Still, even if there are mathematicians able and willing to explain schemes to biologists, and even if there are areas within biology where schemes arise e. The answer to the question is: probably not. However I do have an opinion about the area I work in, namely genomics. But the biology of genomics is for real, and it is indeed tremendously exciting as a result of dramatic improvements in underlying technologies e.
DNA sequencing and genome editing to name two. I also believe it is true that despite what is written about data deluge, experiments remain the primary and the best way, to elucidate the function of the genome. Data analysis is secondary. That is what mathematicians can contribute most of all to genomics. Of course sometimes theorems are important, or specific mathematical techniques solve problems and mathematicians are to thank for that.
Phylogenetic invariants are important for phylogenetics which in turn is important for comparative genomics which in turn is important for functional genomics which in turn is important for medicine. But it is the the abstract thinking that I think matters most. The answer matters not only for the technology how to store genomes , but much more importantly for the foundations of population and statistical genetics.
Without the right abstractions for genomes, the task of coherently organizing and interpreting genomic information is hopeless. David Haussler with coauthors and Richard Durbin have both written about this problem in papers that are hard to describe in any way other than as math papers; see Mapping to a Reference Genome Structure and Efficient haplotype matching and storage using the positional Burrows-Wheeler transform BPWT. Perhaps it is no coincidence that both David Haussler and Richard Durbin studied mathematics.
But neither David Haussler nor Richard Durbin are faculty in mathematics departments. In fact, there is a surprisingly long list of very successful computational biologists specifically working in genomics, many of whom even continue to do math, but not in math departments, i. And does it matter? It is certainly the case that to do mathematics, or to publish mathematical results, one does not need to be a faculty member in a mathematics department.
Nature publishes its impact factor to three decimal digits accuracy The impact factor of the Annals of Mathematics, perhaps the most prestigious journal in mathematics, is 3 the journal with the highest impact factor is the Journal of the American Mathematical Society at 3. Mathematicians post all papers on the ArXiv preprint server prior to publications.
Not only do biologists not do that, they are frequently subject to embargos prior to publication. Biologists draw figures and write papers about them. Mathematicians write papers and draw figures to explain them. Biologists author lists have two gradients from each end, and authorship can be awarded for payment for the work. Mathematicians review papers on two year deadlines.
Biologists have their papers cited by thousands, and their results have a real impact on society; in many cases diseases are cured as a result of basic research. Mathematicians are lucky if 10 other individuals on the planet have any idea what they are writing about. Impact time can be measured in centuries, and sometimes theorems turn out to simply not have been interesting at all. Mathematicians do at UC Berkeley my math teaching load is 5 times that of my biology teaching load. Biologists have chalk talks during job interviews.
Mathematicians have a jobs wiki. Mathematicians write ten page recommendation letters. Biologists go to retreats to converse. Mathematicians retreat from conversations my math department used to have a yearly retreat that was one day long and consisted of a faculty meeting around a table in the department; it has not been held the past few years. Mathematics graduate students teach. Biology graduate students rotate.
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Biology students take very little coursework after their first year. Biologists pay their graduate students from grants. Mathematicians believe in God. And how can mathematics find a place within the culture of biology? Yes, there are biologists who do mathematical work, and yes, there are mathematical biologists, especially in areas such as evolution or ecology who are in math departments.
There are certainly applied mathematics departments with faculty working on biology problems involving modeling at the macroscopic level, where the math fits in well with classic applied math e. PDEs, numerical analysis. But there is very little genomics or genetics related math going on in math departments. And conversely, mathematicians who leave math departments to work in biology departments or institutes face enormous pressure to not focus on the math, or when they do any math at all, to not publish it work is usually relegated to the supplement and completely ignored.
He was right. In the mathematics community, there has been almost no effort to engage and embrace genomics. For example the annual joint AMS-MAA meetings always boast a series of invited talks, many on applications of math, but genomics is never a represented area. Yet in my Junior level course last semester on mathematical biology taught in the math department there were 46 students, more than any other upper division elective class in the math department. There is a hypocrisy of math for biology.
People talk about it but when push comes to shove nobody wants to do anything real to foster it. The point is that the UCLA situation is ubiquitous. Mathematics departments are almost never part of new initiatives in genomics; biologists are all too quick to glance the other way. Conversely, the mathematics community has shunned biologists. I get it. The laundry list of differences between biology and math that I aired above can be overwhelming. Real contact between the subjects will be difficult to foster, and it should be acknowledged that it is neither necessary nor sufficient for the science to progress.
The opening paragraph is an edited copy of an excerpt page 2, paragraph 2 from C. Mumford is known for his work on geometric invariant theory. Comments feed for this article. December 30, at am.
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Damian Kao. From my experience, the frosty attitude of biologists towards mathematics is partly rooted in being intimidated by the subject and also perception of its utility lack of. Academics are prideful creatures. I am not sure if this can be fixed. The perception that mathematics is not very useful is short-sighted.
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While I agree that practical applications of mathematics might not apply to a lot of the experimental work being conducted is that a fault of the experimental design? There are a lot of hand-wavy abstractions in biology that could benefit from a rigid mental framework.
It may take me a couple of days to digest a technical mathematics-heavy paper, but at least I know that every part of the thought process is recorded down explicitly in a consistent mathematical language. I cannot say the same for a lot of biology papers where definitions of terms can possibly be different depending on what lab you are in or the historical context of the field. A lot to like and think about here, but I particularly appreciate your Gian-Carlo Rota quote. December 30, at pm. I cannot say that I see mathematics as somehow seeing everything in the right way.
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Mathematicians, including those other than my immediate relations, have ways of deciding which problems are interesting that pose difficulties for a biologist. They even pose difficulties for engineers. It seems to take a number of steps of translation to get from mathematics to many of the sciences; and from there, several steps to real applications. There is real danger when people get their hands on tools with which they are inexperienced. It takes time to even appreciate the skill of a master.
Despite the vast gap that I have experienced, I am not gloomy about the relationship between the fields, because there are growing classes of intermediaries. A sort of multivariate stepped impedance matching. The requirement for mediation certainly appears to slow the progress of solving world problems, but on the other hand, how well did it work out for a mathematician to directly change society in ? It seems to me that there exists plenty of contact between mathematics and biology; in fact there are entire disciplines that apply mathematics to biology.
These are not purely mathematics disciplines, but interdisciplinary fields such as bioinformatics, computational biology, and biostatistics. Why should we prefer that genomics and genetics work be done in math departments rather than in these departments? Or do you think that mathematicians can make unique contributions where these other disciplines cannot? December 31, at am. Jonathan Badger. Just like bench biologists know that sometimes they have to work with real chemists despite knowing a bit of chemistry themselves, computational biologists need to know when real mathematicians are needed.
December 31, at pm. Lior Pachter. As I acknowledged in my post, there are contributions to be made by statisticians, computer scientists and many others. My first independent paper applied percolation theory to study how Bloom filters could be used to accurately store De Bruijn sequence graphs for metagenome assembly ;. Reblogged this on Virgilio Leonardo Ruilova Castillo. Christos Ouzounis. We probably need a new mathematics for a new biology, most likely to come from mathematicians. Problem is that learning curves for both disciplines are very steep.
Few individuals can and do master both. One positive recent development is a large increase in double majors in mathematics and biology or statistics and biology. I was reminded of this last night when I met an alumna of my Math 10 class who then decided to double major in statistics and biology and is now applying to medical school.