What goes on inside the mind of a mathematician? Where does inspiration come from? In this lecture, based on his book of the same title, Cédric Villani describes how he encountered obstacles and setbacks, losses of faith and even brushes with madness as he wrestled with a new theorem that culminated in him winning the most prestigious prize in mathematics, the Fields Medal.
Markets are Efficient if and only if P=NP
Abstract
I prove that if markets are weak-form efficient, meaning current prices fully reflect all information available in past prices, then P = NP, meaning every computational problem whose solution can be verified in polynomial time can also be solved in polynomial time. I also prove the converse by showing how we can "program" the market to solveNP-complete problems. Since P probably does not equal NP, markets are probably not efficient. Specifically, markets become increasingly inefficient as the time series lengthens or becomes more frequent. An illustration by way of partitioning the excess returns to momentum strategies based on data availability confirms this prediction.
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