TITLE: Real world uses of homotopy theory
QUESTION [19 upvotes]: I covered homotopy theory in a recent maths course. However I was never presented with any reasons as to why (or even if) it is useful.
Is there any good examples of its use outside academia?

REPLY [2 votes]: Homotopy methods can be used for solving nonlinear equations (algebraic and differentials) where these equation appear in different problems in engineering and science. One example of these equations is a system of nonlinear algebraic equations which is a model of electrical circuit. This mathematical model consists of two equations which can be easily solved using Newton homotopy to find the value of the current in this circuit. For more information, please see my PhD thesis entitled "Newton homotopy algorithms for solving nonlinear systems" and my papaers presented in some conferences and published in some journals upon my name: Talib hashim Hasan.