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On this website (and on the Internet in general), it looks to be in vogue for physicists and mathematicians to move into biological fields to apply their mathematical knowledge and also the general methodology to biological problems. However, there's very little discussion on biologists moving into mathematical or physics fields. I am roughly two years away from taking an undergraduate degree and am torn very much between my love for biology and mathematics and consider it likely that I might end up in academia.

Is it feasible for someone who studied biology to move into a math field? Is it possible, but rare? Would the possibility of doing a joint degree, or a biology degree with a higher amount of math content, sway this at all? Or are such people better off doing a pure math degree and then moving into a biological field later on?

  • My point is that you can think of many physics chemistry engineering labs were a mathematician can do while there should be few - if any - mathematical "labs" where a chemist a physicist or a biologist could bring something on permanent basis and long standing research. I think you should pursue math , making it close as possible to your interests. Do biology only if you can do so in a modern environment or institution where you know active fields of research are consistent with your two passions. Besides scholar curriculum, you will be teached by or get in touch scientists as future you :) – Alchimista Oct 25 '17 at 23:42
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There are a giant range of fields that use elements of math and biology. This could be quantitative biology, mathematical biology, systems biology, biophysics, bioinformatics, bioengineering, etc. All of these have slightly different cultures and questions they're interested in, and you might enjoy any of them. There are programs with undergraduate degrees in many of these hybrid fields, which could suit you.

Fomite's answer shows that you can start in either direction and end up in a combination. But my recommendation would be, if you are interested in working in academia in a position that combines mathematics and biology, it might be easier to ensure your undergraduate major has at least some mathematical elements, i.e. choose either mathematics or a hybrid major with math/physics/engineering.

One reason is (possibly unfair) stereotypes about biologists and mathematicians. The stereotype about mathematicians + physicists is that they don't care about the biological details. But the stereotype about biologists is that they don't understand the mathematics. This makes it harder for people with a biology background to be hired in a mathematically-driven group. (Harder - but not impossible!)

The less cynical reason to start with at least some mathematics is about depth vs breadth. Biology as a subject has colossal breadth, which can be wonderful! But it means that one great topic (say ecology) is not necessarily a prerequisite for another (cell biology). But on the mathematics side, if you want to use partial differential equations to model a biological system, you probably need calculus, linear algebra, ordinary differential equations, etc. first! I think, therefore, the track from high-school-level skills to research-level skills in mathematical biology is longer in mathematics than it is in biology.

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    I would suggest another reason as well: In my experience, math programs are ill-equipped (and often disinterested) in catching up non-Math students interested in getting a stronger quantitative background, whereas many Math Bio programs are more experienced with dealing with students with limited biology. This is a problem I'm currently dealing with at my own institution. We have tons of ways to get a math/CS student more biology, but very little coursework paths for the opposite. – Fomite Oct 26 '17 at 0:47
  • @Fomite - that would potentially be very useful. I'm sure this has to exist somewhere ("bio to qbio boot camp") but I haven't seen one. Things like the qbio summer school all assume you have at least seen ODEs. Have you found an example outside your institution? – AJK Oct 26 '17 at 16:44
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"Math" means many things - just at the start, that can mean something like applied math vs. pure math, for which this answer has very different tracks to it.

I'd say it breaks into two potential tracks:

Track One: "I want to be a mathematician" - you want to move in this direction, and either do math for its own sake, or math as it's applied to a wide number of different things. Here, in my experience, the answer is "it's possible, but hard". There will be expectations about your coursework background that you may not have been able to do without effectively double-majoring, but it's not impossible.

Track Two: "I want to be a very mathy biologist". As you've noted, the "in vogue" way to do this is to move from math to biology, but the other way is certainly possible. There are a number of labs that would fall under the heading of "Mathematical Biology" that accept biology majors into their ranks, and if you're willing to put in the work, there's no reason you couldn't build a very strong background in math in the process, while keeping the value of having subject-matter expertise (something that is undervalued, IMO).

I took the latter track, and have ended up moving from an undergraduate background in laboratory microbiology to something that very much fits the description of "mathematical biology".

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The good (or possibly bad) news is that you don't actually need all that much mathematics to work in mathematical biology. On the other hand, if you think you might want to eventually do academic work in pure mathematics, a background only in mathematical biology will probably be insufficient.

I think the main reason that the usual direction is math -> math bio rather than bio -> math bio is psychological: more people with a math-heavy background are willing to learn the necessary biology than the other way around.

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    I'd suggest beyond willingness, there's also some pretty heavy tracking. In my experience, people who are good at math and interested in science, in the U.S., get channeled toward Math, Physics and Engineering, while those slightly less comfortable with math early on get pushed in the direction of the life sciences. – Fomite Oct 25 '17 at 21:33
  • @Fomite Maybe I'm an exception, but I have a PhD in a biological science in the US (though in a field that's more quantitative than some others) was good at math and interested in science, and I never felt tracked or pushed to those other disciplines. I think the push might actually be in the other direction: there's a lot more funding in biological sciences or applied math than in basic math. – Bryan Krause Oct 25 '17 at 23:01
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The other answers address what is possible if you want to work in an applied mathematics field like mathematical biology. But I do want to point out that it is virtually impossible to go to graduate school in pure mathematics without a degree in mathematics. I am aware of a couple of people who did this, but they were pretty exceptional and still had the equivalent of a strong undergraduate mathematics education by the time they started grad school. I've served on graduate admissions many times (in pure mathematics at a couple of different private research universities), and I cannot recall ever seriously considering admitting someone who was not a math major (and even people who were applied math majors were at a severe disadvantage, though a couple were admitted).

  • For what it's worth: a few years ago my department admitted a PhD student whose undergraduate degree was in electrical engineering. This student wanted to study theoretical mathematics... – Pete L. Clark Oct 26 '17 at 5:21
  • @Pete L. Clark : Out of curiosity, how did that work out? Were they able to pass their qualifying exams in a reasonable amount of time? Our concern is always that they won’t have the background or mathematical maturity to succeed in our first year graduate classes. – Andy Putman Oct 26 '17 at 12:44
  • Yes, the student passed their qualifying exams more rapidly than average and they are expected to graduate this year. Maybe it is relevant to mention that the student's undergraduate education was in a country with a less flexible system: if you enroll as an engineering student, you need to finish as an engineering student. For a domestic student, given how common double majors are, I would wonder how interested they could be if they didn't manage to complete the requirements of a math major. – Pete L. Clark Oct 26 '17 at 14:59

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