An early career scientist’s thoughts on mathematics.

| 25 Comments

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“It would be fine if Wilson restricted the article to his personal experience, a career path that is obsolete for a modern student of biology.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.

25 Comments

Melissa,

I think you’re oversimplifying and misrepresenting Wilson’s point.

Sayres wrote:

Blindly trusting in a mathematician’s computations is just as foolish as a mathematician unquestioningly accepting the results of a biological experiment.

Wilson wrote:

Wilson didn’t say “Blindly trusting in a mathematician’s computations”. He said:

If you think critically, and find collaborators who are good at mathematics and statistics, you can be a successful scientist

This is not the same as “blind trust.” If you collaborate with someone who is mathematically skilled, AND if you have strong physical intuition, then your nerd-collaborator can go to your whiteboard and sketch out the math for you and you better understand it.

Then your nerd-collaborator can write it up as software, and make a graph of the results. Even if a scientist is not mathematically skilled, if he has strong physical intuition, he can understand and interpret the plots. Thus a mathematically skilled scientist [read: nerd] must be good at plotting and visual representation.

Let’s be clear that Darwin’s Origin of Species has no math, nor did Descent of Man. As far as we can tell, Darwin SUCKED at math but had strong physical intuition.

If Mendel’s genetics had been widely known in Darwin’s time, and if Darwin had had mathematical collaborators at the level of the neo-synthesis guys of the 1930’s, evolutionary theory would have had a HUGE jump start.

Darwin’s suckage at math did not prevent him from advancing a testable hypothesis, because he:

1. Had EXTRAORDINARY physical intuition, and

2. Was constantly, constantly, asking himself: “How can I TEST this theory?”

With these two rare properties, Darwin could triumph. However, it would have been better if he been able to correspond with Haldane, Sewall Wright, Kimura, Tomoko Ohta et al.

And now, I will describe my personal experience, if you may tolerate for a moment such self-centeredness.

My Ph.D. is in a highly mathematical branch of science. So I was not the bad-math guy, I was the nerd that bad-math guys went to consult with.

I point this out not as self-flattery, but in order to rebut any accusation that I am biased against math. If anything I’d be biased FOR math.

I have known scientists who had BOTH strong physical intuition AND great math skills. But I’ve also know scientists who had strong physical intuition and NO great math skills.

I learned to have a lot of respect for this second category of person. They would come to me and ask me how to solve such-and-such equation. I would go off, solve it, and sketch it out on their white-board.

Sometimes they would say to me, “Whoa! Too complicated!” and then do their own thing. Other times they would learn what they needed to learn to address the particular problem they cared about.

My conclusion is that such collaborations, between nerd and non-nerd, can be fruitful on these conditions:

The non-nerd must satisy these criteria:

1. The non-nerd has EXTRAORDINARY physical intution, and

2. The non-nerd constantly, constantly, asking himself: “How can I TEST this theory?”

The nerd must satisy these criteria:

1. The nerd can communicate his mathematical results visually e.g. with plots or analogies,

2. The nerd can instruct the non-nerd in just enough math so he can do what he needs to do.

Oh, and one more criteria:

3. The nerd must always keep in mind that no matter how beautiful mathematical equations are, they have to be TESTABLE by experiment!

For truly on countless occasions throughout my life I have had this experience: persons for a time talk pleasantly with me because of my work among the sick, in which they think me very well trained, but when they learn later on that I am also trained in mathematics, they avoid me for the most part and are no longer at all glad to be with me.

Galen On the Usefulness of the Parts of the Body

Margaret Tallmadge May

Ithaca, New York: Cornell U. Press, 1968

Book X, chapter 14

volume 2, page 502

Calculus isn’t just for kidney stones.

Glen Davidson

I minored in mathematics in college. (Major was computer science.)

My personal belief — inherently nonreplicable, not statistically significant, etc. — is that math-aversion is as much pedagogy-aversion as subject-aversion. In short, we teach math so badly that we drive people away from it both in terms of competence and in terms of interest.

Math is the only “language” for which American pedagogy insists that one must master an entire part-of-speech-and-person vocabulary before moving on to another part of speech… or even any understanding of what that part of speech is. Just imagine trying to learn conversational German while waiting to introduce the formal Sie until the third year of study… or discovering the difference between the past perfect and the pluperfect as a prerequisite to studying modal verbs in any tense, even though the formal grammar of the modal verbs is closely related to that of the pluperfect. And then there’s the umlaut!

Of course, it doesn’t help that so many teachers in early classrooms are not, themselves, all that happy with math, and betray that unhappiness to their students!

An early career scientist’s thoughts on mathematics

would look better.

Glen Davidson

When I studied public administration, we were required to take a course in computer programming. And a lot of the students asked why, since they never expected to do any programming.

