# Great Scientist ≠ Good at Math?

April 8, 2013 6:42 AM Subscribe

Do you need to know math to do science? Harvard professor emeritus E. O. Wilson says, "no." Jeremy Fox, an Associate Professor of Population Ecology at the University of Calgary disagrees.

If you try to do general relativity or quantum mechanics without getting the maths, sorry, you ain't getting it.

posted by Decani at 7:05 AM on April 8, 2013

posted by Decani at 7:05 AM on April 8, 2013

*Many of the most successful scientists in the world today are mathematically no more than semiliterate.*

Of course he means "semiliterate" in the metaphorical sense of not knowing by heart a dozen ancient languages on top of the usual complete mastery of Greek and Latin, but it still seems like an odd statement. No more than semiliterate.... but nonetheless having completed many thousands of hours of study of calculus, probability, statistics, etc. This has a sort of "Do not worry about your difficulties in mathematics, I can assure you that mine are greater still" arrogance to it.

*For aspiring scientists, a key first step is to find a subject that interests them deeply and focus on it. In doing so, they should keep in mind Wilson's Principle No. 2: For every scientist, there exists a discipline for which his or her level of mathematical competence is enough to achieve excellence.*

It's OK to speak Spanish in the halls.

posted by three blind mice at 7:08 AM on April 8, 2013 [1 favorite]

Echoing three blind mice somewhat, there's a world of difference between being unable to *do* the math and being unable to *understand* it. Being able to read and understand some equations or statistical reasoning is critical. Being able to create that work is not, necessarily.

posted by Slothrup at 7:15 AM on April 8, 2013 [1 favorite]

posted by Slothrup at 7:15 AM on April 8, 2013 [1 favorite]

*Call it Wilson's Principle No. 1: It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations.*

That seems a bit specious. He doesn't need to know the math, because he can easily find somebody to do the work for him?

posted by mhoye at 7:17 AM on April 8, 2013 [1 favorite]

I am a biologist with very average math skills, and as such I think I read what Wilson said with a little more charity than I would if I was a computational or population biologist. What I read was a suggestion that students with an interest in biology should remain in biology programs, even if you're not very good at math. He's encouraging people who might not have had the best elementary or early educations to stick with the field. In my mind, this is an excellent idea, as the people teaching and working in the field are remarkably un-diverse.

I think what Wilson is saying is essentially this: You don't need to be an accountant to run a business, you can hire, trade or collaborate with one. You do need focus though.

posted by kuujjuarapik at 7:19 AM on April 8, 2013 [23 favorites]

I think what Wilson is saying is essentially this: You don't need to be an accountant to run a business, you can hire, trade or collaborate with one. You do need focus though.

posted by kuujjuarapik at 7:19 AM on April 8, 2013 [23 favorites]

Try having this discussion with lawyers and law students. At least Wilson recognizes that math plays a role in doing the hard work of science, even if he short changes both the role and those that can do the math. Many lawyers (and these are our public policy makers, mind you), count having avoided math and science in school as a

posted by monju_bosatsu at 7:21 AM on April 8, 2013 [4 favorites]

*success*.posted by monju_bosatsu at 7:21 AM on April 8, 2013 [4 favorites]

*If you try to do general relativity or quantum mechanics without getting the maths, sorry, you ain't getting it.*

But there is a lot of other science which requires only a moderate amount of maths - I've known chemists, zoologists, botanists, psychologists, even epidemiologists who have only undergraduate level maths and probably would not describe themselves as being especially talented in maths. When they need to do higher level maths, they collaborate with statisticians, etc.

The point is that people should not write themselves out of science just because they are only average at math. No, they will probably not be theoretical physicists. But they may do perfectly fine in hundreds of other fields - many of which (eg health) have better job prospects.

posted by jb at 7:21 AM on April 8, 2013 [2 favorites]

People have strange ideas about math....I remember talking to a woman who was thinking about learning database administration but was worried because she hadn't done well in calculus.....I told her no one would make her do any definite integrals and that she should pursue her interests.

posted by thelonius at 7:22 AM on April 8, 2013 [2 favorites]

posted by thelonius at 7:22 AM on April 8, 2013 [2 favorites]

This is why biologists aren't real scientists ;)

posted by zscore at 7:23 AM on April 8, 2013 [10 favorites]

posted by zscore at 7:23 AM on April 8, 2013 [10 favorites]

By the way, if you're interested in doing an experiment and want the help of a statistician... get them involved before you do the experiment, not after. The statistician will be able to give you input about which experimental designs can best answer the questions you have.

posted by Jpfed at 7:30 AM on April 8, 2013 [20 favorites]

posted by Jpfed at 7:30 AM on April 8, 2013 [20 favorites]

YOU don't have to have the math skills, but you need math skills. They both agree on this.

