I'm a math prof. But, I've always loved reading about biology (the paleobiology of microbes and some small animals mostly) it's my hobby but I want to learn more maybe take a course. My longer term goal would be to be able to be of better assistance to my online friends who are biologists who are always asking me to help with the statistics in their papers. (I have been able to help, but I feel like I could do better)

When I study math, I aim to be able to identify and prove all major results from memory, state all definitions, and solve new problems and proofs. I have a process it works.

But with biology I often find that there are multiple definitions or there are big differences between textbook content and studies. It's really upsetting. I understand why this is true, that's just the nature of science, but I don't understand how to best navigate when a topic has multiple interpretations that are all possibly true. I get really hung up on not being able to find one definition for some terms.

Should novices and students stick to textbooks and "widely accepted" definitions? Or should one make and effort to keep up with the most recent research and learn to live with the ambiguity?

I can take one course for free at my university each term. Should I start with 101? Or can I do that through self-study and start with something more specialized?

What is a good self-study book?

My only science background is a few newtonian physics courses.
I'm kind of scared to go to the biology department and ask. Biologists are really intimidating when you teach something simple and clear like math.

  • $\begingroup$ Possible duplicate of Introductory biology text for an outsider $\endgroup$
    – Remi.b
    Sep 15, 2017 at 19:05
  • $\begingroup$ Every field is different! I am not sure if anyone could give much more advice. In general, the existence of several different definitions in the literature rarely causes any trouble in practice. Often enough, authors care about defining the terms they are using when dealing with terms that has been defined in several different ways. $\endgroup$
    – Remi.b
    Sep 15, 2017 at 19:07
  • $\begingroup$ It is always a bit scary to start a studying an entire new field. The teaching philosophy may differ from what we're used to, same goes with the type of mental effort but in the end, it always work out. Don't be intimidated by your fellow biologists. Most biologists are quite literate on a number of side fields (typically, data analysis, math, computer science, chemistry, ...), they will understand how lost one can be when starting to learn a new field. $\endgroup$
    – Remi.b
    Sep 15, 2017 at 19:14
  • $\begingroup$ Part of your question might be more on-topic on Academia.SE but I'm not sure they will be able to give much more advice. Good luck! $\endgroup$
    – Remi.b
    Sep 15, 2017 at 19:14
  • $\begingroup$ I don't think this question would be well-received on Academia, it doesn't really fit their scope of on-topic questions. In general, StackExchange isn't really intended for opinion-type questions like this. $\endgroup$
    – Bryan Krause
    Sep 16, 2017 at 0:47

2 Answers 2


I started in cell and molecular biology, but moved to applied math and computer science, so perhaps I can give my thoughts.

Personally, I found that biology learning was more about big ideas and visualization. The first is because biology has an extraordinary amount of details (e.g. Molecular signaling pathways, biochemical properties of different molecules, the location of different foramen in certain fossils, etc...), so it is truly impossible to remember them all. You should focus on learning what to look up, not what is actually occurring. Something you work on will be gradually memorized on its own, so don't spend effort memorizing things you can look up (you're not an undergrad :) ). So don't remember that histone acetyltransferases use acetyl-coa to act upon the NH3+ groups of lysines. Just remember that those enzymes modify chromatin in a way that alters transcription, thus changing the cell and its behavior. The second (visualization) is because it is very hard to understand biology without pictures! So use them, not text (no kobayashi and nomizu style). Mathematicians like symbols but (at least in the molecular case) there are too many of them (and they are mostly useless names... e.g. P53). Much of biology is about seeing visual results (blots, fossils, medical images,...) and interpreting them.

Note that (I think) the first suggestion is harder in biology than in math, because math partitions naturally into theorems, corollaries, lemmas, and their applications (roughly in order of importance of what you need to know :) ). Biology as a field is more of a fast moving chaos of observations and changing inferences. But of course there is a constantly growing core of the field that is not in flux.

One good thing about biology is that one can be an expert in one area but know little about most others. Math is a little more intertwined. So there's no need to read a "general bio" book. Just read an intro book to your target topic (e.g. Ecology, evolution, cell bio, molecular biophysics, bioinformatics ...). They will cover the relevant parts of other fields, usually. I know genetics experts who know basically nothing about cell trafficking for example. But you will definitely need some background to read the latest literature (i.e. Don't skip straight to Cell papers).

