us understand, though, that it is no simple matter to prove the ABC Conjecture. Japanese mathematician Shinichi Mochizuki has claimed to solve the problem in the course of a 500 page long proof, and that proof will be investigated by other mathematicians whose skills are far greater than my own limited capacity in such matters. It will probably take some months for the theory to be confirmed or denied, but if it does, many unsolved mathematical problems will be quickly solved, something that many mathematicians, no doubt, would relish in helping to demonstrate the rationality of the world and of its elegant design. And as limited as my own skills are in such matters as number theory, I too appreciate anything that shows the rationality of the world’s original design, whatever a mess of it that we have made.