My talk on October 19th is about “Monsters” in Mathematics. The foundation in mathematics prior to about the 19th century was modelling our physical world. We can think of it all the way back to Euclid and his Geometry, where he was working a lot on intuition. By the 17th century and Newton (arguably) discovered Calculus, known as “Newtonian Calculus” mathematics was still predicated on our physical world. We learned probably in the first week of Calculus I the basic ideas of limits by taking a secant line on a curve and moving one of the points closer and closer until we reached an instantaneous rate of change. This basic form of Calculus helped immensely in the field of physics… yet by the early 1800s problems were occurring in mathematics that its’ current structure could not explain.
With this the idea of “Monsters” were brought into Mathematics: Continuous functions with no derivatives, 1-dimensional curves covering a 2-dimensional plane, and the Cantor Set are some examples. The rest of the talk will explain why such “Monsters” were seen as insane, “psychotic” and “pathological” because they defied intuition. With the discovery of such Monsters it led mathematics to reject pure intuition as a proof that things were true. As such, Mathematics move to a purely logical field and every theorem had to be proved rigorously.
I look forward to teaching the class about these psychotic ideas.
See you all Wednesday,