Wednesday, April 24, 2013

An early career scientist's thoughts on mathematics.

E.O. Wilson wrote an essay entitled, "Great Scientist Good at Math". If you haven't read it, here is my summary of E.O. Wilson's statement:
I didn't learn much math, and I am a successful scientist because I think critically and found collaborators who were good at math. If you think critically, and find collaborators who are good at mathematics and statistics, you can be a successful scientist without personally knowing much math. 
The name of my blog is mathbionerd. I loved math in high school (thanks Mr. Boerner), and majored in Mathematics in college at Creighton University. I did a summer research experience at the University of Nebraska, Lincoln in the Mathematics department. And, for graduate school, I applied to both Mathematics programs and Bioinformatics programs, ultimately choosing the latter, but volunteering to be a teaching assistant for Calculus. I currently study biological questions and large datasets using computer programs and statistical models. So, uh, yes, I think math is important.

Edward Frenkel has an excellent piece responding to Wilson's essay. I completely agree with his conclusion:
"It would be fine if Wilson restricted the article to his personal experience, a career path that is obsolete for a modern student of biology. We could then discuss the real question, which is how to improve our math education and to eradicate the fear of mathematics that he is talking about."
The first thought that struck me, too, about Wilson's essay is that he is giving antiquated advice to modern students. But, the more I thought about it, I realized that the mark he missed is much larger than that. In any field of scientific research, we can gain more insights by taking a different perspective. This perspective may come from collaborators, but truly successful scientists are able to integrate new opinions, and see their own data in new light. Collaborators are very important, but we should be able to critically assess the contributions of our collaborators. Blindly trusting in a mathematician's computations is just as foolish as a mathematician unquestioningly accepting the results of a biological experiment. The roots of scientific inquiry are curiosity and skepticism. Curiosity is developed by what we want to discover, but do not yet know. Skepticism occurs when  new data are evaluated, within the context of what we know. The two go hand in hand to result in new, exciting, discoveries. But, being curious without being skeptical makes for poor scientific inquiry. 

We become scientists because we are curious. While in training, we learn how to be skeptical by increasing our base knowledge. I cannot imagine a point in my career when that training will end. It can be uncomfortable to be a novice, to admit when we don't understand, and to take the time to learn new material, especially after years of training. But we must, if we are to continue to make progress. This may mean learning more about cardiac disease, or aphid digestion, or polio replication, or linear algebra, or differential equations. 

Are there good scientists who are not good at math? Of course there are.

Must one be good at math to be a good scientist? Not necessarily.

But, can anything be gained from perpetuating the notion that math is untouchable, except by experts? No.


bill.everett said...

Dear mathbionerd,

This is a personal communication and not intended as a comment. You can leave it as a comment if you wish.

Have only read this post just past the initial E.O. Wilson summary and have a feeling we should be in touch somehow.

I am neither a scientist nor a mathematician (but have published two papers in a math journal, e.g., see where you can click on author and send me an e-mail, please).

A little background: I encountered N. Rashevsky's book Mathematical Biology on a bookshelf in the Genetics Foundation at UT Austin in Fall 1962, bought the two-volume Dover edition, and read it. In 1965, I bought his monograph on the mathematical biology of social behavior and later his monograph on a mathematical approach to history. In late 1968 or maybe 1969, he happened to sit down next to me at a public lecture by Herbert Simon on artificial intelligence at UM Ann Arbor. After the lecture, he asked me what I thought about the lecture. I answered. He started explaining his reactions and thoughts. I noted his use of concepts from organismic set theory. He was surprised that at my familiarity with his theory and introduced himself. I introduced myself. He asked, "Are you the guy who was corresponding with me from Alaska and requesting reprints?" I nodded. When I was in Kiev for a couple days in August 1993, I was able to visit the university where Rashevsky had taken his doctorate (fiz-mat) in 1919 and honor the memory of an original thinker and, for a while, a friend.

I am not a scientist nor a mathematician, but I have had opportunities to "pick the brains" of few who were scientists and/or mathematicians.

-- Bill

PS. I have bookmarked this blog post and will read it as soon as I can find the time. Maybe I'll have a real comment then, maybe not. All the best.

Andrew Mauro said...

I'm really glad I saw this post yesterday. As a newly minted (and starting midyear) high school chemistry teacher whose masters work was in mathematical modeling of aggregation and having done a year of doctoral studies in computational/theoretical chemistry, I've been stressing the importance of being able to use mathematics as a tool and how important it is to use mathematical reasoning in problem solving.

As a result, my students have been complaining and asking if they could learn chemistry without math. I hope that showing them these articles can assuage their aversion to math in science.

Also, I had to laugh when you had said that experimentalists shouldn't blindly trust equations or calculations. It reminded me of working with a collaborator on my masters thesis project. He was always questioning what our equations were saying and their physical basis. It is certainly great practice to never take work or results at face value without asking questions.

Thanks for the great post!


mathbionerd said...

Thank you, Andrew!

Congratulations on your new job. I hope this does help convince them of the importance of math to all of the sciences, if even just a little.

Charles said...

Math is a language, and as such, you can either spend too little time with it, making you ineffective at communicating, or too much time with it, turning you into a pedantic navel-gazer. I think Wilson's point is, he didn't want to become the latter; and Frenkel's point is, you can't shut your eyes and make the world disappear, in a connected world you have to be able to communicate. It's just a matter of not being too extreme in either direction. (Unless you can find funding that will allow you to drift off into the nether regions of mathematics and divorce yourself from reality entirely...).

Just an interpretation.