“Math professor, programmer, consultant, manager, statistician:” John D. Cook has successfully endeavored to incorporate mathematics to the maximum throughout his professional life. Speaking of such, his blog The Endeavour regularly earns acclaim for its lucid appraisal of math as it appears in both academia and everyday situations. Anyone who loves math, or wishes they could be better at it, will find several gems in this interview with this clear-headed professor.
Can you recall the instant in your life when you decided to pursue mathematics as a formal career?
I always wanted to study math. I briefly toyed with the idea of majoring in music, but I pretty much always assumed I’d do something with math. I didn’t give a career much thought. I just wanted to study math, and assumed I’d find a job using it. I thought I might teach, or do consulting, or work for a company. As it turns out, I’ve done all three.
Does one need to be a math genius or prodigy in order to fashion a professional career in mathematics?
No, but the requirements are different depending on what you mean by “a professional career in mathematics.” There is a continuum of possibilities. At the pure end you have someone whose title is “mathematician.” These are rare. There are a lot more people who use math to varying degrees. It gets fuzzy whether to say whether someone has a career in mathematics at some point.
Jobs as a math professor are very competitive. And if you get one of these jobs, you’ll have to spend a large portion of your time either teaching or chasing grants or both. If you get a nonacademic job in math, you’ll probably need to know about computing. And with either route you’ll need to know how to write well.
Many of our students, both math-impassioned and math-challenged, are on the lookout for useful study tips. Being an elite academic and mathematician, what study techniques would you recommend?
Don’t read math books passively. When you come to a proof or an example, try it yourself before reading further. If you need to, copy the theorem or problem on a piece of paper and shut the book. If you’re able to do it on your own, you’ll get a big boost in confidence. If not, you’ll be prepared to appreciate the solution in the book.
Prepare for classes. At least skim over the new material before class. Have a set of questions in mind. For example, you might have a specific thing in mind that you don’t understand, and you’re listening intently for that to come up. And if it doesn’t, ask questions.
That brings up another point: Ask questions! Most students are too shy to ask questions, so they waste the opportunity to have an expert address their specific needs. Those who are bold enough to ask get all the help.
What electives or courses away from mathematics do you feel harmonize well with intentions for a career in the discipline?
Science or engineering. Computer science. Anything that requires you to communicate: literature, journalism, etc.
Your blog, The Endeavour, impressively alternates between math-centric topics (D programming, C++) and more inclusive posts (“tl;dr,” Emily Dickinson vs. Paris Hilton”). Has that balance between a high math passion and a desire to relate that passion to others outside the discipline been a theme in your career?
I enjoy making connections, either within math or connecting math to applications. That has been a theme in my career. So has communication. Writing a proof, writing a computer program, and writing an essay are all exercises in clear communication.
What personality traits would help someone succeed in professional mathematics? Which traits would hinder someone from doing well?
I keep coming back to communication, maybe because people in technical fields think it’s unimportant. They may go into a technical career to avoid having to communicate with people. But this will hold them back, at least eventually. Even if you’re a genius, that will only take you so far unless you have people skills too.
Do you believe that math (both basic fields and higher, advanced fields) can be studied successfully online, or is a traditional classroom environment preferable?
I’m skeptical of online education. Education is interactive. One minute of personalized feedback can be worth more than an hour of passively watching lectures. Sometimes the interaction is non-verbal, but it’s still happening. Maybe students look confused and a professor reacts, maybe even subconsciously.
Your background in applied math has led to stints in several occupations (statistician, software developer, etc.). What other posts can an education and passion for mathematics accommodate? Would a bachelor’s degree in math be sufficient to pursue these positions, or is higher education a strict requirement?
To some extent, you write your own job description wherever you go. If you’re hired to do one thing, but people see you can do something else, you’ll get opportunities to do that too. So someone hired into a non-mathematical job may still find a way to do math if they can see how math would help their employer.
I don’t think formal degrees matter much, outside of bureaucracies such as government agencies or large corporations. Even then credentials matter more on the way in more than they matter once you’re inside.
What advice or warnings would you offer to prospective students of higher math in the 2010s?
Master the basics, such as calculus and linear algebra. If you think you understand these after taking the required courses, you’re probably mistaken. Read further on your own. Go back and review frequently, understanding things a bit deeper each time in light of new experience.Until you understand something deeply, you’re unlikely to apply it.