Ever wonder what a mathematician actually does? Or how you can train computers to take over the world? Or what kind of degree could give you the flexibility to be involved both in medical imaging research and machine learning?
This week, Yellow Parachute sat down with Alex Gutierrez, a 5th year PhD candidate in Mathematics at the University of Minnesota and National Science Foundation Fellow, to chat about finding his passion for mathematics, the importance of mentorship, grit, and how detecting planes in the sky and cancer in the brain rely on the same mathematical principles.
For Alex, “Math is a less a field than a set of tools and a way of approaching problems…” Problems such as how to make computers smarter and MRIs more versatile. One of Alex’s main research interests is statistical signal processing. Statistical signal processing has its genesis in the development of radar during WWII, used to locate enemy ships and aircraft. Radar works by sending electromagnetic waves in every direction, and measuring the signals that bounce back. The problem is that the electromagnetic waves bounce off everything, from birds to clouds to planes. There are all kinds of blips and false alarms. As Alex puts it, “You’re trying to decide is this a flock of birds coming over the horizon, or are these German bombers?”
The measurements Alex is working with these days come from MRI, or Magnetic Resonance Imaging. Instead of German bombers in the sky, MRI aims to locate cancer in the body, for instance. “That’s the goal of statistical signal processing. Given these noisy signals, can we detect or estimate whatever it is we’re trying to find, whether it be German Bombers or cancer?”
MRI machines require subjects to be completely immobilized and horizontal in a claustrophobic tunnel, but Alex’s team is working on developing a machine that would fit just over the subject’s head, and have a window in front, like a space helmet. “So we can see what the brain is doing as you’re moving your arms. Or as you’re trying to catch or throw a ball.” This would enable new types of neuroscience.
Machine learning is a bit more self-explanatory. “It’s the branch of artificial intelligence where you’re trying to teach a machine to do any task currently done by humans. So I’m trying to teach a computer, essentially, first of all to recognize, say, the difference between cats and dogs, but second of all, can you teach a computer to recognize what a cat looks like to the extent that it could draw the cat itself?”
Machine learning lies at the intersection of statistics, mathematics, and computer science, a field that’s currently exploding. That’s why CAPTCHA problems, the puzzles you complete when signing up for a newsletter or logging into your bank account to verify that you’re a human are getting much more complex—computers are getting better and better at imitating humanity. “So you’re on the dark side?” YP asks Alex. Alex doesn’t respond.
So how did he get here? From his impressive credentials and exciting research, you might assume Alex has been laser-focused on mathematics since he could add two and two, but in fact, his path was a winding one. He entered undergraduate as a business major, and switched to biology, chemistry, and Spanish before a certain professor, and a paid research opportunity, opened his eyes to mathematics. That professor, who had a physics background, was able to make math fun and applicable to the world: “Everyone in the math department is fond of saying how math is everywhere, but very few people can actually justify why it’s everywhere, and what we mean by that. But he was close enough to physics and close enough to a bunch of different areas that he could explicitly make that connection, and did, all the time.” Alex never looked back. “I’ve really been lucky to have great mentors the whole way, which has made it easy to want to continue.”
In addition to good mentors, Alex cites the importance of perseverance, or grit, in succeeding in his field. “So much of it is just having resilience. Work ethic. There is this cult of genius in math departments where everyone thinks that you must be a genius to succeed. I don’t very much subscribe to that. I think that the people who are successful are the people who are staying at it and working hard.”
But lest you think Alex is all work and no play, he’s recently become an avid rock-climber; he spent spring break climbing the red sandstone cliffs of Red Rock Canyon outside of Las Vegas with several fellow mathemateers. Partially because of the often collaborative nature of mathematical research, Alex says his department has a fun and healthy social scene. Plus, his degree has sent him all over the world, to summer schools and conferences in Canada, Germany, Austria, and Hawaii.
So what advice does he have for a young person who wants to get in on fields exploding with groundbreaking research, and travel the world while doing it? “It’s hard to get a true flavor of math when you’re taking calculus in high school, for example. Research problems are certainly nothing like problem sets. Take some sort of logic class or introduction to proof class as soon as possible, and that will really be the true gauge of whether they might like this. But also, stay pretty well-rounded. I’ve very happy I explored biology, chemistry, other sciences…There’s no need to specialize early.”
And of course—seek out mentors. And stick with it.