That said, everything Wilson says about hypothesizing and imagination are skills that are required for mathematics. Formulating your scientific ideas will go much better if you are skilled in mathematics.

posted by Mental Wimp at 7:32 AM on April 8, 2013 [2 favorites]

That said, everything Wilson says about hypothesizing and imagination are skills that are required for mathematics. Formulating your scientific ideas will go much better if you are skilled in mathematics.

posted by Mental Wimp at 7:32 AM on April 8, 2013 [2 favorites]

The response article makes a rhetorical move I very strongly dislike. Namely, it takes statements about possibility to be statements about necessity. "People do X." is construed to mean "People

Wilson doesn't discount the power of mathematical knowledge, but points out that for many scientistis — even those with great mathematical talent — scientific discovery is not just a number-crunching exercise. Many discoveries are made via intuition and abstract thinking, and then later confirmed by mathematics. He is not saying that that is how every discovery is — or should be — made, and I honestly don't understand why people would read the article to imply that.

posted by cthuljew at 7:35 AM on April 8, 2013 [5 favorites]

*only*do X."Wilson doesn't discount the power of mathematical knowledge, but points out that for many scientistis — even those with great mathematical talent — scientific discovery is not just a number-crunching exercise. Many discoveries are made via intuition and abstract thinking, and then later confirmed by mathematics. He is not saying that that is how every discovery is — or should be — made, and I honestly don't understand why people would read the article to imply that.

posted by cthuljew at 7:35 AM on April 8, 2013 [5 favorites]

*By the way, if you're interested in doing an experiment and want the help of a statistician... get them involved before you do the experiment, not after. The statistician will be able to give you input about which experimental designs can best answer the questions you have.*

Can't second this enough. And the reason this is true? The statistician has to be educated to the science behind the experiment to the extent that she can choose the proper experimental design and and statistical analysis. If you've never worked with a good statistician before, you will be surprised at the depth of subject matter knowledge necessary for good design and analysis.

posted by Mental Wimp at 7:35 AM on April 8, 2013 [1 favorite]

*Formulating your scientific ideas will go much better if you are skilled in mathematics.*

I would say that

*testing*your scientific ideas will go better if you are skilled at math. Designing your experiments certainly will. But making the observations that lead to the experiments requires intuitions that can be independent of math.

posted by kuujjuarapik at 7:37 AM on April 8, 2013 [1 favorite]

I think of E. O. Wilson as the old "scientist-as-explorer," who drove across the US with Tom Eisner to catalog insects they found. In that light, I could see his wish for people to not shy away from sciences for fear of their lack of skill in math.

And I agree with

posted by filthy light thief at 7:44 AM on April 8, 2013

And I agree with

**cthuljew**that the linked response piece is a bit hyperbolic, seeming like the author was already formulating a blog post after reading the WSJ title that is trolling for attention.posted by filthy light thief at 7:44 AM on April 8, 2013

*Wilson's Principle No. 1: It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations.*

Dear god, this. This for an hour. I am currently dealing with an electrical engineer, a guy who has this really complicated method of analyzing mRNA microarray data as "nodes" in some complex modeling system to determine what genes are most important or most inter-related between two or more groups. It doesn't work without massive amounts of data points. Problem is, he has ZERO idea what it all means, nor does he care. He shoves out a pile of data, says "these are the important nodes" and then asks (I am not kidding here) "What physiological process or behavior is this data modeling?" I cannot fathom this approach. In my field, we define the problem first and then plan the study, not the other way around. He has a method and is looking for a problem he can solve with it. It boggles my mind.

