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Mathematics and Biology

Posted: Wed Nov 04, 2009 10:25 pm UTC
by polymer
Haldo, I'm currently a freshman at university, and I have friends who are excited about Biology. One of the reasons they are excited about it is because it's a mathless science from their point of view. The language of Biology is certaintly not mathematics, but I would think math is nevertheless still a useful tool. A biology professor I'm working for recently discussed the mathematical analysis necessary for filtering out fMRI data, confirming this suspicion. So for future reference I was curious, can you sneak through biology without having to care about mathematics? And if so is that an unwise tactic? I'm personally a physics and math major so I like to defend my subject from time to time. :)

Re: Mathematics and Biology

Posted: Wed Nov 04, 2009 11:59 pm UTC
by antonfire
Mathematical Biology is a very active field right now, I believe.

Re: Mathematics and Biology

Posted: Thu Nov 05, 2009 12:17 am UTC
by psychosomaticism
While I would say that math ability is second to memorization and procedural knowledge, it's incredibly important, especially if one wants to do anything with microbiology, molecular biology, or genetics (the list goes on). Even ecology relies on population data. So yeah, math is always important.

Re: Mathematics and Biology

Posted: Thu Nov 05, 2009 3:11 am UTC
by iop
Your friends are right in that traditionally, biology has been a fairly math-less science in the sense that there was no much need for statistics, modeling, or computational data analysis. This is partly due to tradition, and partly because it wasn't really necessary. If you want to know whether two proteins interact, you design an experiment with the appropriate controls so that the answer is either yes or no. There is no 30% vs. 31% interaction.

There are may fields in biology that aren't very quantitative yet, and if you show something using, say, complex image analysis and intricate data analysis, you may get the comment: "Nice, but why don't you show this with an experiment?"

Having said that, quantitative analysis is becoming more and more important, and in certain cases, like complex signaling networks, it is impossible to intuit the outcome of a perturbation, so you are required to do modeling. Of course, many tools in biology that are based on math are written such that they appeal to an audience that shuns math, and thus it is still not absolutely necessary to know math. It's just very helpful if you're curious about what you're actually doing.

In conclusion: They are right that math is not required for biology. It's just not very wise to not know it.

Re: Mathematics and Biology

Posted: Thu Nov 05, 2009 3:13 am UTC
by Omegaton
You don't really need much more than algebra to get through biology in college, even if they require you to take calculus... I haven't applied an ounce of calculus since I took it in high school. However, statistics is extremely important. On the other hand, statistics in biology is like having a car. To drive it you don't have to know the inner workings; to use statistical tests and interpret their results, you don't have to know how to do the calculations and do any actual math. However, I will note that it seems the more you know about statistics the better off you are...

Re: Mathematics and Biology

Posted: Thu Nov 05, 2009 3:42 am UTC
by hotnewrelease
Omegaton wrote:statistics in biology is like having a car. To drive it you don't have to know the inner workings; to use statistical tests and interpret their results, you don't have to know how to do the calculations and do any actual math.


AGHGHGHGHGHGHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHh

Statistics are misapplied ALL the time in biology and it's a huge problem (provided it's a part of biology that needs the math), because when a statistician points this out, biologists who don't understand the math can't understand what they're doing wrong. If you can't refine your approach, doing science is hard.

The article below is a great reason why you SHOULD know math if you're going to us statistics biology:

www.pashler.com/Articles/Vul_etal_2008inpress.pdf

I'm not saying that all aspects of biology need math - mathematizing the mechanics of baby delivery seems pointless to me. But if your work does depend on statistics, please, please, please know how they work.

Re: Mathematics and Biology

Posted: Thu Nov 05, 2009 4:26 am UTC
by Omegaton
I agree that misuse of statistics in biology is a big problem and that you need to know how they work. When doing statistical tests, you need to know what type of variables a test can be used for, whether or not your data breaks assumptions of normality and equal variance, and other such things. These are in fact quite important to using statistics properly. However, knowing and doing the actual math behind many of the basic statistical tests is not always important. If you know the assumptions of a statistical test are met, I say put it in the computer and get your p value and go.

