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Mathematicians have found their place in finance. (telegraph.co.uk)

Exploring the world of math

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The fast-paced world of finance has always been filled with big numbers. Astronomical numbers. Mind-bogglingly huge numbers that inspire the question: How does this much money even exist? Investors turned to mathematicians for help answering this question. Thus, quantitative finance was born. Simply, quantitative finance is a math-intensive subfield that lets investment firms use computational methods to gain insight into markets.

Sebastian Dragnea is a McGill alumnus currently working as a quantitative analyst, known as a ‘quant,’ at Morgan Stanley, an investment banking firm. He graduated from McGill in 2014 with a joint honours degree in Mathematics and Computer Science. The decision to enter quantitative finance was, for him, natural.

“I liked both sides [of the program],” Dragnea explained. “I enjoyed programming and I enjoyed the math [….] So I wanted a job that combined both of those and the best field I found that combined [them] was quantitative finance. What I found at Morgan Stanley was that I was doing a lot of programming, but also doing math, and also applying a third field of finance, which involved different ways of looking at data.”

Despite working at one of the best-known investment banks in the world, Dragnea only took one finance course at McGill.

“That’s pretty common in quantitative finance,” Dragnea explained. “If you come in with a strong background in data analysis or applied math or programming, that’s all the skills you need, and then you can learn finance on the job.”

This is because the required skills and expectations from a quantitative analyst differ wildly from those of more stereotypical Wolf-of-Wall Street-style investment bankers, whose intensive schedules are infamous.

Projected growth from 2014 to 2024 in mathematical sciences careers was 28 per cent

“A typical workday starts somewhere between 7:30 and 8:00 [a.m.],” Dragnea explained. “I’ll check the [financial] news in the morning, make sure all of our software is working and implement any updates. Then, while the markets are open we have shorter term and longer term projects.”

Short-term projects include tasks like doing research for traders on bonds, or looking at particular funds. At the end of the day, after the market closes, a quant might work on longer-term projects to answer questions that can have a major impact on future success. 

“‘How do we automatically price this security?’” Dragnea said. “That can be anything from short term feed analysis to an idea of research-style questions: What’s the data? What can we infer from this? Okay, this is a strategy we should employ. What’s an algorithm that can implement this?’” 

But the biggest challenge of working in finance, Dragnea explained, is that it’s complicated.

“I’d say the biggest surprise was how much of an imperfect world it is in finance,” Dragnea said. “In physics, a lot of the problems you’re solving have very fundamentally true solutions which are correct all the time, whereas in finance you end up with a lot of approximations, and doing your best in an imperfect world.”

On the other end of the spectrum are the researchers who are seeking to push the boundaries of what is theoretically possible. Especially in more applied fields like computer science and combinatorics, the distinction between academia and industry is growing increasingly fuzzy. Currently a PhD candidate at Carnegie Mellon University, Nicolas Resch graduated from McGill in 2015, and has since been doing research in interactive computation and coding theory.

“I’m studying theoretical computer science, [which is] a mathematical framework for computation,” Resch said. “This lets us design more efficient algorithms [to create better computer programs] and understand the limits of computation, [to understand what computer programs can’t do].”

Our ability to express problems mathematically—and then solve those problems—is what has allowed humanity to travel to outer space, to fly, and to communicate almost instantaneously across the globe.

Experts in sought-after fields like machine learning frequently straddle the line between universities and corporations; a chief example is Andrew Ng, who co-founded Coursera and is both an associate professor at Stanford and chief scientist at Baidu; the equivalent of Google in China. This type of work often involves communication between two individuals on a channel, a process known as ‘interactive communication.’

“The goal is to come up with ways for two people to talk back and forth over a channel even if the channel sometimes distorts what they’re saying,” Resch said.

Even though this is theoretical computer science, people communicate over noisy channels every day. Memory registers are struck by cosmic rays, 1s are mistakenly flipped to 0s in transistors, and hardware is misconfigured on networks.

“[One area I’m working in] is called ‘knowledge-preserving interactive coding,’” said Resch. “The idea is you have two people—called, as always, Alice and Bob—who want to talk back and forth in a noisy environment so some of their messages are being corrupted. The […] requirement is that they don’t reveal anything that they know that they wouldn’t have revealed in non-noisy environment.”

Although this sounds a bit abstract, it’s something that people do in their own interactions every day. Resch compares this to a student taking a test. If a teacher gives the student a problem to solve, the teacher wants to be sure that the student is able to solve the first problem before moving onto the next; however, in a noisy communicative environment, the teacher may be tricked into thinking the student solved the problem when he or she really didn’t. 

Compared to the lucrative salaries available in industry, the incentive to enter academia is usually more personal. Spending five or more years trying to solve a single problem requires both a passion for the subject, and an immense quantity of patience.

Enrollment numbers in the school of computer science at McGill has exploded, increasing from 138 to 465 declared majors in the last 5 years

“I guess I just really like learning math, so I wanted an excuse to learn about all of the topics that I found interesting,” Resch said. “I figured I would spend a lot of time reading about math regardless of what I was doing, so I might as well try to get a degree out it. I also really like research, so it seemed like a PhD program would be ideal for me. And I guess my dream at the moment is to become a professor, so a PhD is really a must.”

Although mathematics has a reputation for being abstract and removed from the real world, its students, like Resch and Dragnea, find in it a beauty and a powerful ability to describe the world, from finding patterns in economic markets to describing how information is transmitted. Numbers and structures are everywhere, and mathematics can give us the power to make sense of them. Perhaps those high school math classes were intended to do more than combat grade inflation—the proof is left as an exercise to the reader.

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