And it isn't even data, per se. It's a list of line numbers from an Excel file. No matter how many times I ask for it, he can't even use the individual gene accession numbers as identifiers, he uses the line numbers from the spreadsheet, because to him it's just a big math problem while to me and my colleagues there is no point in pursuing it if the "nodes" (genes) actually have fuck-all to do with the behavior we are trying to explain. And unless I know with absolute certainty there is a 1:1 correlation between line numbers and gene accession numbers, I can't look up the genes and verify that ANY of them are involved in our behavioral measures.

He wants to know where we are going to publish it, without understanding that you can't just crunch numbers and send it off in biology. There must be some connection to reality. The model is not the interesting part, unless you have also shown that the model accurately reflects the biology.

Jpfed: "

*By the way, if you're interested in doing an experiment and want the help of a statistician... get them involved before you do the experiment, not after.*"

...unless, of course, the statistician gives you bad advice and leaves you with ~$10,000 of wasted microarray data because he asked a grad student to design the experiment for you and now can't explain exactly what the setup was and his analysis of the data makes zero sense, biologically. Because then, you're stuck asking an engineer with a really complicated model if there's anything you can salvage from the study.

(I guess this is what I get for saying "Gee, sure, I'll take a look at that old microarray data and see what we can do with it...")

posted by caution live frogs at 7:47 AM on April 8, 2013 [16 favorites]

*This is why biologists aren't real scientists ;)*

Yet every time I go a restaurant with friends, who is that can calculate the tip without whipping out a smart phone? It's not the particle physicists, I'll tell you that much.

posted by maryr at 7:47 AM on April 8, 2013 [4 favorites]

,,,and you don't need to be able to read music to be a great musician. But if you can't, you almost certainly aren't.

posted by hexatron at 7:49 AM on April 8, 2013 [1 favorite]

posted by hexatron at 7:49 AM on April 8, 2013 [1 favorite]

*who was thinking about learning database administration but was worried because she hadn't done well in calculus.*

Well - not calculus, but I'd expect a competent DBA to be able to understand why two queries are equivalent, which can require more formal logic than most people afraid of math will be comfortable with.

posted by dhoe at 7:49 AM on April 8, 2013

*and you don't need to be able to read music to be a great musician. But if you can't, you almost certainly aren't.*

Really? You know about the strong tradition of blind musicians, right?

posted by OmieWise at 7:50 AM on April 8, 2013 [5 favorites]

I published a bunch of neuroscience papers with decent stats, and my math skills are not great. Anything more complex than an ANOVA or a chi-squared test I consulted our departmental biostatistician. Seemed more sensible than fucking it up myself.

posted by gaspode at 7:54 AM on April 8, 2013

posted by gaspode at 7:54 AM on April 8, 2013

*If you try to do general relativity or quantum mechanics without getting the maths, sorry, you ain't getting it.*

But the field theory of electromagnetism was conjured into being by Michael Faraday, an autodidact chemist with only basic arithmetic skills... the magic being that, per special relativity, the electromagnetic field doesn't exist in any measurable sense; it's a convenient, or mathematical, fiction.

posted by ennui.bz at 8:02 AM on April 8, 2013 [1 favorite]

*Many discoveries are made via intuition and abstract thinking, and then later confirmed by mathematics.*

This is as true in mathematics as it is in any of the empirical sciences. Pure mathematicians put a great deal of effort into developing "intuition" as to what is going to be true and what isn't. But I will just replace every instance of the word "mathematics" in this thread with the word "computation", and keep on reading.

posted by Elementary Penguin at 8:03 AM on April 8, 2013 [3 favorites]

Decani: If you try to do general relativity or quantum mechanics without getting the maths, sorry, you ain't getting it.Um, duh; but that's hardly the point of the article. Read it. He doesn't ever suggest those two scientific avenues are part of his statement.

posted by IAmBroom at 8:04 AM on April 8, 2013

Discoverblogs Gene Expression:

posted by T.D. Strange at 8:05 AM on April 8, 2013 [3 favorites]