This likely varies by field, and if you're using more complex statistics you should get familiar with them because you're going to have to explain why you're using them to the rest of those non-math biologists. Plus, it certainly doesn't hurt to be familiar with statistics. But do you need to know how to calculate the t-statistic to use a t-test? I say no.

Re: Mathematics and Biology

Posted: Thu Nov 05, 2009 7:08 am UTC
by rflrob
There are lots of people (like me!) who use lots of math in biology. If you can, you might want to see if your university has Biophysics or Quantitative/Computational Biology seminars. Going to these seminars, in really any field, are great ways to see how biology is actually practiced (and also sometimes a source of free coffee/snacks/lunch, if you're lucky). They won't always break the equations right out there on slide 1, but there's usually some pretty nifty stuff going on.

Re: Mathematics and Biology

Posted: Thu Nov 05, 2009 2:34 pm UTC
by Mokele
Being completely honest - If you don't like math, including/especially statistics, you shouldn't major in biology. A BS in biology will get you a job at Starbucks or a cubicle wasteland, and any graduate degree in biology means actually doing science, which means stats, experimental design, variables, etc. Doesn't matter what your sub-field is, you'll have to do some serious stats for almost anything.

It's far from just plug-and-chug at the end. Unlike physics or chemistry, biological experimental design is limited by issues such as minimizing number of animals used while maximizing results, dealing with complex non-independences that *cannot* be gotten rid of, individual variability in physiology and behavior, etc., which means you need to do a fair bit of math before you even start. A fair chunk of modern statistics were invented by biologists in order to deal with the crazy data we get from the natural world.

Re: Mathematics and Biology

Posted: Thu Nov 05, 2009 2:51 pm UTC
by Izawwlgood
Mokele wrote:A BS in biology will get you a job at Starbucks or a cubicle wasteland, and any graduate degree in biology means actually doing science, which means stats, experimental design, variables, etc. Doesn't matter what your sub-field is, you'll have to do some serious stats for almost anything.


I have a BS in biology, I work at UChicago in a biophysics lab. I took math up to Calc, then took some biostats. I've used neither at work, which isn't to say they weren't useful.

Don't be fooled, bio is/can be rather math intensive, but don't think for a second that the above bolded is particularly gospel.

Someone brought up this thread about 2 years ago, and I recall saying "Bio isn't particularly math heavy, and while math is useful, you can get away with not using any math for a number of things in bio!" and getting jumped. I pointed out PCR/DNA/Protein blotting as something that is interpreted visually, with relative increases/decreases conveying your data. Frankly, you can apply math to anything, and it'll be useful in just about every situation, but if you hate math, you can probably still be a pretty stellar biologist. You'll just be missing out on a pretty useful tool.

Re: Mathematics and Biology

Posted: Thu Nov 05, 2009 4:41 pm UTC
by qetzal
As a career scientist with a PhD in mol bio, I agree with Izawwlgood. It is possible to be a great biologist without being all that great in math. HOWEVER, that's very much dependent on what field of biology. As others have pointed out, math and stats are absolutely essential for many areas of biology, and extremely useful in most others.

I didn't really appreciate the importance of stats when I took it in college. Since then, I've come to appreciate it more and more. I wish I had much more formal training in how to use stats appropriately. (It's easy to find programs that will perform just about any stat test you like. The skill is in knowing which test to perform.)

It's funny how often you need stats in biology, even for fields where it may not seem obvious. Lots of biologists get by with little or no stats, but most of them would be better off with it.

Re: Mathematics and Biology

Posted: Fri Nov 06, 2009 1:10 am UTC
by polymer
Thanks for the replies, the consensus I'm getting is that mathematics, although it's a useful tool, is not a prerequisite for all fields of biology. That's good to know, thanks again!

