The two cultures of mathematics and biology

http://liorpachter.wordpress.com/2014/12/30/the-two-cultures-of-mathematics-and-biology/

by Fede_V • 12 years ago

126 69 12 years ago

liorpachter.wordpress.com

impendia• 12 years ago

Mathematics full professors that are female is a number in the single digits.

I'm not going to let this slide. This would be scandalous if it were true; however:

http://www.mi.uni-koeln.de/Bringmann/ https://www.math.psu.edu/wli/ https://web.math.princeton.edu/~smorel/ http://www.math.tamu.edu/~ptretkoff/ http://en.wikipedia.org/wiki/Maryam_Mirzakhani http://math.uchicago.edu/~wilkinso/ http://www.math.wisc.edu/~lsmith/ http://www.maths.ox.ac.uk/people/frances.kirwan http://math.stanford.edu/~ionel/ http://gauss.math.yale.edu/~ho2/

I could easily keep going.

Edit: As ninguem2 points out, apparently the author was referring to the percentage of female math professors. Nevertheless, if you do not count only doctoral-level departments, even that appears to not be true:

http://www.ams.org/profession/data/cbms-survey/chapter4.pdf

(This study is counting all tenured professors, rather than full professors only, but the proprortion is well enough north of 10% that I feel it's safe to extrapolate.)

Of course, the proportion of female math professors is terribly and inexcusably low, but the situation is at least slightly less bleak than is painted here.

ninguem2• 12 years ago

He is talking about percentages, not absolute numbers, as in most math departments less than 10% of full professors are women.

GFK_of_xmaspast• 12 years ago

From the AMS study, Table 1, PhD math departments, 420 female out of 4669 total is, by most calculations, less than ten percent.

kaitai• 12 years ago

It's interesting to note in particular that these departments graduate many more women by percentage than they then hire.

Great article! I think a big problem in math is a certain insularity that suspiciously pushes away people who do interdisciplinary or education work unless they're also publishing "real math", narrowly defined.

elberto34• 12 years ago

I think they were right to reject it. I have done plenty of math but I still couldn't 'grasp' the significance of the scheme system, and while I'm sure it is very important to the few people who understand it, I doubt the readers of Nature are among them.

j2kun6• 12 years ago

Are all readers expected to grasp the significance of every article in Nature? More pertinent to the reason the article was rejected: shouldn't every scientist have heard of complex numbers and polynomials? It is, after all, part of every secondary school curriculum.

epistasis2• 12 years ago

Lior Pachter is one of the great thinkers and communicators in computational biology. I never miss one of his talks, they're always energetic and enlightening.

aabajian• 12 years ago

Perhaps even more interesting is the gap between mathematicians and medical doctors. Disclaimer: I was a math major who went to medical school.

There is age-old question of, "What should I major in if I want to go to medical school?" Turns out that mathematics majors have the following statistics:

1. Highest average MCAT Physical Sciences Scores 2. Highest average MCAT Biological Sciences scores (higher than biosci majors) 3. Second-highest MCAT Verbal Reasoning scores (second only to Humanities majors) 4. Highest overall average MCAT scores. 5. Second-Highest average Science GPAs (biosci majors are 0.02 higher) 6. Highest average Overall GPAs

Source: https://www.aamc.org/download/321496/data/factstable18.pdf

'Course, math majors make up < 1% of medical school applicants (0.81% to be exact), so this very well may be selection bias. Still, it seems as though what medical schools are looking for are individuals with analytical (mathematical) reasoning skills.

EDIT: It's also worth noting that in many countries an undergraduate education is not a prerequisite for medical school, so there's likely to be even less math-major physicians outside of the US.

rimantas• 12 years ago

My friend math teacher used to say: "only 5% are good at math, but those 5% are good at everything".

jonathansizz• 12 years ago

Nobody is good at everything. But there is certainly a vocal contingent of maths/physics types who think they are.

fidotron• 12 years ago

Anyone that thinks medicine relies on strict logical reasoning isn't familiar with the reality of medical practice.

dnautics2• 12 years ago

I was a math major and that comports with my very good MCAT score (although I took it after chemistry grad school). I wound up not going to med school; my boss https://en.wikipedia.org/wiki/Hamilton_O._Smith was also a math major who was doing biology (and HAD gone to med school). His buddy Clyde Hutchison, was in his day a very good programmer, he wrote one of the first FORTRAN scripts to identify open reading frames in DNA.

IndianAstronaut• 12 years ago

The result is that biology loses out due to the minimal real contact with math– the special opportunity of benefiting from the extra sense is lost, and conversely math loses the opportunity to engage biology

When I was a biology grad student, I was the only person in the department that tried to do active collaboration with the math department. I took more math classes during my graduate program than biology classes.