*First, a disproportionate number of the famous and successful scientists alive today are old, like E. O. Wilson. Just because you could get by with a certain level of mathematical fluency as an enfant terrible in the 1970s does not mean that that will cut it in the 2010s. Great scientists who are mathematically weak often have collaborators, post-docs, and graduate students, who do their bidding. It might be a different matter if you aren’t one of the Great Ones of the earth. From what I can tell scientists who are doing the hiring who don’t have mathematical skills prefer candidates who do have mathematical skills.*posted by T.D. Strange at 8:05 AM on April 8, 2013 [3 favorites]

I'm a physicist with two kids who have a rare medical condition. This has lead to me reading a

Sometimes I get frustrated when our medical professionals seem less able to understand the relevance of these questions than I am, and less able to read and judge the merits of the related studies. (I learned all my stats in quantum mechanics and statistical mechanics classes, but I know enough tell the difference between a rock-solid conclusion and low statistical significance.)

At times like this, I think of all the medical students I TA'd who looked at their required physics and math classes in college as "weed out classes" that they resented having to take, and I really wish they'd paid more attention.

Maybe you don't have to know as much math to make some kind of progress in the life sciences as you do in physics, but to the extent that you don't, I think you're handicapped, and I think you should try to fix that.

(And I, as an experimental physicist, am handicapped by not knowing nearly as much electrical engineering as I should, because that is one of the tools of

posted by OnceUponATime at 8:10 AM on April 8, 2013 [9 favorites]

*lot*of papers outside my field, and asking a lot of questions of our medical practioners. Often, those questions are quantitative. 'What are the time constants associated with metabolism and excretion of this amino acid? What is the steady-state condition? What are the gradients across the blood-brain barrier?"Sometimes I get frustrated when our medical professionals seem less able to understand the relevance of these questions than I am, and less able to read and judge the merits of the related studies. (I learned all my stats in quantum mechanics and statistical mechanics classes, but I know enough tell the difference between a rock-solid conclusion and low statistical significance.)

At times like this, I think of all the medical students I TA'd who looked at their required physics and math classes in college as "weed out classes" that they resented having to take, and I really wish they'd paid more attention.

Maybe you don't have to know as much math to make some kind of progress in the life sciences as you do in physics, but to the extent that you don't, I think you're handicapped, and I think you should try to fix that.

(And I, as an experimental physicist, am handicapped by not knowing nearly as much electrical engineering as I should, because that is one of the tools of

*my*job, that I disdained to learn about while I was in training. Now I regret that, and I'm trying to catch up.)posted by OnceUponATime at 8:10 AM on April 8, 2013 [9 favorites]

OmieWise:You're actually both correct. The vast majority of any group that isn't explicitly composed of "great musicians" almost certainly aren't -and you don't need to be able to read music to be a great musician. But if you can't, you almost certainly aren't.

Really? You know about the strong tradition of blind musicians, right?

**hexatron**'s statement is important-sounding, but virtually meaningless. And, of course,

**hexatron**'s implication - that reading music is very nearly essential to great musicianship - is questionable at best.

It's a path many follow, but there are masters of many non-Western traditions that prove it's hardly the only path... not to mention the blind ones.

posted by IAmBroom at 8:11 AM on April 8, 2013

mhoye:Yes; it's not specious at all. I've been hired for just that reason, in the past. It's simply collaboration; it's analogous to a musician hiring a brass player, because (although the musician can compose, write lyrics, and play the shit out of the piano and guitar) they simply don't know how to play a trumpet at a professional level.Call it Wilson's Principle No. 1: It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations.

That seems a bit specious. He doesn't need to know the math, because he can easily find somebody to do the work for him?

posted by IAmBroom at 8:14 AM on April 8, 2013 [1 favorite]

*Great scientists who are mathematically weak often have collaborators, post-docs, and graduate students, who do their bidding. It might be a different matter if you aren’t one of the Great Ones of the earth.*

I'm not sure about that. I'm at a relatively small, not especially well-known university, and the department of biological sciences has a statistician on staff. She frequently assists the graduate students in the department with their research. So here, even the graduate students have a statistician they can call on for help. I can only imagine that larger, more prestigious institutions have even better resources.

posted by Mitrovarr at 8:14 AM on April 8, 2013

*So here, even the graduate students have a statistician they can call on for help. I can only imagine that larger, more prestigious institutions have even better resources.*

Not in my experience. I have worked (and still do) in the best departments in the world for my field, and when everyone on the faculty is both an excellent biologist and an excellent statistician, the departmental statistician is redundant. I don't actually remember a department that had one.

