At the NJIT conference two weeks ago, I was asked to sit on a panel on “Future roles for mathematics and statistics within the biological sciences”. To start the discussion, the moderator Farzan Nadim asked two questions. The first was on whether biology needed mathematics (the implication being that mathematics was not the basis of biology as it is for physics) and the second was how to educate biology students in mathematics and statistics. Mathematical ecologist Stuart Pimm of Duke, immediately jumped in to protest that in evolutionary biology and ecology, mathematics has always played a dominant role. He also made the tongue-in-cheek quip that we didn’t need to train Americans in mathematics or science because we could always import them. Robert Miura followed with some personal observations that there was a cultural divide between mathematicians and biologists, one example being that mathematicians look for dimensionless quantities to determine what’s big and small (e.g. important and unimportant) whereas biologists think in terms of dimensional quantities that make sense experimentally (e.g. it’s important to know if the current you are measuring is in picoamps or microamps).
I started by agreeing with Stuart that evolutionary biology and population genetics had always been mathematical but that there was a paradigm shift after Watson and Crick. With the advent of molecular biology, mathematics began to play a much less important role because there were so many mechanisms to be discovered. We don’t know what most of the twenty thousand or so genes in our bodies do and how they are regulated. A biologist can easily have a productive career doing single gene knockout experiments and see what happens to some system. A more ambitious one can study double knockouts or triple knockouts and trying all combinations can keep all biologists occupied for much longer than the age of the universe. Then there are the effects of small RNA molecules and epigentic effects. Basically there is no end in trying to catalog all of the possible mechanisms. Thus, I think that there is a challenge to convince biologists, at least molecular biologists, that mathematics is useful.
However, I do believe that mathematics can be helpful for biology. For one, it may never be possible to understand how a biological system works by simply doing gene knockouts. I used the analogy of trying to figure out how a car works by doing knockout experiments. First you find that if you knockout the door lock, the car won’t work. Then you knockout the door and it works again. Knockout the ignition switch, doesn’t work, and so forth. Some car biologists may focus on the radio, others the gas tank. Some may try to figure why there is a large sound when the car turns on. In essence, it takes more than knowing what the parts are and even what they do individually to figure out how a car works. Clearly this is already accepted in bioinformatics and so-called “systems biology”. Biologists realize that computational and statistical methods are necessary when confronted with millions of bits of data. Mathematics has also taken hold somewhat in systems neuroscience, where concepts from probability theory, information theory and dynamical systems are used by experimentalists, often in collaboration with theorists, but sometimes not. Thus, I think that as biologists start to grapple more with systems with feedback and multiple dimensions, they will begin to realize that their internal models and intuition are insufficient and they will be forced to turn to mathematics.
Now the question is how do we educate biology students in mathematics. My answer was simple. We make it a requirement that all biology students take mathematics courses. I suggested that they should at least know 1) calculus up to differential equations including some qualitatitve theory of differential equations and phase plane analysis, 2) statistics, and 3) linear algebra. I think with a background in these areas they should have some sense of when something they are puzzled by could have a mathematical answer and also be able to converse with mathematicians. I actually went further and suggested that an educated citizen of the modern world should know some mathematics because many decisions that directly affect our lives are based on mathematics and especially statistics.
In fact, we should re-evaluate what it means to have a liberal arts education. What is the canon of knowledge that an educated person should have? I think everyone should have a basic understanding of science and mathematics. Maybe we should design a required one semester or year course called “Science and mathematics survival tools for the modern world.” It could include basic statistics and mathematics that would be useful in everyday life, like knowing what statistical significance means, or what the probability of running into your hairdresser’s boyfriend’s son at the bottom of the grand canyon is? (The chance of running into someone with some connection to you unexpectedly is quite high because you know a lot of people. It’s the multiple testing problem in statistics). They should know how to solve n linear equations in n unknowns. They should know about the central dogma of biology and the standard model of physics. They should learn some basics about molecules and thermodynamics (e.g. there are no perpetual motion machines and water cannot have a memory of a solvent that has been diluted away). They should learn about ethics. I think this would be an interesting course that students could really enjoy. These topics don’t need to be covered in depth; the students just need to know that they exist and how to get more information if they want it, including a follow up course.