On the biology side, I got ridiculed for all the 'hand waving' that seems to happen with the math. Biologists want to see concrete experiments and results.

On the math side I found people to be much more open and fascinated by the biology, but they had a tough time explaining what they were doing to a lay audience.

No easy answers, but I think more programs should graduate people with dual skills in both subjects(and of course have job opportunities for those grads, instead of having them jump into industry like I did).

Pyret• 12 years ago

On the biology side, I got ridiculed for all the 'hand waving' that seems to happen with the math. Biologists want to see concrete experiments and results.

How interesting. Usually, it's the math folk who ridicule everyone else for being sloppy with their reasoning. For example, physics = hand-wavery :D

wwweston• 12 years ago

Mathematicians tend to be very particular about reasoning (and by comparison even other scientists can be sloppy).

However, they can also be pretty free with their assumptions (which can be wild, though if reasoned from carefully usually turn out to be useful even if nobody anticipated that they would).

People working with mathematicians probably spend a lot of time wondering why they're so persnickety about some things most people would consider obvious ("but how do you really know 2+2=4?") but sometimes not so much about whether the constructions they're working with actually reflect a particular concrete reality.

Fomite9• 12 years ago

It's a different kind of hand waving. When presented with a system of ODEs describing a system, a mathematician may be content with some assumptions that make the analytical solution more straightforward, or not be terribly worried about particular values for parameters because they're looking at the more general behavior of the system.

Biologists (or in my case epidemiologists) may, on the other hand, be very concerned about why the value you chose for a particular parameter is 6 instead of 7, and whether or not it's really exponentially distributed.

j2kun6• 12 years ago

The issue with physics isn't that they're hand-wavy, it's that they teach their students demonstrably false things. Such as, an infinite point-impulse is a function with integral 1, and the sum of all positive integers is -1/12, and other such nonsense about "convergent" sequences. They balk at the nuance of mathematics when it actually matters to us.

jamesli2• 12 years ago

Biology is enormous, as the author pointed out. Our understanding in biology at present might be less than 1% than the whole knowledge. For most biological research, it doesn't require any advanced knowledge in math beyond basic statistics.

For example, many labs have been studying an important gene and how other genes are functionally related to it for more than 10 years. The research involved are simply tedious, but indispensable, biological experiments. It is a waste of time to study math for this work, because it doesn't apply, except some basic statistics on data analysis.

Disclaimer: I have advanced degrees in both biology and computer science, and has multiple years of biomedical research experience. I have met exceptionally smart people working in both biology, CS, math, and physics. Yes, these smart biologists don't understand advanced topics in math and physics. I believe, however, if they had studied math or physics, they would have been excellent mathematicians or physicists.

eli_gottlieb2• 12 years ago

Wouldn't it be entirely useful for biologists to know more advanced statistical methods?

jostmey• 12 years ago

Well said.

The study of biology is further complicated by the large number of confounding factors that muddle experimental results. Because of this, it is hard to know exactly when it is appropriate to bring in mathematics. Without a proper understanding of all the variables, math can only get you so far.

m_mueller• 12 years ago

IANAB. From what I understand, DNA research seems to have lots of still low hanging fruits for simple mathematical models to achieve big breakthroughs. Yamanaka won a nobel price for cell reprogramming that simply came from neglecting the previous brute force method to find the correct molecule combination that lead to many years of Biologists trying out combination after combination. Instead he basically deduced it through simple modelling and applying the scientific method. A quick google has brought the following thesis, which bases some more modelling on Yamanaka in order to refine stem cell reprogramming [1]. From my point of view, the really outstanding work in biology currently rather comes from outsiders that break out of the usual methods of biologists, such as the applied mathematician Erez Lieberman Aiden who showed how genome folding works and actually has an important function (activating / deactivating regions in order to program cell functions), purely through mathematical modelling of the signals we can get out of current instruments and throwing HPC at it. I'm pretty sure the field would benefit greatly from more cross pollination from other fields.

[1] https://www2.hu-berlin.de/biologie/theorybp/docs/dipl_scharp...

[2] http://www.sciencemag.org/content/326/5950/289.short

epistasis2• 12 years ago

I think there's definitely a trend in institutions to integrating these fields. Princeton has an Integrated Science program [1] which includes highly quantitative study of biology.

And genomics in general has forced the combination of biology, stats, and math. Classical genetics and evolution departments are often seeded with lots of appreciation for mathematics, as well.

However, pure molecular biology doesn't often have that much to say to non-applied math, and vice versa.

http://www.princeton.edu/integratedscience/

tjradcliffe2• 12 years ago

I'm a physicist who has worked in genomics and found biologist's attitudes toward math to be fairly weird. Some get it, most don't. But the way physicists think about math is for the most part antithetical to the way mathematicians think about it. To a physicist, math is a language for talking about things with in-built protections against contradictions. Math looks more like a very special natural language to us, which attitude drives mathematicians nuts.