The equivalent role seemed to be filled by someone who could actually code properly.

posted by cromagnon at 8:22 AM on April 8, 2013 [2 favorites]

T.D. Strange: "

Well, more correctly, great scientists~~who are mathematically weak~~ often have collaborators, post-docs, and graduate students, ~~who do their bidding~~ because no one who wishes to be successful is going to get anywhere these days running as a lone wolf. It's just too damn hard, and no matter how smart you are, when two or three people (who may individually be slightly less smart than you) team up, you're on the short end of the stick in comparison.

And science is becoming increasingly specialized. I'm a behavior guy, myself; but I collaborate with a pharmacologist because she understands intracellular stuff in a way that I will never match, because she spent her doctoral training doing that while I was taking courses in evolutionary bio and animal behavior and circadian biology. Both of us have been working with another PhD, a guy who lives and breathes HPLC, because we each

posted by caution live frogs at 8:30 AM on April 8, 2013 [5 favorites]

*Great scientists who are mathematically weak often have collaborators, post-docs, and graduate students, who do their bidding.*"Well, more correctly, great scientists

And science is becoming increasingly specialized. I'm a behavior guy, myself; but I collaborate with a pharmacologist because she understands intracellular stuff in a way that I will never match, because she spent her doctoral training doing that while I was taking courses in evolutionary bio and animal behavior and circadian biology. Both of us have been working with another PhD, a guy who lives and breathes HPLC, because we each

*could*learn how to run the machine, but if we have him do it, all three of us are free to do what we each do best, which makes all of us more productive. And that's only three of us. That doesn't include the senior PIs, clinicians, cardiologists, surgeons, statistician, postdocs, undergrads, grad students, lab techs, colleagues we bounce ideas off of in the hallway, etc. - scientists roam in packs these days, because there is protection in numbers and funding is scarce.posted by caution live frogs at 8:30 AM on April 8, 2013 [5 favorites]

**caution live frogs**, I hear you a thousand times over. I took the Introduction to Machine Learning class while getting my Master's in Computer Science and I remember how in every class session the professor would go up, start with an intial equation, and very carefully walk through the derivation of a model that it was actually possibly to implement, pointing out pitfalls along the way and writing down every step.

After he had done this I'd raise my hand and ask what kind of data this was good for, and his reply, every single time, was completely abstract - "You have a classification problem where you know the number of classes", "You have a lot of samples and a small number of dimensions", and so forth. I would then ask what an actual example of such a data set was, and thankfully I got an answer, but it always took pushing.

A few of the homeworks had very obvious data sets - the Iris one, simple handwriting recognition for Arabic numerals - but most of them weren't labeled at all, and I remember asking what the sample data we were given on one assignment was and waiting a few days for one of the TAs to figure it out. It was only important as dots on a graph.

The thing that really upsets me about this is that while the derivations are very important, particularly in that they help you understand

*why*each model has its own peculiar strengths and weaknesses, just knowing the right method to use in a given situation and using a pre-packaged solution like SciPy opens up a world of research possibilities to people who are never going to make a classifier that's .01% better on a given standard data set but still have work that needs doing.

I find it heartening that there's guides to data analysis that aren't focused on implementing well-understood algorithms from scratch any more - I just saw a link to this Practical Intro to Data Science the other day - and I hope to see more of it.

posted by 23 at 8:40 AM on April 8, 2013 [2 favorites]

It's also more complex than "Is numerical ability as a precondition of biological understanding? Y/N"

Biological systems are messy and noisy; full of uninteresting nonlinear interactions and low effect sizes. Most physicists I know find it inconceivable that there could be anything actually worth knowing about the things I work on - and that's a direct quote from one of the nicest ones ;)

I think, by that, she meant "satisfying to know", which is sufficiently subjective that I didn't feel offended. This of course doesn't mean you don't need numerical ability to get the most out of those messy systems, just that the physicists' search for universal laws isn't the primary reason biologists get involved in biology (or more accurately that the universes we work in are smaller).

