The two cultures of mathematics and biology(liorpachter.wordpress.com)
liorpachter.wordpress.com
The two cultures of mathematics and biology
http://liorpachter.wordpress.com/2014/12/30/the-two-cultures-of-mathematics-and-biology/
69 comments
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.
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.
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
[1] https://www2.hu-berlin.de/biologie/theorybp/docs/dipl_scharp...
[2] http://www.sciencemag.org/content/326/5950/289.short
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.
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.
Well,
Another way to consider this is that biologists have not pushed back hard enough to mathematicians in the sense of asking for some tools which would allow for just slurping up a vast amount of unstructured, unprocessed data and getting something out of it.
It is certainly true that mathematical modeling as it is done now currently will indeed only get you so far.
But spirit of math in conjunction with physics has been to create tools that allow leaps and bounds. If we want to follow that spirit, it seems appropriate to ask for tools to help with messy things that now can't easily be dealt with. It may not be possible but it seems worthwhile to go all the way to the brick wall and pound on it.
Another way to consider this is that biologists have not pushed back hard enough to mathematicians in the sense of asking for some tools which would allow for just slurping up a vast amount of unstructured, unprocessed data and getting something out of it.
It is certainly true that mathematical modeling as it is done now currently will indeed only get you so far.
But spirit of math in conjunction with physics has been to create tools that allow leaps and bounds. If we want to follow that spirit, it seems appropriate to ask for tools to help with messy things that now can't easily be dealt with. It may not be possible but it seems worthwhile to go all the way to the brick wall and pound on it.
Unfortunately biologist have been taken for a ride many times by people selling mathematical snake-oil. For example, the whole field of DNA microarrays [1] turned out to be an illusion woven out of applying complex statistical tools to "vast amount of unstructured, unprocessed data". There really is no way you can gain real understanding from poorly designed and unrepeatable experiments by apply obscure mathematical tools.
1. http://en.wikipedia.org/wiki/DNA_microarray
1. http://en.wikipedia.org/wiki/DNA_microarray
Luckily, complex numbers and polynomials are not snake oil.
Wouldn't it be entirely useful for biologists to know more advanced statistical methods?
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.
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.
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.
It depends on what research they're doing. It's also quite easy to be led astray and produce poor work by trying to throw the newest, shiniest thing at something when a much more basic technique will do.
For example, for much of the work I do, you could get away with never using anything more sophisticated than ANOVA.
For example, for much of the work I do, you could get away with never using anything more sophisticated than ANOVA.
I take the opposite stance - if biologists knew about advanced statistical methods they might be tempted to use them.
The general rule in biology is if you need to use statistics you did the wrong experiment. The reason for this rule is it is all too easy to use clever statistical methods to solve a flawed experimental design.
The general rule in biology is if you need to use statistics you did the wrong experiment. The reason for this rule is it is all too easy to use clever statistical methods to solve a flawed experimental design.
It should be noted that "Biology" also encompasses fields where you are limited to uncontrolled observational experiments, which often necessitate more advanced methods.
True, but in this case you should have chosen another field :)
I agree that more advanced statistical methods would be useful. A surprising number of scientists have poor knowledge about statistics whilst being dependent on it to prove their research.
If anyone is depending on statistics to "prove" anything, they're in trouble.
How do you prove that a medicine is safe and effective if not through large scale studies, which you then use statistics to show whether your hypotesus was correct or not?
With statistics I can definitely prove that something holds with a confidence, of, say 0,95, under the model assumptions [...].
If you mistake the p-value on a frequentist hypothesis test for a Bayesian posterior probability, you've already messed up.
Touche, 95% of people who prove things on the internet use statistics.
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/...
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/...
>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
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
Worth mentioning that the "Fundamental Theorem of Natural Selection" was proposed by R.A. Fisher who was responsible for developing the following techniques and theorems (among many other things):
- Analysis of variance (ANOVA)
- Maximum likelihood estimation (MLE)
- Fisher's exact test
- The Fisher-Yeats shuffle algorithm
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.
This is so true. Trying to use the mental tools that work well in physics with biology will lead you astray most of the time.
> 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
How interesting. Usually, it's the math folk who ridicule everyone else for being sloppy with their reasoning. For example, physics = hand-wavery :D
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.
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.
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.
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.
In my experience mathematicians are definitely concerned whether, say, the assumption of exponential distribution is really justified. But what they are interested in is typically a quite general class of (in this case) distributions, where they typically begin with the "simple" cases (which are often normal or exponential distributions).
nod That example was more to illustrate one of several choices a mathematician might make in order to make a problem analytically tractable that might bother a biologist.
Another way of putting it is "A mathematician might be interested in the general properties of dynamical systems, and a biologists entire research agenda at the moment may very well be this set of equations with a very specific parameter set."
Another way of putting it is "A mathematician might be interested in the general properties of dynamical systems, and a biologists entire research agenda at the moment may very well be this set of equations with a very specific parameter set."
> Another way of putting it is "A mathematician might be interested in the general properties of dynamical systems, and a biologists entire research agenda at the moment may very well be this set of equations with a very specific parameter set."