The odd thing is that this difference in attitudes between physicists and biologists seems to me to be at least as much historically contingent as really dependent on the subject matter. Physics is hugely sprawling too, and a great deal of it is only passingly-mathematical.

If Darwin had been more mathematically minded he could have easily come at the problem of the origin of species from a viewpoint as strongly idealized and mathematically compact as Newton did with regard to physics. Newton was admittedly blessed with a very-nearly ideal system to study (the solar system) but was able to apply his ideas to other systems using a wide variety of increasingly sketchy approximations.

But I'm still pretty sure a mathematical mind on the order of Newton's could find a way to state evolution by variation and natural selection as a theorem rather than a theory, that follows necessarily from the laws of probability and the facts of chemistry (many of which Darwin didn't know, but still). It is at the very least a fun idea to speculate about: http://www.amazon.com/Darwins-Theorem-TJ-Radcliffe-ebook/dp/...

dnautics2• 12 years ago

The biggest gulf between physics and biology is the general principle that ockham's razor is a poor heuristic for biology. A second source is that biological phenomena exhibit strong path-dependence, and physicists are typically trained to think from a path-independent (state function) point of view.

thisisdave• 12 years ago

I'm still pretty sure a mathematical mind on the order of Newton's could find a way to state evolution by variation and natural selection as a theorem rather than a theory, that follows necessarily from the laws of probability and the facts of chemistry

Apart from the chemistry part (where I don't understand what you mean), biology has had this for 85 years, with numerous extensions and generalizations [1].

[1] http://www.ias.ac.in/jgenet/Vol74Nos1&2/19.pdf

dang• 12 years ago

Mumford's Grothendieck obituary was posted to HN a couple weeks ago but unfortunately didn't get any discussion.

https://news.ycombinator.com/item?id=8755800

mbq• 12 years ago

I once was on a workshop organised by and for mathematicians which supposed to be about biology. There was a talk where guy was discussing PDE system describing some colony growth; at some point near the beginning he concluded that the results for real input are "boring", and one can get "intriguing chaotic behaviour" with negative cell number, and continued with that assumption (;

Fomite9• 12 years ago

Many similar experiences, from having someone say "I was under the impression this was interesting for its own sake" at an applied math talk, or asking a group of mathematicians how to actually implement their biologically (and logistically) impossible solution to influenza containment.

throwawayxx• 12 years ago

I started a PhD on the boundaries between mathematics and biology.

I quit soon after finding out that my (mathematics) supervisor had been actively blocking me from communicating with biologists, including blocking meetings with my (biology) co-supervisor.

I gather they thought real, practical concerns would be a distraction from the purity of theoretical problems.

danieltillett5• 12 years ago

If it makes you feel any better these sort of games go on whenever cross discipline research occurs. It is all about controlling the research undertaken by the student.

Balgair• 12 years ago

Bashing Nature is almost cliche at this point, anyone in the research world knows about the issues there by now. However this is comical: "...in which he describes the rejection by the journal Nature of an obituary he was asked to write" I mean, who in their right mind rejects an obit that they asked someone to write? The power that the Nature editors wield is awesome in the ivory tower, and it has gone to their heads.

That said, I was a mathy undergrad and now am in a neuro PhD program. The gulf is large indeed. I think the largest difference for me is the relation to science in general. As a mathy person, we are all about the predictive powers of science. I do A, then B happens at time T. In bio, it is not that at all. Bio is an observational science. I see A, then I see B at time T. Sure, you can make predictions, but what these events all have to do with each other is almost impossible to predict in a living organism/environment. As such, when bio people hear Partial Differential Equation, they go running for the hills.

Case in point, PDEs are no big deal for me, I took an entire class on them. But in one class we had to read a paper on using PDEs to model genetic interactions with a sugar input and then write up 1 single page on it (with some guidelines). Oh man, the riot! 59 of the other people in the class were up in arms about this. They tried to get the points on the paper halved, then eliminated, then the teacher to rescind the assignment, which they were all successful in doing. Then the non-stop complaining ensued for weeks in the halls. All because we had to read a paper with PDEs written out in it. My lord.

On the plus side, it leaves a huge hole that none of the bio people want to crawl down. This is a positive for mathy people, as the bio is ore memorization than anything. The bio field is rocking and rolling already from the intrusion that mathy people are mediating. Now, if your lab does not have a CS major in it, you are going to fall behind. The idea that quants and big data people are necessary is just starting to grab hold of the bio world. Now is a good time to get into grad school in the bio field if you have a math background as they are just now starting to realize they need you. It's just hard to get through classes though.