One issue that occurs throughout science, but also in math, is that learning is a process of improving models. In math, we might start with linear algebra, then basic manifolds, and eventually with, say, finsler spaces. In physics, we go from Newton to Einstein. In biology, we start with a basic model and set of rules, but gradually add exceptions and details to it. I think this is where much confusion can arise, because things that were correct in the simplified model might be wrong in the better, more complex one.

Also, models are being updated at an insane rate in biology. Often that means that previous models were wrong (though the evidence underpinning them is not); hence definitions and results might change over time! Science improves over time, and this is a good thing. Of course, in math, once something has been proved, it will never change. (Although definitions, or at least notation, in math can be very inconsistent too). Of course, if there are inconsistent definitions, you can ask here and see what people think. I will agree that biologists are less concerned about detailed rigor than being correct overall. Generally scientists will either define such things themselves or cite a reference with their chosen definition.

My suggestion for your question is to learn the basic widely accepted definitions first, then go to the literature. Often it is the case that different groups think different things. Most likely, one or both will be proven wrong eventually. Each paper is likely to be internally consistent; the only ambiguity is usually in areas where no one knows the correct answer or interpretation. Two groups in conflict usually have reasonable hypotheses consistent with the evidence, and if they can't decide how to mesh their ideas, probably we can't either. So don't worry about it too much.

So when a topic has multiple interpretations that are possibly true, use your math background and consider it from a Bayesian perspective :) most likely all the interpretations are at least partly true, and have some non zero probability of being true. And as you read more papers, update your posterior. :)

Also, don't worry about talking to biologists (as the other commenter states). In fact, among the sciences and engineering fields, my opinion is that biologists are on average the friendliest and least arrogant :)


Biology is the most vocabulary intensive science to learn. You are learning a lot of new terms all the time because biology is a very descriptive science. With my students I recommend flash cards, mnemonics, word banks, basically the same tricks you might use to learn a new language. Additionally draw things, a lot, and encourage your teacher to sketch things. Biological concepts are often tiered or interwoven enough that even simple diagrams can make it much easier to understand.

as you said definition are not set, basically different branches of biology will use slightly different definitions, (defining species based on ability to interbreed works ok with animals but is useless for bacteria for instance.) you are not seeing changes in definition with new research as much as you are seeing different working definitions for different branches. For the purposes of a class the exact definition is less important than the concept. think of the difference between a book and a pamphlet, you cant really say where one stops and the other starts on the spectrum of printed media but you are relatively sure most of the time which one you are looking at. As much as I don't like recommending it wikipedia often has very nuanced descriptions of biological terms which can also be helpful.

One important concept in biology is that almost everything lies on a continuum or spectrum, very few things are truly discrete. Organisms don't exist in discrete categories we invent those categories to make it easier for us as humans to think and talk about them, which works fine on the large scale but can get very blurry on the more detailed scale. Because of this terms are often vague on the macroscale but get get more precise as you get more specialized. (this is why there are no less than eight separate definitions of species, how would you define it in fossils for instance) It also means that even basic concepts often have several conditions/assumptions that have to be true before they even apply. The fact that almost everything in biology is conditional is a big impediment to understanding when you first start.

There is an old joke in biology that there is an exception to every rule including this one. This is because biology constantly comes back to the real world for its information, it is focused on description and prediction less proofs. Even in a single organism there are so many interactions on so many levels that generalized rules simple fail to predict details ( for a comparison, imagine trying to do calculations when you are only allowed one significant digit).

I definitely recommend starting with the basics, this is important in any science, jumping right into more specialized classes is like trying to learn quadratics without understanding basic algebra, you are just making it harder on yourself. In biology it is especially bad becasue you hit a wall of terminology which biology needs just to keep from describing things as "that squishy grey bit squirts the yellow stuff on the red pastey stuff"

If you are truly very focused on math, mathematical/theoretical biology may be the most interesting as it is concerned with describing biology in mathematical ways. But really the advent of computers has led to a huge surge in applying mathematics to biology, because the complex equations are now practical. But it is important you have a basic understanding of biology first, if for no other reason than to get past the terminology/jargon wall. On the upside biologists know that terminology is an issue so they often have resources to help, that is why so many biological terms are laid out on wikipedia. Additionally a basic grasp of latin root words can be a big help, since so many biological terms use latin roots (originally to make it easier but now when no one speaks latin it makes it harder)

now an obligatory comic. enter image description here


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