17 Equations that Changed the World
This book covers the 16 equations (and one inequality: second law of thermodynamics). It starts with Pythagoras and ends with Black-Scholes (-Merton) formula for valuing derivatives. The book covers complex numbers, waves, Fourier transforms, thermodynamics, quantum mechanics, the logistic equation and chaos. The discussions, though, qualitative and informal reveal both the profundity of Mathematics and the complexity of the world we live in. The book uses equation as the starting point of the noble human endeavour of Mathematics. The narrative gives each equation a historical context and an exploration of how one insight frequently unexpectedly connects with another domain and once ‘revealed’ (or created, depending on one’s philosophical bent) translates into applications in the ‘real’ world.
The author aims to highlight the importance of Mathematics as a human endeavour. However, there are cautionary tales to prompt the careful and intelligent use of models. Always remember the assumptions and the limitations of models.e.g randomness. imprecision or incomplete information, deterministic chaos (providing a horizon of predictability).
I found the chapter on the Black-Scholes equation the best insight into the Global Financial crisis as well as the most potent of the ‘cautionary tales’. The author ends by arguing that such ‘failures’ are human errors of judgement and motivation for more Mathematics not less. As a layperson, I agree.