The two cultures of mathematics and biology (2014)

[jp57]

The estrangement he observes aren't that surprising, in either direction. Many universities have both Math and Applied Math departments. Why have both unless the mathematicians in the Math department don't want to work on applications? I have spoken with people who say if you're working on an application, "it's not really math."

In biology, there is almost certainly a self-selection effect in which the field attracts people who want to study science but are not comfortable with math, or just people who have a particular interest in plants or animals, which is uncorrelated with math skills.

I suspect there is a self-selection effect in the other direction too. I was always good at math, but I never wanted to major in it or go to grad school in it. I got a PhD in AI and machine learning, which was quite mathematical enough, and yet I can't recall ever interacting with anyone from the math department. As far as I knew, they wanted to do "pure math" and weren't interested in applications. So the people who want to do practical things select them selves into other majors like physics, engineering, and computer science.

[nyssos]

> Many universities have both Math and Applied Math departments. Why have both unless the mathematicians in the Math department don't want to work on applications?

"Applied Mathematics" as a field is not literally "mathematics applied to something"; it's a fuzzy group of related topics (things like numerical analysis, PDEs, or computational linear algebra) that's grown large and culturally distinct enough to have its own department, much like theoretical CS or statistics. There are plenty of "applied" mathematicians who don't work on applications, and some "pure" mathematicians who do.

[jltsiren]

Each field has its own culture and its own way of thinking. People are often socialized to a particular culture in the university or even earlier, and it sticks. You can learn other fields on your own, but it's hard to adopt the culture without socialization.

I did theoretical computer science in the university, leaning towards more applied stuff by the end of my PhD. I'm still a computer scientist at heart. I can follow some topics in research mathematics, but I don't think like a mathematician and I'm not interested in the same things. I work in bioinformatics these days, but I often zone out when people start talking about the stuff that goes in the results section of a paper. I'm not a bioinformatician, and I'm not interested in the same things. I've seen a similar culture gap between bioinformatics and "proper" biology, but I don't have first-hand experience with that.

[kridsdale1]

“Pure Math” might as well be poetry, just in a given linguistic domain.

[dsign]

There are currently 251131639 sequenced proteins in UniProt[^1], so, that's a very lower bound on the number of things a modern biologist has to amuse themselves with. Many still consider biology as the study of each individual biological organism, system, or protein. But since there are so many of those, I argue that biology must become a science of methods of understanding, and not a science of bare understanding. It's the difference between a company that produces mining machinery and a company that sends miners with pick and shovel underground. And that transformation is going to require for biologists to become system scientists and engineers, steeped to the brim in math, biochemistry and computer sciences.

[^1]: https://www.ebi.ac.uk/uniprot/TrEMBLstats

[DrScientist]

Why is there any science at all above pure maths? Why isn't physics, chemistry, geology etc etc just maths?

That's because choosing the right level of abstraction is really important for making practical progress.

For example penicillin was discovered and used to save millions of lives without any rigorous mathematical understanding of how the drug interacts with it's target.

I'm not saying maths isn't incredibly useful and increasingly important in the study of biology, I'm just saying that approaches that don't need maths ( beyond simple counting et al ) are also very important as well - biology is so complex, it's too easy to get bogged down in the detail.

Also I do wonder sometimes whether mathematicians don't actually understand some of the maths they work on - they can follow the mathematical logic but can't "see it". ie then find their way through the logic maze by following a logical thread in the darkness - better than stumbling around randomly - but it doesn't mean you understand the maze - and because they don't understand it beyond the 'following the logical thread' they can't communicate it to others.

Perhaps the latter is unfair - I'm not a mathematician - I'd be interested to hear other views on that.

[RandomLensman]

There is an element to this, but at the same time things tend to get incredibly messy at the level of whole complex organisms. (Btw., that also holds for mining/geology: you can do a lot of complex measurements from the surface, drill some holes and still be wrong about what you encounter underground).

[fritzo]

While Pachter enumerates differences in culture and breakdowns in collaboration, I feel the root cause is individual social attitude. The two cultures differ because their self-selected members differ in personality. What drew me to study math was the department's attitude of anarchy and irreverence. Status didn't matter, funding didn't matter, appearance didn't matter, prerequisites didn't matter, you just needed two people and two pieces of chalk and a blackboard and an afternoon. By contrast biologists I've worked with have been acutely attuned to hierarchy and funding strategy and marketing and credit attribution - social maneuvering that would fall as flat in math departments[1] as "third cohomology group" falls flat on Nature's reviewers.

[1] in my limited experience of two math departments

[klyrs]

In my limited experience...

