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.

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

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