And, conversely, Fox's own field of population ecology (as are a lot of biological fields) is changing rapidly because of the insights from metagenomics - and that was because someone had both the bright idea to go looking for wide-scale microbial patterns over time and the technology to do so - and had nothing really to do with mathematical ability at all. So for me, Wilson's right that the big ideas aren't constrained to come from advances in applied mathematics within a field, but wrong in not recognising that the numerical barrier to entry is getting higher every year. Both, not one or the other.

posted by cromagnon at 8:44 AM on April 8, 2013 [3 favorites]

Biological systems are messy and noisy; full of uninteresting nonlinear interactions and low effect sizes. Most physicists I know find it inconceivable that there could be anything actually worth knowing about the things I work on - and that's a direct quote from one of the nicest ones ;)

I think, by that, she meant "satisfying to know", which is sufficiently subjective that I didn't feel offended. This of course doesn't mean you don't need numerical ability to get the most out of those messy systems, just that the physicists' search for universal laws isn't the primary reason biologists get involved in biology (or more accurately that the universes we work in are smaller).

And, conversely, Fox's own field of population ecology (as are a lot of biological fields) is changing rapidly because of the insights from metagenomics - and that was because someone had both the bright idea to go looking for wide-scale microbial patterns over time and the technology to do so - and had nothing really to do with mathematical ability at all. So for me, Wilson's right that the big ideas aren't constrained to come from advances in applied mathematics within a field, but wrong in not recognising that the numerical barrier to entry is getting higher every year. Both, not one or the other.

posted by cromagnon at 8:44 AM on April 8, 2013 [3 favorites]

*Yet every time I go a restaurant with friends, who is that can calculate the tip without whipping out a smart phone? It's not the particle physicists, I'll tell you that much.*

It's easy. First we use units in which the total bill is equal to 1, then we just take the desired tip percentage of that. Simple and intuitive!

posted by atrazine at 8:50 AM on April 8, 2013 [7 favorites]

Wilson's statement doesn't add up.

posted by fairmettle at 8:56 AM on April 8, 2013

posted by fairmettle at 8:56 AM on April 8, 2013

I loved science in middle & high school but at the college level it increasingly became about boring-ass math so I dropped both.

posted by 2bucksplus at 9:17 AM on April 8, 2013

posted by 2bucksplus at 9:17 AM on April 8, 2013

T.D. Strange, Razib Khan is also mainly interested in quantitative genetics, so you should probably take that with a grain of salt. There are plenty of younger people working in molecular biology who are not particularly math-y.

posted by en forme de poire at 9:55 AM on April 8, 2013

posted by en forme de poire at 9:55 AM on April 8, 2013

Decani: "

Maths is an

Even in the two examples that you gave, QM and Relativity require vastly different subsets of mathematics. QM is almost

It's almost interesting that Mathematics is considered a separate discipline from the sciences. Math is a toolkit for doing science, and that the composition and use of that toolkit varies considerably and distinctively from one field to another.

posted by schmod at 10:27 AM on April 8, 2013 [1 favorite]

*If you try to do general relativity or quantum mechanics without getting the maths, sorry, you ain't getting it.*"Maths is an

*awfully*huge umbrella.Even in the two examples that you gave, QM and Relativity require vastly different subsets of mathematics. QM is almost

*entirely*about computing probabilities; Relativity is much more difficult on a conceptual level than it is on a mathematical level -- once you figure out what you're trying to solve, the math's usually quite basic; Thermodynamics requires a*ton*of statistics, which people (myself included) often have a tough time wrapping their heads around; Condensed Matter Physics uses a bit of everything; Computer Scientists use a ton of discrete mathematics, which Physicists rarely ever need to touch.It's almost interesting that Mathematics is considered a separate discipline from the sciences. Math is a toolkit for doing science, and that the composition and use of that toolkit varies considerably and distinctively from one field to another.

posted by schmod at 10:27 AM on April 8, 2013 [1 favorite]

**caution live frongs**:

*He has a method and is looking for a problem he can solve with it. It boggles my mind.*

-- sounds a lot like "Big Data"

posted by grubby at 10:40 AM on April 8, 2013

I had a transformative experience with this issue while reading "Wind Waves" by Blair Kinsman (written in the '60s). An older (1st?) edition of this book (not the one I can find on-line) had a preface about the mathematics necessary to understand the book. It was a little bit of a rant about how mathematics is a tool that scientists use to beat other scientists with, and how it shouldn't be that way.