Re: Mathematics and Biology

Posted: Fri Nov 06, 2009 2:27 am UTC
by UmbrageOfSnow
There are some good biologists who don't do math, but there are also a lot of bad biologists, just saying.

I've seen a decent amount of shoddy experimental design and blindness to the whole "statistically significant" concept.

And people that come ask me for help any time they need something at a different concentration than it currently is. And then proceed to write it down for future reference. Some people just refuse to be taught how to fish.

tl;dr You can get any degree and still be a dumb***

Re: Mathematics and Biology

Posted: Fri Nov 06, 2009 2:40 am UTC
by Omegaton
Whew, totally was expecting to come back and be torn to shreds. Glad to see I'm not alone.

Re: Mathematics and Biology

Posted: Fri Nov 06, 2009 2:53 am UTC
by psychosomaticism
UmbrageOfSnow wrote:There are some good biologists who don't do math, but there are also a lot of bad biologists, just saying.

I've seen a decent amount of shoddy experimental design and blindness to the whole "statistically significant" concept.

And people that come ask me for help any time they need something at a different concentration than it currently is. And then proceed to write it down for future reference. Some people just refuse to be taught how to fish.

tl;dr You can get any degree and still be a dumb***


But isn't this why biology degrees generally include a class in statistics as well as at least a couple lower level chemistry? I thought Organic chem, biochem, stats and calculus, at least intro to, was commonplace.

Re: Mathematics and Biology

Posted: Fri Nov 06, 2009 2:57 am UTC
by Omegaton
Taking a class in undergrad is a far cry from remembering how to use it on the job...

Re: Mathematics and Biology

Posted: Fri Nov 06, 2009 3:03 am UTC
by psychosomaticism
Okay, point taken. Still, is it not the onus of the scientific employee to actually have these job skills for doing their job professionally? I don't consider myself an expert in dilutions and concentration with the few chem courses I've done, but I'd sure as hell be motivated to learn it real good were my salary and coworker respect dependent on it.

Re: Mathematics and Biology

Posted: Fri Nov 06, 2009 4:08 am UTC
by UmbrageOfSnow
In my experience most biology majors (although not most of the ones I respect) just memorize their way through all classes. This is more-or-less okay in organic chemistry, etc., but it means that you get NOTHING out of statistics classes. And this approach leads to a good number of PhDs too (once again, not usually the leaders-in-the-field types).

Re: Mathematics and Biology

Posted: Fri Nov 06, 2009 5:36 am UTC
by hotnewrelease
Omegaton wrote: When doing statistical tests, you need to know what type of variables a test can be used for, whether or not your data breaks assumptions of normality and equal variance, and other such things. These are in fact quite important to using statistics properly. But do you need to know how to calculate the t-statistic to use a t-test? I say no.


This is what I mean by understanding the math. To understand whether your data breaks assumptions of normality, etc., you have to know how they work, there's no way you can do new research and apply just memorize when a given type of test is applicable. For instance, if you're going to use fourier analysis, you should know when that analysis is appropriate. Is your system linear and time invariant? Probably not. How serious are the violations? To guage that, you have to have a good idea of what's going on, as it's usually a pretty subtle thing.

Do you have to know off the top of your head exactly how a your Matlab code calculates a t-test? Hell no. But you'd better know how a t-test works, when it works, how serious violating the assumptions are, etc. Otherwise saying 'clearly the data meets the assumptions for a t-test" is a kinda pointless statement if you don't understand why.

The article I linked to above was a review of fMRI papers published in such papers as Nature, Science, Neuron, etc. Over half the papers (including ones published in those journals) had rather serious statistical errors. Did these errors mean the results were wrong? No. Does it mean they were *bad* biologists? No. But it certainly raises an eyebrow to the review process if poor statistics are getting by.

I think that's a good example of you you can certainly be a respected biologist who is well published without understanding statistics, but you might be a better one if you did.