Status matters. Politics are nasty. Every subfield has its own culture, its own royalty. Better funded professors get more and higher status students. Bigotry is common, and so are "quirky personalities" -- and due to the tolerance of weirdos, bigotry is assumed to not exist. Mathematicians are not without their people problems. Just like every other slice of humanity, they lie to themselves.

[tbitrust]

> Status didn't matter

Allow me to doubt that mathematics departments are immune to status competition.

[dang]

Discussed at the time:

The two cultures of mathematics and biology - https://news.ycombinator.com/item?id=8819811 - Dec 2014 (69 comments)

[miguelmurca]

While I agree that it's very questionable that Nature would invite someone to write an obituary (or what have you) and then reject it, I fail to see what's so controversial about the text being overly technical. I work in Physics, and "[...] locus of solutions of sets of polynomial equations by combining the algebraic properties of the rings of polynomials with the geometric properties of this locus, known as a variety" is still an incredibly tough sentence to parse on the first pass. I cannot imagine how it would read for someone who is either unfamiliar (or only passingly familiar) with, for example, the concept of a ring; "algebraic properties of a ring of polynomials"? This just seems like a case of https://xkcd.com/2501/ , with a hint of arrogance in thinking everyone working in STEM must be as comfortable with abstract concepts of mathematics as mathematicians are.

[melagonster]

this is unfortunately, author keep talk about this is useful in phylogeny, but biologists who work on phylogeny is not popular in the group of biologists who frequently publishing articles on Nature.

[dullcrisp]

Just curious if you removed the words “rings of” would you have the same objections?

[tech_ken]

> ... what mathematicians can deliver to genomics that is special and unique, is the ability to not only generalize, but to do so “correctly”.

I think this isn't really special or unique to mathematics. Certainly it's something that some mathematicians work hard to be good at, but many great mathematicians never play this game. Look at like Terry Tao, the man is undoubtedly one of the (if not the) greatest living mathematician, but IMO his best work tends to be these crazy mind-bending proofs or developments within specific areas of math. He's not a Grothendieck or a Hilbert who reorganizes concepts in elucidating ways or creates powerful generalizations. This isn't a knock on Tao, it's just pointing out that research fields are broad and require different skillsets. In terms of hard science it's IMO kind of the difference between a brilliant theorist and a brilliant experimentalist.

Taking that comparison one step further, biology also has its theoreticians and its experimentalists. Being a skilled theoretician, understanding how to organize abstract concepts to the right level of generality, is definitely something that math can help you improve at, but it in no way is limited to mathematics. For example, Stephen Jay Gould was IMO brilliant at operating abstractly, but he had no formal mathematical training I'm aware of. Critical thought belongs to every field, even ones outside of research science (ex. Law, Philosophy).

> But wouldn’t it be better if mathematicians proved they are serious about biology and biologists truly experimented with mathematics?

For the reasons above, this isn't clear to me. Does a first-year Ecology PhD really need to think critically about Hilbert spaces? They might find it to be a fun exercise, and I could see how they could get benefits from it, but they could get similar benefits from like any advanced philosophy course, IMO. I'm all for collaboration when it benefits both fields, but collaboration for collaboration's sake seems like a time sink without an obvious impact.

caveat: this is all said 10 years after the post was written, I do think the cultural divide the author talks about has closed somewhat since writing, so maybe this arrangement is now just more palatable to me.

[vaidhy]

This article was written in 2014 and I do not know if the specifics are still true. However, I think mathematicians and biologists work in two different levels of abstraction.

One is a lawful good with occasional venture into chaotic good, only to reform the chaos. The other is a true neutral with lot of expeditions into chaotic evil just for fun.

[dekhn]

Well, it's 2024, I'm a biologist, I read the thing about schemes, and I still don't understand what they are or how they would help me understand biology any better.

[waterheater]

For a ten year old article, it holds up remarkably well. Grant writing and academic research are typically divergent skill sets. Since research grants (the vast majority from DHHS, NSF, and DoD) have become a major source of revenue for universities, the most valuable faculty to a university are those who acquire grants, leading universities to hire faculty who will likely acquire many grants. These faculty select for similar students, and the cycle continues. Because pure mathematics research is intrinsically resource-minimal, the same paradigm doesn't work over there.

In a possible reflection of that reality, I have a strong feeling that, on average, university biology departments are housed in much newer and nicer buildings than university mathematics departments.

[anthk]

Read The Computational Beauty of Nature. Also, compile the samples from the GitHub repo. If the samples panic X or your window manager, use DieHard.

[Herring]

These kinds of articles are not helpful. "Why isn't A talking to B? Isn't that so sad?".

People are busy (on both sides). If Mathematicians want to want to get Biologists' attention, they should do something like Deepmind's AlphaFold - tackle a long-standing extremely difficult problem in biology using mathematical approaches.