Math Minds: David Craft

Dr. David Craft is a modern-day renaissance man. He graduated from Brown University with a degree in Mechanical Engineering, then went on to a mathematical Ph.D. in Operations Research from MIT, and currently works with Harvard Medical School in oncology research. Among his many interests are Gallery 263, foraging, and creating music. He is also working on a new book- it will be titled Something About Infinity- and it presents interesting mathematical topics in an enjoyable, easy read.

He sat down with Tori and Zach this past week to discuss the math side of his life, and to get his perspective on the challenges of math modeling in medicine.

David Craft, Ph.D.

So we’ve done a little research on your background, and you have a lot of interests, I can tell. So, what did you start with? What did you study at school?

At undergraduate I studied mechanical engineering, and I studied… well, I usually say I studied applied math at MIT, but really it was a subject called Operations Research. It’s Applied Math for real world operations.

What do you do now? You are an assistant professor at Harvard Medical?

Right, but it’s a pure research job. I have a nice position where it’s research, and I get to work on whatever I want in the field of radiation therapy for cancer treatment. So the basic idea is this: when you have a tumor that you have to hit with radiation, it’s like a puzzle- how to bring the radiation beams in. We try to conform to the target and try to avoid everything else. That’s the balance, it’s sort of a high dimensional tradeoff because there’s the tumor, but all these different organs around it like the heart, or the liver, or whatever is nearby, and you have to play a sort of balancing game amongst all those things so that’s where the  math comes in.

So after all of these hobbies, jobs, and working in Oncology, what is bringing you back to pure mathematics?

Well, every couple of years I’ve come back to just reading a book on math; popular or in-depth books, but not quite textbooks. I’ve always quite enjoyed that, it reminds me of my school days and I like that. So the reason that I wrote this particular book is that I would be talking to friends and describe some little piece of mathematics. For example, that the number of primes is infinite. Just little topics. And I really enjoyed saying that to people, and then getting them to understand what it would mean to prove such a statement, and then getting them to understand the proof. The fact that you can do that all within like 20 minutes, even for people who wouldn’t consider themselves good at math, Is just great.

I never became a math professor because I really like the one-on-one. I have been a math professor [at Williams college] for a year, and it was good, but I like the on-on-one. I’ve had a lot of those one-on-ones with people at bars or parties, and I decided at some point that I could probably cobble these little vignettes into a book.

So what would you say is your mathematical specialty?

Optimization. That includes linear optimization or linear programming, and more generally, convex optimization, continuous, discrete, it’s all in that field. That’s what I mainly studied at MIT when I was there, and it’s the field I’m most comfortable with.

Is there anyone in particular that you would credit with guiding you to mathematics?

My first advisor at MIT, Larry Wein. To say the least, he’s a really good mathematical modeler. He taught me to take a problem and quickly condense it for the real world, down to the core essence. I also had an advisor at Brown, Allan Bower. I did my senior thesis with him, and that was my first chance to really get into modeling. I worked with microvoids in this semiconductor metal-people were interested in seeing these holes and how they would travel against the current. It was a really detailed finite analysis model of that, and it was my first exposure to using heavy-duty mathematics to understand and solve real problems.

What is your favorite math class that you’ve ever taken?

I liked a lot of them at MIT… Linear Programming- it’s basically applied Linear Algebra. It was just such a nice, one-semester length topic that you can really start from basic ideas of vectors and linear independence and you can get all the way to strong theory of linear programming duality, and some advanced algorithms to solve linear programs. It’s just so consolidated and the theory is so tight; it’s a complete picture.

Dr. Craft foraging in the Boston wild.
image: bostonmagazine.com

Do you have a favorite mathematician?

Maybe this statistician from the 20^th century- Sir Ronald Fischer. He modernized many of the statistical tools that we use today. It’s hard to actually understand how he came up with a nova, for example. He was a heavy duty mathematician and I think he was a genius. Of course, I’m a big fan of Einstein’s math too.

What is the most difficult part about your work in oncology?

What I generally end up working on is the machine delivery of radiation, because that is the kind of problem that I can actually write down on a piece of paper. What a lot of people are moving towards, and what a lot of mathematicians are chomping at the bit for is modeling how cancer grows and dies by radiation. They want to use differential equations and they want to use models to do it, and that works great for Astronomy when you’re looking at 3 bodies in a field. But when you have the human body you have hundreds of thousands of molecules , and it’s difficult to see what’s going on in the body at that microscopic level. Drug companies will develop some drug, begin testing it, and it alleviates some totally different disease. So it’s really the blind leading the blind out there in biotech, and there’s real mysteries about it.

So in my area, we struggle with how to best deliver radiation to a patient. It could be 5 days a week straight, or two days on one day off. We just don’t know, and mathematical models are so hard to test. So I think we need to rethink about this, and develop new methods. I don’t think this idea of using traditional differential equations like we all learned applies to cancer. There’s too many parameters, too many ins and outs, too many uncertainties. We need new strategies.

So how did you go from Mechanical Engineering to Oncology? If you started over now, would you do more biomedical engineering?

I did mechanical engineering for a couple of years once I graduated from Brown. I worked at GE, and then I came back to Boston. I was thinking about what I should do for grad school, and I knew I wanted to do something that would positively impact the world. I was thinking about either public policy programs or a math or science program like statistics that I could then apply to something like international development and global poverty.

I got into the MIT Operations Research program, and that is a really useful type of mathematics. It was my top choice and I decided to go. When it was coming time to graduate, I knew I didn’t want to go directly into a faculty role. I wasn’t exactly sure what I wanted to do, and I saw a post-doc opportunity at MGH to study optimization and radiation therapy. That was 10 years ago and I’ve been there ever since!

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Thank you so much for visiting the Center of Math, Dr. Craft! It was a pleasure to meet with you.