That said, most bio majors apply to med school, I think, and I wouldn't say they need to know how the statistics work that generate the X-Ray, so long as they can identify how to fix the bone, etc. These things, like the proverbial 'car' are well-established and we don't need to know the nuclear physics behind the X-ray machine.

I guess I'd say this applies to areas of biology with a strong signal processing component. If that's not there, math's not necessary, but if it is, I think math is pretty important to make meaningful statements, or recognize errors.

Re: Mathematics and Biology

Posted: Fri Nov 06, 2009 5:59 am UTC
by Izawwlgood
I would soundly ignore most of what the above poster wrote. Seriously.

An understanding of your field is what you'll need, and that means, if you study actin dynamics, you know about actin dynamics. If that includes picking up some math to describe what's relevant in the field, then you pick up that math. If that means learning some organic chemistry, you brush up on that.

Biology, more then any other field I've encountered, benefits from a little knowledge in just about everything. People on this fora have joked about the ordering of 'true' sciences, placing psychology and biology on one side, and math on the other, but my take on the matter is that biologists need to learn more fields outside of biology, to be as interdisciplinary as possible, to excel today. I haven't read a paper in the last 2 years that didn't have an engineer, programmer, or physicist as a collaborator. Biologists are certainly not the 'gentleman scientists/collectors' of a few hundred years ago, but they are, in my opinion, still the most diversely skilled scientists today.

Also, when I say I got by with minimal math (if you can call Calc and biostats minimal, which I'm sure plenty of people can), I don't mean "Hooray, I didn't have to use math at all!", but "Fuck, I wish I had the brain for this shit, because being able to have better then a rudimentary understanding of math would make me infinitely more useful as a scientist". Really, I wish I had minored in engineering.

Re: Mathematics and Biology

Posted: Fri Nov 06, 2009 7:02 am UTC
by UmbrageOfSnow
As to actin dynamics, heck of a lot more exciting if you've taken differential equations.

And I agree with the poster 2 above me.

Re: Mathematics and Biology

Posted: Fri Nov 06, 2009 8:17 am UTC
by hotnewrelease
@izawwlgood

When you say :

Izawwlgood wrote:I haven't read a paper in the last 2 years that didn't have an engineer, programmer, or physicist as a collaborator.


You're saying "math is important to every paper I've read in the last 2 years."

My point was actually less strong than what you seem to say above. I didn't say "math is important to every paper I've read" or "biologists who don't know math aren't good biologists."

I know many amazing biologists who don't, but they either don't have to apply it or have others do it. My response was to Omegaton's assertion that one can use statistics without knowing how they work. Of course, if you're collaborating with an engineer, a programmer, a physicist, then they can verify any math parts, and that's just as good, maybe better than learning it yourself, but I was more referring to "groups that publish" rather than singular persons. In any case, you have to admit math's important to collaborate with someone from those fields.

If you think that should be ignored, well, so did the authors of those fMRI papers. Oops.

Re: Mathematics and Biology

Posted: Fri Nov 06, 2009 1:30 pm UTC
by Velifer
I think you need a little bit of math to get the most out of a bio program, but it's not critical. Biology is a rather broad category. The posts above that speak to a broad knowledge base--those are the ones to listen to. A BS in Bio with no other translational skills won't carry you very far. Math (another really broad category) skills and bio skills are a great combination.

Some simple equations for jobs I've seen recently:
Bio + 0 = Burger flipper.
Bio + stats = Biostatistician
Bio + stats + GIS/databasing = Really employable epidemiologist
Bio + regression = Agricultural economist
Bio + C++ programming = Epidemiological disease modeler. (Damn I wanted that job... can't I write it in BASIC?)
Bio + game theory = Ecological modeler
etc...

So, using Scott Adams' notion that to be successful, you should be fairly good at two things, adding math to Bio isn't necessary, but it gets you there. You could always do bio + MBA and be a hospital administrator or something.

