
The two cultures of mathematics and biology - Fede_V
http://liorpachter.wordpress.com/2014/12/30/the-two-cultures-of-mathematics-and-biology/
======
IndianAstronaut
>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).

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

~~~
jamesli
It is, for sure.

There are some other points to consider. First, the dataset sizes for most
biomedical research are very small. Most advanced statistical methods don't
apply. Due to curiosity, I took some advanced stat courses and tried to apply
the methods to our lab's data. It didn't provide any significant improvement
compared to basic ones, like linear regression, logistic regression, etc.

Second, biomedical research is highly collaborative these days. For some
research that generate a large amount of data, either the researchers
themselves understand statistics very well, or they collaborate with
statisticians very closely. There is a field called biostatistics. Most
biostatistics professors are either math or stat major, and many of them are
adjoint professors in biomedical departments.

Biomedical research is really tedious and time-consuming. The professors I
knew when I was doing biomedical research worked more than 60 hours a day, and
they wish they had more time. One young woman professor came to the lab at
8am, left at 6pm, spent some time with her 4 children, and came back to lab at
9pm again, and worked until midnight, on every weekday. She brought her
children to the lab on Saturday, and worked the whole day. IMHO, it is better
for her to focus all her energy on the biomedical part, which she is best at,
and collaborate with statisticians.

~~~
Fomite
This is a very important point I think - only in very rare cases have I found
my research actively improved by having a more sophisticated method available,
and most projects have a statistician as a collaborator already. If not,
they're readily available. It benefits a biologist to know what the
statistician is talking about, and not just treating the analysis as a black
box, but there's a reason we have subject matter experts. Sometimes, someone
saying "Make sure to use robust variance" is enough information.

------
mbq
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 (;

~~~
Fomite
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.

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

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

------
chubot
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...](http://www.nytimes.com/2014/11/25/science/the-lives-of-alexander-
grothendieck-a-mathematical-visionary.html?_r=1)

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
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
"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
:-)

------
elberto34
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.

~~~
j2kun
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.

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

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

~~~
kaitai
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.

------
epistasis
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.

------
dang
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](https://news.ycombinator.com/item?id=8755800)

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

------
pvaldes
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
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.

------
throwawayxx
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.

~~~
danieltillett
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
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.

~~~
Fomite
"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.

~~~
wolfgke
> 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.

~~~
Fomite
I would suggest starting with "What happened, and why I did it". Having
explained my fair share of stochastic simulations of systems of ODEs to
clinicians, I think the core of the problem is heading into the mathematical
tall grass way to quickly.

~~~
wolfgke
> I think the core of the problem is heading into the mathematical tall grass
> way to quickly.

In my experience non-mathematicians don't like listening to loooong
mathematical talks (although those would be necessary for introducing the
topic in a more smooth way).

------
kasperset
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](http://www.nature.com/nbt/journal/v31/n10/full/nbt.2721.html)