I surely won't disagree, but I want to add the point that when the model turns out to be wrong (and most will), also the biologist will have an interest to know, whether just some parameters (say values of constants, wrong probablility assumption) are wrong or the fundamental model has to be reconsidered.
I surely won't disagree, but I want to add the point that when the model turns out to be wrong (and most will), also the biologist will have an interest to know, whether just some parameters (say values of constants, wrong probablility assumption) are wrong or the fundamental model has to be reconsidered.
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.
I've never heard a physicist claim the sum of all positive integers is -1/12. Such people may exist, but they are extremely rare.
And the Dirac delta is the limit of a function with integral 1, not a function.
Maybe you need to hang out with a better class of physicists? There are certainly plenty of mathematicians who believe odds things, but I'd be leery of tarring the whole lot with the same brush.
And the Dirac delta is the limit of a function with integral 1, not a function.
Maybe you need to hang out with a better class of physicists? There are certainly plenty of mathematicians who believe odds things, but I'd be leery of tarring the whole lot with the same brush.
The sum of all positive integers can actually be considered to be -1/12 in a self-consistent fashion. It isn't equal in the same sense that 2+2=4, and it's still true that the limit at infinity of the partial sum of the positive integers doesn't exist.
On the other hand, it really is a useful result. The negative part is, for example, why the Casimir force is attractive.
Here's an article about the whole thing, with links to the various Numberphile videos and Phil Plait articles that have been done about it: http://physicsbuzz.physicscentral.com/2014/01/does-1234-112....
On the other hand, it really is a useful result. The negative part is, for example, why the Casimir force is attractive.
Here's an article about the whole thing, with links to the various Numberphile videos and Phil Plait articles that have been done about it: http://physicsbuzz.physicscentral.com/2014/01/does-1234-112....
Forgetting for a moment that the entire post is an appeal to authority (in other words, ignoring all logic) here's the culprit quote from the post:
> In the Wikipedia article, they have an equation that looks like this \zeta(-3)=1/120, but the stuff on the left hand side is just another way of writing 1^3+2^3+3^3 +4^3+...
If you can't explain why the above claim is screwy, then every time you claim, "the sum of all positive integers is -1/12," you need to qualify it with "I have no idea why, but I know there's some complicated mathematics that removes the word 'sum' and 'positive integers' and replaces them with more complicated concepts I'm don't have the time to learn about, and we physicists abuse it to say what I just said."
> In the Wikipedia article, they have an equation that looks like this \zeta(-3)=1/120, but the stuff on the left hand side is just another way of writing 1^3+2^3+3^3 +4^3+...
If you can't explain why the above claim is screwy, then every time you claim, "the sum of all positive integers is -1/12," you need to qualify it with "I have no idea why, but I know there's some complicated mathematics that removes the word 'sum' and 'positive integers' and replaces them with more complicated concepts I'm don't have the time to learn about, and we physicists abuse it to say what I just said."
He also says things like
> If QED is correct ... then I would argue that the things that go into QED calculations must be just as correct.
Also not how logic works.
> If QED is correct ... then I would argue that the things that go into QED calculations must be just as correct.
Also not how logic works.
The nuances of mathematics are really extremely important in modern theoretical physics, too, given that most problems in quantum field theory have historically involved divergent integrals that physicists need to converge. (This is also what's preventing a quantum theory of gravity.)
Physics today does have some remarkably talented mathematical thinkers, like Edward Witten, but most of them are involved in very fanciful theories like string theory.
Physics today does have some remarkably talented mathematical thinkers, like Edward Witten, but most of them are involved in very fanciful theories like string theory.
the sum of all positive integers is -1/12, and other such nonsense
Sure sure, but do know that a lot of all that hacky regularization stuff can be made mathematically sound after all --see for instance [1,2].
[1] http://www.maths.qmul.ac.uk/~tp/talks/casimir.pdf#page55
[2] http://terrytao.wordpress.com/2010/04/10/the-euler-maclaurin...
Sure sure, but do know that a lot of all that hacky regularization stuff can be made mathematically sound after all --see for instance [1,2].
[1] http://www.maths.qmul.ac.uk/~tp/talks/casimir.pdf#page55
[2] http://terrytao.wordpress.com/2010/04/10/the-euler-maclaurin...
Of course I know (I'm a mathematician, I'm the one who cringes at all that). The abuse doesn't stop there though... :(
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/
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/
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 (;
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.
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.
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.
Anyone that thinks medicine relies on strict logical reasoning isn't familiar with the reality of medical practice.
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.
My friend math teacher used to say: "only 5% are good at math, but those 5% are good at everything".
Nobody is good at everything. But there is certainly a vocal contingent of maths/physics types who think they are.
>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.
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.
He is talking about percentages, not absolute numbers, as in most math departments less than 10% of full professors are women.
From the AMS study, Table 1, PhD math departments, 420 female out of 4669 total is, by most calculations, less than ten percent.
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.
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.
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.
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.
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.
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.
"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 :-)
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.
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.
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.
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
My attempt at motivating schemes: http://www.win-vector.com/blog/2014/12/lets-try-to-motivate-...
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)
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)
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.
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.
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.
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.
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.
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.
"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.
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.
> 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.
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.
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.
> 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).
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).
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
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).