Re: Mathematics and Biology

Posted: Fri Nov 06, 2009 2:04 pm UTC
by Izawwlgood
Velifer, I have "Bio + 0" (Well, creative writing minor?), and I am not flipping burgers. All this "Biology BS on it's own means you'll be working at McDonalds" talk is stupid. You realize that Biology is a rather large field, yes, you stated yourself, and being interdisciplinary can apply within the field itself! I work with an MD/PhD, who couldn't do anything involving numbers to save his life. We collaborated with a crystallagrapher from the botany department... You see what I'm saying?

@hot: I'll highlight the actual line that I was referring to when I mentioned 'ignore', the rest of what you said was actually just dandy;
hotnewrelease wrote:That said, most bio majors apply to med school


I'm kind of surprised at the sweeping generalizations I'm seeing people make here pertaining to Bio majors. Are many of you really JUST Math/Comp Sci/Physics/Engineers that have no idea at all what other majors do?

hotnewrelease wrote:My point was actually less strong than what you seem to say above.


I don't work in a 'just biology' lab.

Re: Mathematics and Biology

Posted: Fri Nov 06, 2009 2:29 pm UTC
by Velifer
Izzawlgood, you do bring up a good point about bio being big enough to be interdisciplinary within itself, but bio+bio != bio+0, and bio+writing is actually a very valuable skill set. The other type of success that Scott Adams mentions is harder: being among the top people in your specialty.

His advice rings true in my case. Knowing bio+ has led to interesting jobs.

And come on, it's Scott Adams. He's not a career guru any more than I am. We're both just spouting off about our experience. Hell, I'm sitting in a cube typing this instead of sipping cocktails on my yacht, and Scott Adams writes a comic strip that's still printed on paper. Randall Munroe he is not!

Re: Mathematics and Biology

Posted: Fri Nov 06, 2009 4:53 pm UTC
by Izawwlgood
Part of bio's incredible breadth though allows for being the best in your field. At UVM I worked with a guy who was the worlds eminent South Angolan Boll Weevil (or something like that) expert. I imagine his peer network consisted of 3 or 4 other people... And admittedly, being the eminent South Angolan Boll Weevil expert entailed molecular, behavioral, physiological, and ecological expertise.

But being the expert in your field can just as likely entail being in a small group considering a particular phenomenon, and using a variety of means to support it.

Re: Mathematics and Biology

Posted: Sat Nov 07, 2009 4:35 am UTC
by iop
hotnewrelease wrote:I know many amazing biologists who don't, but they either don't have to apply it or have others do it. My response was to Omegaton's assertion that one can use statistics without knowing how they work. Of course, if you're collaborating with an engineer, a programmer, a physicist, then they can verify any math parts, and that's just as good, maybe better than learning it yourself, but I was more referring to "groups that publish" rather than singular persons. In any case, you have to admit math's important to collaborate with someone from those fields.

I agree partly. I've seen too many collaborations that failed simply because the biologist had no clue about math, and the programmer had no interest in biology. In other words, the collaborator may not be able to really verify the math part, because they don't really understand the question the biologist is trying to solve, because they are not used to thinking about complex systems. Conversely, if the biologists do not understand how math and physics work, they don't know whether what the collaborator does makes any sense at all. Unfortunately, 'learning math, physics and statistics' is not simply learning recipes - recipes you can always look up. Rather, it is being able to actually understand what you're looking up, to know what there is to look up, and to acquire a certain way of thinking. Fortunately, to understand many of the most basic concepts you need just a good grasp on logic - and that is something good biologists are amazing at.

For example, someone recently came to me with the following problem: They measured fluorescent intensities in an image from a protein that was present in varying levels (because they wanted to see whether certain perturbations affected it), and a 'control protein' that was present in constant levels. The question was: Should you subtract the control intensity, or should you rather divide by the control intensity?

The apparently not-so-obvious answer is: First, you actually check whether there is any correlation between the fluctuations in the two intensities.

Re: Mathematics and Biology

Posted: Sat Nov 07, 2009 8:49 pm UTC
by hotnewrelease
Good point.

