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Mathematical Finance

Fri, 02 Mar 2018 09:26:09 GMT

I wrote this piece for the National Institute for Economic and Social Research's Rebuilding Macroeconomics project.There are three types of mathematicians: those that can count and those that can’t. This aphorism challenges the public perception of mathematics as being concerned with calculation and is liked by mathematicians because it enables them to highlight what mathematics is concerned with, which is identifying and describing relationships between objects. A more sophisticated misunderstanding relates to the way mathematics is conducted. The error originates in how mathematicians present their work, as starting with definitions and assumptions from which ever more complex theorems are deduced. This is the convention that Euclid established in his Elements of Geometry and led Kant to believe that synthetic a priori knowledge was possible. Euclid actually started with Pythagoras’ Theorem, and all the other geometric ‘rules’ that had emerged out of practice, and broke them into...

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