From Set Theory To Self-Driving Cars


By Zachariah Tyree, PhD (Research Scientist at General Motors R&D)

~ I have a PhD in Pure Mathematics. A common sentiment within this field is that Pure Mathematics sits somewhere above Applied Mathematics and quite a distance above other scientific disciplines. The ranking is even implicit in the name “Pure Mathematics”, as opposed to “Adulterated Mathematics” or perhaps “Contaminated Mathematics.”

Most of my peers in graduate school were targeting positions in academia. Initially, so was I. Over time I began to reevaluate my goals, as I found I did not care for the teaching aspect of the profession. I decided instead to target industries known for hiring mathematicians, and so shifted my research area from Logic and Set Theory to Probability and Statistics, with the aim at going to work in finance.

While my colleagues applied for grants and submitted papers to conferences, I began improving my coding ability and applying for internships. It was an uphill battle at first. Many people I was competing with for internship opportunities had backgrounds in applied mathematics or finance and could point to industry problems they had already tackled. I had proved some asymptotic theorems about a narrow class of harmonic functions. Employers seemed unimpressed.

Eventually I landed an internship building predictive models at an investment bank, and then another internship at Oak Ridge National Lab building discriminative models to detect in-vehicle network intrusions. At the Lab I published a paper on this topic with my internship mentor, Dr. Bridges, who presented it to a consortium of automotive companies interested in vehicle security. Thanks to his recommendation, I was invited to interview for a position at General Motors in “Autonomous Vehicle Research and Development”.

The position was for a research scientist working on artificial intelligence to develop decision and planning algorithms for self-driving cars. The interview process was intense, and I was sorely lacking in much of the background material. They gave me a month to study and develop a project to show I was capable of bridging the gap from academia to industry. During that month I spent every waking hour reading up on artificial intelligence and working on the project. Come the day of the interview, I showed the results of that effort – an artificial intelligence system that can count cards in Blackjack better than a human can. The system worked, and I got the job.

At General Motors, I am excited every morning to wake up and come to work. I get to tackle exciting projects in a high-profile field, surrounded by brilliant people I can learn from each day. It is not where I expected to end up, but I can’t think of a job I’d rather have.

If I could advise my younger self, I would say not to assume industry problems in mathematics are easier or less “pure” than those from academia. I work on problems every day that I’m pleased to say I have absolutely no idea how to solve. And real world problems bring with them unique sets of constraints not found in academia. An elegant solution within the self-driving car space must consider computational complexity, run time, power consumption, security, financial impact, and so on. These added considerations mean that even a seemingly straightforward problem can prove to be quite formidable. So I encourage any mathematician who enjoys working on a wide range of projects to consider becoming a researcher in industry.

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