# Category Archives: Front Page

A great discovery solves a great problem, but there is a grain of discovery in the solution of any problem. Your problem may be modest, but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery.

George Polya

# Welcome to My Website

I am a mathematics researcher pursuing credentials and a career in actuarial science. I work as an actuarial associate for Brighthouse Financial on the VA Hedging team. See my resume linked below for details about past education and experience with mathematics. See the Research Interests and Publications page for information about … my research interests and publications.

Richards Resume

# My Approach to Mathematics

The earliest experience with mathematics that I can remember is answering word problems posed by my father as a small child. While we waited for the bus, he would ask me questions about trains leaving from a city at different times and at different speeds, and when one would overtake the other. These problems were riddles, knots to untie, mysteries to solve. This experience of math as a sort of detective game has shaped my approach to mathematics ever since. Throughout my childhood and adolescence, and much more so now as a mathematical researcher and quantitative professional, I have viewed mathematics in this way. The metaphor of mathematics as a knot to untie is particularly apt. When I approach a research problem, it is very much in the manner that I approach a complicated knot. I first try to simplify it in any way I can, even if it is not clear how doing so will finally untie the knot. I pull a bit, and try to loosen at one point. When I am stumped at that point, I turn the knot over, and try to loosen at another point. Just so with a mathematics problem. If I am trying to establish some implication, say “Thing One implies Thing Two”, then the first thing to do is suppose that Thing One is true, and see what follows, even if it is not clear how what follows will lead to Thing Two. Can I simplify at all? Can I rephrase Thing One in other terms? If I am stumped, then I turn the problem over, and try working on Thing Two. Can I find some other, intermediate “Thing Three” which implies Thing Two? In this way, working from both ends, I try to “meet in the middle” to finally form an unbroken chain of implication beginning with Thing One, and ending with Thing Two.

My early experience of mathematical problems as exploratory exercises also shapes my approach to teaching mathematics. One of my first goals as a teacher of mathematics is to invite my students into the development of the mathematical theory they are learning.  If my students walk away from my class thinking that what mathematics is is a list of formulas which can be applied mechanistically to certain problems to “magically” obtain an answer, I have failed in this goal. If, on the other hand, my students walk away thinking that “mathematics is for them”, that mathematics is a way of exploring the world that is accessible to them and to which they can contribute in a meaningful way, then I have succeeded in this goal. Mathematics is a house with many rooms, ever growing, and in my courses we explore together a small region of that house.