Fomite9• 12 years ago

"Bio is more memorization than anything" - no offense, but this was not so much my experience of biology and related fields. At the same time, I've noticed that many math folks make no effort to reach out to the other side - recognizing that PDEs are a big deal to some people, intimidating, and not exactly terribly approachable. Or assuming because they know the math, surely the biology will just fall into place.

I have seen some very interesting math papers with appalling biology in them.

I think the issue I have with this post, and the article in general, is the very one sided "You need us, take more math" tone. With funding being harder and harder to get in pure math, math also needs applications - biology among them as it potentially unlocks NIH funding. It's not a one-sided failure.

wolfgke5• 12 years ago

At the same time, I've noticed that many math folks make no effort to reach out to the other side - recognizing that PDEs are a big deal to some people, intimidating, and not exactly terribly approachable.

Being a mathematician, I don't know any other way than to say: "Read this and this text and understand it. Then you'll grasp what I'm talking about.". I can tell you that even for many math students, say, PDEs are intimedating and not exactly terribly approachable at the beginning. But the difference is that by reading texts, hearing lectures etc. they simply get over it and get quite used to them. So, I believe, the mathematicians you talk about are quite honest in the sense that they are really doing their best, but simply don't know a better way to talk about their topic.

jmount• 12 years ago

My attempt at motivating schemes: http://www.win-vector.com/blog/2014/12/lets-try-to-motivate-...

chubot• 12 years ago

Meh, I think he just didn't explain what a "scheme" is very well. Compare it the NY Times piece. From that, I immediately understand that it is an elegant generalization of solutions to polynomial equations.

http://www.nytimes.com/2014/11/25/science/the-lives-of-alexa...

Compare it to:

''The proper foundations of the enlarged view of algebraic geometry were, however, unclear and this is how Grothendieck made his first, hugely significant, innovation: he invented a class of geometric structures generalizing varieties that he called schemes. In simplest terms, he proposed attaching to any commutative ring (any set of things for which addition, subtraction and a commutative multiplication are defined, like the set of integers, or the set of polynomials in variables x,y,z with complex number coefficients) a geometric object, called the Spec of the ring (short for spectrum) or an affine scheme, and patching or gluing together these objects to form the scheme. The ring is to be thought of as the set of functions on its affine scheme.''

Sorry, this writing is just awkward. I can see why the editors of Nature rejected it.

I think the audience of Hacker News is closer to mathematics than the audience of nature (programming being more closely related to math than biology). I doubt that anyone in this thread unfamiliar with schemes was able to get much useful from Mumford's obituary. I don't even see many comments on the exposition.

snowwrestler• 12 years ago

To me the difference is that the rejected obit attempts to summarize how Grothendieck's innovations worked mathematically, but what most readers want to know is why they are important.

This is similar to the insight in the tech world that customers don't buy technology because it is built well, they buy it because it solves a problem for them.

flatfilefan• 12 years ago

"most readers want to know is why they are important". This happened to me in my second year studying physics and applied math. The math teacher did not know how to explain the importance of the math around the eigenvalues etc. Only a year later when taking quantum mechanics we got to the applications of that math. However in hindsight I hope he was trolling me :-) otherwise we need a separate curriculum for math teachers to get in touch with the reality :-)

pvaldes• 12 years ago

In fact is not related with mathematics or biology. Is just a literary problem. They are not paying enough attention to the inner flow of their work.

An example:

"This is the field where one STUDIES the 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.

Traditionally, this HAD MEANT complex solutions of

polynomials with

complex coefficients but

just prior to Grothendieck's work,

Andre Weil and Oscar Zariski HAD REALIZED that

much more scope and insight WAS GAINED by

considering solutions and

polynomials over

arbitrary fields,

e.g. finite fields or

algebraic number fields."

........ This is "almost lisp code" in its structure.

The inner flow here is really dislocated here with all those interruptions and changes of direction and meaning. There is also a problem with the timeline. They talk in the same paragraph about at least four, maybe five different moments in time, shown in this order: 5,1,4,3 and maybe 2 (being 1 the oldest and 5 the current time). This is driving to distraction to the reader probably (I find it pretty annoying at least)

UhUhUhUh• 12 years ago

That's a good point. It seems to be very difficult for mathematicians to formulate their thoughts in a non-formal manner. When they try to, it's almost like they speak in a learned second language. That said, mathematics is not really bound by any type of "reality" either, whereas other fields, even physics, certainly are. A little more reality in math and a little more abstraction in the rest would probably help.

kasperset• 12 years ago

This reminds me of how Stephen Altschul had to take help from Sam Karlin(mathematician) in order to so solve sequence similarity problem. Stephen had made his problem look like a mathematical one so Sam could take interest in it. This led him to create BLAST one of the most successful tool in Computational Biology. Link: http://www.nature.com/nbt/journal/v31/n10/full/nbt.2721.html

The two cultures of mathematics and biology

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