The instructor (a colonel in the Air Force) basically said: You aren’t expected to become wizard programmers. But when some geek comes into your office and dumps a big heavy printout on your desk and says “We just modeled the air war over Europe in WWIII, and it says we need 37 more jets” you have enough knowledge of programming to understand that it’s a crock.

I think the same works for math. You don’t have to be a mathematician, but you do need enough familiarity with math to know what it can do and what it can’t, to know that calculations are based on assumptions, etc. At the very least, so that you won’t read Dembski’s books, bristling with nasty-looking equations and Greek symbols, and get snowed.

diogeneslamp0. I am simplifying, but I didn’t say that Wilson said to trust blindly. That is my conclusion alone. And, in fact, the second quote you have, is from my charitable interpretation of Wilson’s statement (not from Wilson’s statement directly). If you read his article, nowhere in there does he state that you should be critical of your mathematical collaborator’s work. To be fair, he also doesn’t say to trust blindly, but he does give examples where the biologist works on the biology and the mathematician works on the math.

I am sure there are many good scientists who are not good at math, but I argue that it can only help them to try to learn a little of the math that is related to their question. Yes, we need collaborators who are experts, but we should also be unafraid to learn a bit of the fields of our collaborators so that we have a deeper understanding of our own work. Wilson does not advocate for this. Instead he seems to advocate for division of labor. I think there is some division of labor, but there should also be a general understanding of all aspects of the question.

cepetit.myopenid.com said:

My personal belief — inherently nonreplicable, not statistically significant, etc. — is that math-aversion is as much pedagogy-aversion as subject-aversion. In short, we teach math so badly that we drive people away from it both in terms of competence and in terms of interest.

I agree, and this applies to many “hard science”.

Flint said: …you have enough knowledge of programming to understand that it’s a crock.

I think the same works for math. You don’t have to be a mathematician, but you do need enough familiarity with math to know what it can do and what it can’t, to know that calculations are based on assumptions, etc.

Exactly!

I remember reading Martin Gardner’s original article on hexaflexagons in Scientific American in 1956 when I was in high school - I read his Mathematical Games column for decades. That’s what turned me on to math.

As an undergraduate, I took math in order to keep up with the math in my physics courses. I liked math somewhat, but I kept taking math out of an anxiety that I was too mathematically stupid and didn’t know enough math to get through physics. At some point, someone informed me that if I took two more math courses, I would also have a major in math; so I did. With some of those same anxieties, I continued taking math courses all the way through my PhD in physics; the result was that I ended up with as many applied math courses as I did physics courses.

But my real interest was in experiment; I loved working in the lab designing, building, and doing experiments. Nevertheless, I have found myself in positions of having to do theoretical work as well as having to come up with algorithms and computer programs in order to do my work in physics; so all that math actually turned out to be useful in the long run. My anxieties about math turned out to be irrational leftovers from somewhere back in my youth. Now I love math.

There were many changes taking place in the way math was taught while I was going through all this. Math is taught much better these days than it was back in the 1940s and 50s. Looking back, I might not have had so much anxiety about math if it had been taught as it is today. Kids getting math today are much farther ahead going into college than we were.

On a related side note; one of the physics professors in high energy experimental physics at the University of Michigan had a way of sorting out grad students he would accept as PhD candidates under his mentorship. After an interview in his office, he would feign an afterthought and ask the prospective candidate to help him get a large, long table out of his office and into the hallway (or in the other direction if the table was already in the hallway). He played dumb and let the student do all the guiding. If the student jockeyed the table through all the obstacles and around corners and through the doorway successfully on the first try, the professor took him on as a candidate.

diogeneslamp0 said:

Melissa,

I think you’re oversimplifying and misrepresenting Wilson’s point.

Sayres wrote:

Blindly trusting in a mathematician’s computations is just as foolish as a mathematician unquestioningly accepting the results of a biological experiment.

Wilson wrote:

Wilson didn’t say “Blindly trusting in a mathematician’s computations”. He said:

If you think critically, and find collaborators who are good at mathematics and statistics, you can be a successful scientist

This is not the same as “blind trust.” If you collaborate with someone who is mathematically skilled, AND if you have strong physical intuition, then your nerd-collaborator can go to your whiteboard and sketch out the math for you and you better understand it.

Then your nerd-collaborator can write it up as software, and make a graph of the results. Even if a scientist is not mathematically skilled, if he has strong physical intuition, he can understand and interpret the plots. Thus a mathematically skilled scientist [read: nerd] must be good at plotting and visual representation.

Let’s be clear that Darwin’s Origin of Species has no math, nor did Descent of Man. As far as we can tell, Darwin SUCKED at math but had strong physical intuition.

If Mendel’s genetics had been widely known in Darwin’s time, and if Darwin had had mathematical collaborators at the level of the neo-synthesis guys of the 1930’s, evolutionary theory would have had a HUGE jump start.

