Let us talk about careers in data science! Mathematics, statistics, data analysis skills are quite big on the job market these days, I hear questions from people all over the world (literally - from Cambridge to Kazakhstan) about the best way to apply their technical skills.
To learn about math careers, I asked my friend Alexander Isakov. Alexander did his bachelor at Harvard in physics and math, and then stayed at Harvard to do a PhD in physics, which he finished this year (congratulations!!) Alex has tried himself in many fields, to much success: his PhD focused on physical and social networks; he invented a medical device for surgeons and spun it off into a well-funded startup; he started a data science company.
For the past few years, Alex has worked on understanding the behavior of complex systems both in his role as an academic and as a businessman. "I have always been interested in understanding the macroscopic world; how we affect the world we actually see and consciously interact with every day and how it affects us, often without our knowledge", he says.
In graduate school, he studied how people assemble into groups to perform risky tasks. In a collaboration with Luke Glowacki, Nicholas Christakis, James Fowler, and several other prominent scientists, he studied data from a small society in Africa to understand how people form groups to conduct stealth raids. On a different note, together with L. Mahadevan (his advisor) and Ben de Bivort, Alex made models and led a team of undergraduates as they did experiments on how fruit flies recover straight walking behavior after leg injury. They discovered that proprioception, the ability to sense where body parts are and how much force they're applying, plays an important role in the recovery process, which provides insights into many more organisms than just flies. "It's all a matter of individual units coming together and learning to coordinate, be they legs, bacteria, or even humans", he says.
In business, the problems Alex solves seem more accessible, and the tools he uses are different - physics equations give way to techniques from data science and machine learning. But, at the end of the day, he thinks they share a common spirit. "How do we predict customer and employee retention? How do we optimize online customer experiences? These are all questions of human behavior, and companies have been observing and collecting data for years - we help them figure out what it means, and how to convert it into actionable strategies that lead to business improvement."
As a true scientist, Alex approached my request for advice very seriously and devised what I called the Framework of Achievement for Quants (FAQ). The framework includes three main components: 1) learn the theory; 2) think of an application; 3) devise the implementation. I asked Alex to expand on his ideas and talk about building a successful career in data science. Alex, take it away.
1. Learn the theory.
"I am a big fan of understanding the theoretical underpinnings of the sciences; therefore, you should take rigorous math and science classes to understand the foundations and learn to think rigorously and abstractly. If we think of specific skills to learn in the first two years of college, there are two main categories: a) the basics of mathematics, including multivariable calculus and linear algebra, as well as foundational proof-based coursework and b) learning to model the world with both differential equations and statistics.
In terms of statistics, many courses tend to be a bit more applied, though of course I encourage you to take some that dig deeper into the theory. You will come out with a basic understanding of probability, how to model processes that have noise (and believe me, the real world has lots of noise), how to predict events that occur sequentially in time, and so forth. If you take statistics-type classes in social sciences departments, you will also know the specific tools as they apply to those fields. In economics, for example, you will spend a lot of time dealing with time series. In more foundational statistics courses, however, you will learn more generally about methods that have broad applicability across disciplines.
2. Find interesting problems.
Once you have the theory down, find interesting problems to solve. I recommend going to people that you personally find interesting, and asking them about the challenges they are thinking about.
It is neither necessary, nor do I think advisable, to think of yourself purely as a "physicist", a "chemist", or a "statistician" - that just limits the problems we expose ourselves to. Ultimately, the highest classification that matters is being a curious human being. If you're majoring in statistics and someone tells you about an interesting problem in physics (or literature!), don't dismiss it - see if you can find a way to contribute! We are all human beings first, and scientists second.
3. Implement your skills and do the work.
To implement your theoretical and practical skills, find a project that requires you to either build theoretical or data-driven models (better: both). You can start learning computer programming at various levels of sophistication, and I strongly recommend learning at least basic programming early.
As you develop your computer science skills, approach a professor and ask about a project you could do that would involve some simulations, agent-based modeling, or statistical analysis. Doing a real research project would necessitate new ways of thinking that were not necessarily available to you as a freshman or a sophomore.
If you are interested in data science in particular, go heavier on the stats and programming. But again, the way to get good on the implementation piece is to practice implementation. As you do more programming work, you might discover you want more theory foundation from Step 1; go back to the start of the framework and continue to get better.
4. Solve problems that arise instead of looking for problems that fit your tool.
My PhD advisor (Professor Mahadevan at Harvard) encouraged me from the start to follow the problems, and not to limit myself by tools. Your value as an academic, a businessman, and/or a leader comes from coming up with creative solutions to problems as they arise without worrying about the form of the solution. Sure, it's good to have a big bag of tools - statistics, simulations, differential equations, knowledge of problems in multiple disciplines. But you'll quickly discover that real world problems are not often nails that lend themselves to banging with the hammer given to you in the classroom! They have intricacies and caveats, missing data, multiple paths of approach, and you'll have to deal with the tough challenge of decision-making under various constraints - you will have to use your knowledge and current tools to build others until a solution is reached, and that's the critical skill to learn.
5. What is the difference in your approach on the undergraduate and graduate level?
Graduate school is different from undergrad. In your undergrad, you are more focused on learning tools and being exposed to a broad range of disciplines. I encourage you to work broadly in your undergrad: try projects in different fields. It's good for developing intuition and different perspectives. For example, do a project in stats, physics, and anthropology, and begin early in your career. At the end of a successful undergraduate degree, you should feel comfortable solving a range of problems.
At the graduate level, you are being trained to be the next thought leader - to formulate good problems of your own, problems that contribute in important ways to our collective understanding of the world. Actually, if you follow the advice above, you may be able to start doing that already towards the end of your undergraduate career!
6. How do you work with mentors and advisers?
Don't (necessarily) take the first problem given to you. Don't do things just because you hear a lot of mainstream buzzwords. The key to growth and increasing your skillset is going for interesting problems. You should strive to find a mentor who you think has good problems - in the academic world, that's typically a professor who is a leader in his or her field.
BE SMART. Have advisors. Ask questions. Have courage. Advisors are there to share interesting questions, and ultimately they are fellow human beings. Talk to them: come to the office hours, and speak generally at first, and then move on to questions that you are thinking about now; share what led you to thinking about these questions, and why you think the questions are important.
The key mistakes that I made early on: I thought I knew well enough. I would find one or two people that were a good fit, and I would stick with them instead of growing my network of relationships. However, even if you talk to one or two extra people, you expand your horizons drastically just by getting new perspectives. You can't invent everything on your own; it's not particularly efficient or good use of time.
7. Learn from People that Cross the disciplines.
I really admire the Renaissance man - people that cross disciplines and are extraordinary problem-solvers in multiple fields. It all started with looking up to my parents; my grandfather was also a physicist who invented many, many dozens of patents. I absolutely look up to my advisors, and professor Mahadevan at Harvard in particular.
At the end of the day, I want to do everything. Part of it is to become a leader in several fields; one of these fields is business, where I could solve real practical problems.
In academia, I want to answer questions about humanities and philosophy. How do we understand society from the basic processes of evolution of emotions? How do we actually ask the control theory questions - how can we create institutions and mechanisms for making it better? We should ask questions about the way the practical world works and solve them, ultimately making them better.
Overall, I wish you to have courage to ask better questions and solve important problems.
Links: Alex's data science company, Pallantius, can be found here: www.pallantius.com