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Title:
Why is Number Theory So Difficult?
Speaker:
Abstract:
In this talk, I would like to discuss the difficulty of the world of numbers that everyone is familiar with. There are many difficult problems in number theory. The first theme of this lecture is that “the entanglement of addition and multiplication” is behind this difficulty. In fact, the “entanglement of addition and multiplication” in the world of numbers is so difficult that no one in human history has yet fully understood it. Therefore, in order to solve difficult problems in number theory, we need some clever device to “separate” addition and multiplication. It can be said that one of the ultimate goals of number theory is to understand the “relationship” between addition and multiplication. The so-called ABC conjectures are one of the attempts to reveal such relationships, and the magnificent mathematical device created to solve at least some of them, if not all, is the so-called “Inter-Universal Teichmüller theory” by Shinichi Mochizuki. In the second half of this talk, I will explain the essence of this theory and explain, as clearly as possible, how this new mathematical idea tries to separate addition and multiplication and to clarify their relationship.
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