Darwin’s suckage at math did not prevent him from advancing a testable hypothesis, because he:

1. Had EXTRAORDINARY physical intuition, and

2. Was constantly, constantly, asking himself: “How can I TEST this theory?”

With these two rare properties, Darwin could triumph. However, it would have been better if he been able to correspond with Haldane, Sewall Wright, Kimura, Tomoko Ohta et al.

And now, I will describe my personal experience, if you may tolerate for a moment such self-centeredness.

My Ph.D. is in a highly mathematical branch of science. So I was not the bad-math guy, I was the nerd that bad-math guys went to consult with.

I point this out not as self-flattery, but in order to rebut any accusation that I am biased against math. If anything I’d be biased FOR math.

I have known scientists who had BOTH strong physical intuition AND great math skills. But I’ve also know scientists who had strong physical intuition and NO great math skills.

I learned to have a lot of respect for this second category of person. They would come to me and ask me how to solve such-and-such equation. I would go off, solve it, and sketch it out on their white-board.

Sometimes they would say to me, “Whoa! Too complicated!” and then do their own thing. Other times they would learn what they needed to learn to address the particular problem they cared about.

My conclusion is that such collaborations, between nerd and non-nerd, can be fruitful on these conditions:

The non-nerd must satisy these criteria:

1. The non-nerd has EXTRAORDINARY physical intution, and

2. The non-nerd constantly, constantly, asking himself: “How can I TEST this theory?”

The nerd must satisy these criteria:

1. The nerd can communicate his mathematical results visually e.g. with plots or analogies,

2. The nerd can instruct the non-nerd in just enough math so he can do what he needs to do.

DARWIN TESTED HIS HYPOTHESIS CONSTANTLY. Name one test. I said one.!

Whats with the nerd comment. All science lovers are called nerds by mainstreet. Its a stupid putdown. People who concentrate on these things simply do less concentrating on other things with results. They usually come from circles that did likewise. To do a better job in sciency stuff it should not be in any way seen as nerdy. Gets in the way of achievement.

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Melissa,

When trolls like Byers show up they have only one goal, to disrupt the thread with off topic nonsense. They are incapable of learning, even if given the opportunity. It is customary to dump their posts to the bathroom wall, where a more “spirited” exchange of “ideas” is appropriate. I would recommend this course of action. Failure to do so invariably results in degradation for the thread and all participants. The trolls quickly learn which threads are unmoderated and then a feeding frenzy usually commences. I can provide you with a list of known trolls and associated riff raff if you so desire.

Thank you.

Thanks, DS. I’ll try it out today. I’m just unsure of whether I’m going to have the time to constantly babysit the comments.

I work in the geosciences. We run numerical models of the atmosphere and the ocean. A model domain typically has 1000x1000 grid points, with 20 vertical levels, for a total of 20 million cells. At each of those grid cells we solve the basic equations of state/motion on every time step, typically 10-60 seconds. Hurricane models run for a simulated week or two while the system is approaching landfall.

That’s a lot of math! Fortunately we have digital computers that run in parallel (~64 processors) to complete all those calculations in a reasonable amount of time, and deliver the forecast before the hurricane actually hits a populated area. A timely forecast can save lives and property, as people make preparations and evacuate from risk-prone coastal areas.

Math saves lives.

DS said:

Melissa,

When trolls like Byers show up they have only one goal, to disrupt the thread with off topic nonsense. They are incapable of learning, even if given the opportunity. It is customary to dump their posts to the bathroom wall, where a more “spirited” exchange of “ideas” is appropriate. I would recommend this course of action. Failure to do so invariably results in degradation for the thread and all participants. The trolls quickly learn which threads are unmoderated and then a feeding frenzy usually commences. I can provide you with a list of known trolls and associated riff raff if you so desire.

Thank you.

What has consistently worked for me for 10+ years is to resist answering their PRATTs, (points refuted 1000x) but rather ask them simple questions about their “theory” starting with the basic “what happened when.” Invariably they voluntarily go elswhere. Unfortunately “elsewhere” is usually the same thread, because others can’t resist the temptation to “feed.”

I understand the desire to correct misconceptions that these trolls may give to lurkers, but the latter can be pointed here. Any lurker who is not already hopeless or in on the scam can recognize which claim the troll has recycled, even if the wording is changed.

To bring this on topic, my 2c is that every scientist needs, as a minimum, what John Allen Paulos called “numeracy.” If they’re as proficiant as mathematicians, all the better. What I have found in teaching math off-and-on for decades is that some people find it hard to recognize that the problem they are solving is of the same basic structure as one they solved a few minutes before. Only the “names are changed.” That makes their job much harder. A similar situation occurs with anti-evolution activists, their trained “parrots” and trolls. They try to disguise PRATTs (the DI is particularly skilled at this) but most people, including those who have trouble with the same process in math, can see through the game.

About this Entry

This page contains a single entry by M. Wilson Sayres published on April 24, 2013 8:03 AM.

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