Can there be high drama in mathematics? Really?

(Written October 17, 2015)

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Well, yes, as a matter of fact, there can.  And you don’t need to know math to appreciate that drama.

      Mathematics seems to be the rule book for the universe.  If so, it is a book that has yet to be fully understood by any human being.  The physicist Max Tegmark perhaps said it best when he said that math does not merely describe how reality works, it is reality itself.

      Be that as it may, most of us (including myself) find even the simplest mathematics to be at best boring, and at most something slightly more difficult than impossible.  If we did not need it to keep track of our money, we might ignore it completely.

      Most of us might also consider math to be settled science.  Two plus three equals five, always has and always will.  So how could there be any controversy, much less drama, in mathematics?  Could there possibly be new discoveries yet to be made in math, discoveries that will change how we live?  Is that even possible?

      I don’t know.  It seems that one mathematician has written a book so complicated that not even other mathematicians at the highest levels fully understand it.  Has this book gone beyond the present boundaries and discovered new frontiers?

      His name is Shinichi Mochizuki.  Here is a link to an article about him, followed by some brief excerpts from it in case you don’t wish to read the whole thing.

http://www.scientificamerican.com/article/math-mystery-shinichi-mochizuki-and-the-impenetrable-proof/?WT.mc_id=SA_WR_20151014

[Here are some excerpts.]

In December 2014, he [Shinichi Mochizuki] wrote that to understand his work, there was a “need for researchers to deactivate the thought patterns that they have installed in their brains and taken for granted for so many years”.

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The trouble that he faces in communicating his abstract work to his own discipline mirrors the challenge that mathematicians as a whole often face in communicating their craft to the wider world.
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Born in 1969 in Tokyo, Mochizuki spent his formative years in the United States, where his family moved when he was a child. He attended an exclusive high school in New Hampshire, and his precocious talent earned him an undergraduate spot in Princeton's mathematics department when he was barely 16. He quickly became legend for his original thinking, and moved directly into a PhD.
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People who know Mochizuki describe him as a creature of habit with an almost supernatural ability to concentrate.
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The reason [for controversy] is that Mochizuki's work is so far removed from anything that had gone before. He is attempting to reform mathematics from the ground up, starting from its foundations in the theory of sets (familiar to many as Venn diagrams).
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Well, those are the excerpts.  This article reminds me of the saying that we do not know what we do not know.  In other words, what we do know is like a drop of water in a big lake.  What we know that we do not know is the lake.  What we do not even suspect that we don’t know is the ocean.  We should be humble, more humble than we can ever know we should be.
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