Re: Mathematics and Biology

Posted: Sat Nov 07, 2009 11:14 pm UTC
by Ostonzi
Nowadays the standard of a hardcore science major at any top university would be Complex and real analysis since it has very recently become a standard among science majors to complete Calculus 3 in high school as a bare minimum.
Biochem/ochem/molbio/genetics require advanced calculus to apply.

Re: Mathematics and Biology

Posted: Sun Nov 08, 2009 6:56 am UTC
by BlackSails
Meteorswarm wrote:[Citation Needed] Even at Cornell very few people have completed multivariable calculus by high school, and even those that did re-take it in all but the most exceptional cases.


At NYU, the honors general chemistry class requires that you be taking multivariable at the start of freshman year.

Re: Mathematics and Biology

Posted: Sun Nov 08, 2009 2:14 pm UTC
by modularblues
Izawwlgood wrote:Velifer, I have "Bio + 0" (Well, creative writing minor?), and I am not flipping burgers. All this "Biology BS on it's own means you'll be working at McDonalds" talk is stupid. You realize that Biology is a rather large field, yes, you stated yourself, and being interdisciplinary can apply within the field itself! I work with an MD/PhD, who couldn't do anything involving numbers to save his life. We collaborated with a crystallagrapher from the botany department... You see what I'm saying?

@hot: I'll highlight the actual line that I was referring to when I mentioned 'ignore', the rest of what you said was actually just dandy;
hotnewrelease wrote:That said, most bio majors apply to med school


I'm kind of surprised at the sweeping generalizations I'm seeing people make here pertaining to Bio majors. Are many of you really JUST Math/Comp Sci/Physics/Engineers that have no idea at all what other majors do?

hotnewrelease wrote:My point was actually less strong than what you seem to say above.


I don't work in a 'just biology' lab.


I know a few bio majors who didn't go to med school - they're in grad school instead :-P I think it's important to bridge the bio vocab with math/physics vocab. And also the somewhat different ways of thinking too :P

Re: Mathematics and Biology

Posted: Mon Nov 09, 2009 5:59 pm UTC
by hotnewrelease
I think there are two definitions of "succeed" that people are using here, and asking about the necessecity of math to succeed in biology with respect to one of those definitions.

1) To be a respected biologist who is well published, funded, etc. (i.e. a graduate of a top honors biology program, or in a biophysics lab at uchicago).
2) To do better science (i.e. not draw "inaccurate" conclusions (however that's defined or relevant)).

In scientific displines in general, these two are not always coincident. Standards, accepted methodologies, and tools are always changing. One used to not need much math for physics, either, and an intuitive understanding like Faraday's was quite alright.

The only contention I would stand by is that as mathematical tools become more readily available to biologists via computers, a sound understanding of their principles would be nice for (2), but this does not mean they're required for (1). (Provided you are using those tools, which is not always necessary in my opinion).

Re: Mathematics and Biology

Posted: Tue Nov 10, 2009 12:58 am UTC
by BlackSails
Meteorswarm wrote:
That strikes me as odd, but they must have a weird curriculum - my honors gen chem had no calculus at all. In any case, that's an honors course, and is probably intended more for chemistry majors than biology majors.


Oh, its a very weird curriculum. They have freshman deriving planck's law by considering a large number of quantized harmonic oscillators, calculating heat capacities by integrals and using power series approximations to get solutions in tractable forms.

Re: Mathematics and Biology

Posted: Thu Nov 12, 2009 11:44 pm UTC
by osten
Population dynamics. Differential equations is used for this, which by my meaning is math. And population dynamics is biology.

All hail the attofox

Re: Mathematics and Biology

Posted: Fri Nov 13, 2009 12:07 am UTC
by Izawwlgood
I'd really like to learn how to code, even basic stuff would be useful. I hope grad programs either offer them, or require them.

Re: Mathematics and Biology

Posted: Fri Nov 13, 2009 1:57 am UTC
by Omegaton
Izawwlgood wrote:I'd really like to learn how to code, even basic stuff would be useful. I hope grad programs either offer them, or require them.

My grad program doesn't require it, but there are courses related to applying computers to biology.

Re: Mathematics and Biology

Posted: Fri Nov 13, 2009 4:47 am UTC
by tishikawa
Non-statistical "Mathematical Biology" is largely a scam to leech funding from real biology research, perpetrated by utterly useless math grad students/PhD's.

Re: Mathematics and Biology

Posted: Fri Nov 13, 2009 5:16 am UTC
by Izawwlgood
Omegaton wrote:
Izawwlgood wrote:I'd really like to learn how to code, even basic stuff would be useful. I hope grad programs either offer them, or require them.

My grad program doesn't require it, but there are courses related to applying computers to biology.


Wholly anecdotal, but I spent about 7 months taking beautiful, Cell or Nature quality IF images (if I do say so myself!), with various drug treatments and conditions, yaddayadda, but had trouble conclusively proving what I was seeing/thinking. Then I tried a new experiment that computationally examines adhesion strength (no spoilers) and within two months of trouble shooting basically had a paper. So you know. I like using maths and computers in biology, and wish I was better at it.

That said, about 60% of the paper is qualitative data.

Re: Mathematics and Biology

Posted: Sat Nov 14, 2009 11:12 pm UTC
by iop
tishikawa wrote:Non-statistical "Mathematical Biology" is largely a scam to leech funding from real biology research, perpetrated by utterly useless math grad students/PhD's.

Wow, that has the potential to be an admission of enormous ignorance.

However, I'll give you the benefit of the doubt here. What do you specifically mean with "Mathematical Biology"?

Re: Mathematics and Biology

Posted: Sun Nov 15, 2009 9:37 am UTC
by CrazyIvan
Well, it depends.

First, a bit of background about where I'm coming from: I was a Biology major as an undergrad at a top-tier research University, and currently I'm an Epidemiology PhD student, also at a good research University.

To be frank, the field at this point is such that "Biology" is almost a useless term. I got into Bio because I liked it - but the fact that it didn't seem math heavy had its own appeal. Unlike most of the forum goers here I suspect, my math background was not terribly strong, and due to some unfortunate advising issues my Freshman year, it didn't get better in college. To call Calculus a "fiasco" would be generous. Yet, I still managed to get a B.A., publish a paper and do research.

Much of Biology doesn't "need" all that much math. If your friends are only looking at it from the perspective of "I need a degree", they're golden. Similarly, if they're trying to get lab tech jobs, say at a startup or a pharma company with only a BA/BS/MS, they'll probably still be okay - I've worked in a wet lab as an assistant, and didn't touch anything past fractions while I did it - and the lab was doing cutting edge work. So, if you want to be a "Worker of Biology", Math is pretty non-essential.

But lets say they want to do research - importantly, they want to do their *own* research. Here, we run into trouble. You'll need statistics. Now first of all, this is often viewed by people (including mathematicians) as "Not Math". Myself included - for some reason it doesn't have the same blocks for me that higher math does. And importantly, while you need math to understand what exactly you're testing etc., the math is *still* not all that hard. The underlying engine of statistics is very math heavy, but the practical on the ground stuff is mostly careful implementation of software and examining your data. For example, I can tell you whether or not I'm violating most statistical test's assumptions without ever touching calc. So, having picked up some basic stats, you're set for some microbiology and ecology research, teaching, applied public health, etc.

You are however locking yourself out more advanced "Biology related" fields, like Mathematical Biology, Epidemiology, etc. which are fairly math intensive. Often you'll have extremely Math-oriented collaborators, but it is useful enough to understand what the hell they're talking about.

At the same time, for alot of the work I do, I'd rather have someone who took alot of biology but who is shaky on the math rather than someone who took alot of math but couldn't be bothered with the biology. Especially ones who refuse to acknowledge that people in other fields have expertise - but that's a rant for another day.