If you can find the edition with this preface, it is highly recommended reading.

The bottom line is that mathematics for science can and should be always easily explained to other scientists. If it can't be, it either isn't useful, or someone is being a jerk.

posted by grajohnt at 10:41 AM on April 8, 2013 [3 favorites]

If you can find the edition with this preface, it is highly recommended reading.

The bottom line is that mathematics for science can and should be always easily explained to other scientists. If it can't be, it either isn't useful, or someone is being a jerk.

posted by grajohnt at 10:41 AM on April 8, 2013 [3 favorites]

While Wilson might be technically right that scientific ability is distinct from mathematical ability, at least in some fields of science, I think that publicizing this argument will do more harm than good in the long term. As it is, in the US there is a culturally-ingrained distaste for math, which results in very few pursuing mathematical training. The more the students are told that they can achieve everything they want without math, the fewer mathematically trained professionals there will be. If that trend persists long enough, eventually all those biologists, for instance, will find mathematical collaborators increasingly hard to find.

posted by epimorph at 10:46 AM on April 8, 2013 [1 favorite]

posted by epimorph at 10:46 AM on April 8, 2013 [1 favorite]

*Many lawyers (and these are our public policy makers, mind you), count having avoided math and science in school as a success.*

Ironically, I've been told that math majors actually have the highest LSAT success rate. 'Cause math majors learn how (at least a little bit) how to construct logical arguments, accounting for all possible complications (admittedly in a subject area that in some ways is much simpler than law, due to the things that math majors have to construct arguments about being well-defined).

*It's almost interesting that Mathematics is considered a separate discipline from the sciences. Math is a toolkit for doing science, and that the composition and use of that toolkit varies considerably and distinctively from one field to another.*

Well, there's math, and applied math. Mathematics as an academic discipline is the deductive study of mathematical objects - abstract things with precise definitions. Some fields of math involve calculation; others involve shape; others are much more abstract. But in all cases the "mathematical method" is logical deduction and argumentation. That's quite distinct from the scientific method; math, as an academic discipline, is not a science. But yeah, results from mathematics - applied math - are extremely useful in the sciences.

posted by eviemath at 10:51 AM on April 8, 2013 [2 favorites]

*I would say that testing your scientific ideas will go better if you are skilled at math. Designing your experiments certainly will. But making the observations that lead to the experiments requires intuitions that can be independent of math.*

Most of science has moved beyond simple, qualitative descriptions of phenomena. Mathematical models are now at the heart of most useful sciences. It was no accident that statistics and genetics co-evolved or that mathematical computer models are used to identify novel molecules that can treat specific disorders. Math is not at the periphery or just used to get a p-value, but is at the core these days.

posted by Mental Wimp at 10:51 AM on April 8, 2013 [1 favorite]

And yet, most of molecular biology from the 70s onward made essentially no use of statistics (beyond basic hypothesis testing) to say nothing of mathematical modeling. Even if you crack open a copy of Cell these days, the most quantitative thing you're likely to see is a growth/survival curve or a bar chart. (Maybe a heat map!)

Don't get me wrong, for a biologist I am a big proponent of stats, coding, and math and think a lot of scientists would benefit from a better understanding of these fields. But there's certainly a lot of elegant scientific reasoning that you can do with an extremely basic mathematical toolkit.

posted by en forme de poire at 11:17 AM on April 8, 2013 [2 favorites]

Don't get me wrong, for a biologist I am a big proponent of stats, coding, and math and think a lot of scientists would benefit from a better understanding of these fields. But there's certainly a lot of elegant scientific reasoning that you can do with an extremely basic mathematical toolkit.

posted by en forme de poire at 11:17 AM on April 8, 2013 [2 favorites]

I think my (very strong) opinion runs pretty counter to the general feeling of this thread. First, Wilson didn't need math skills because he was a biologist in the 70s, when getting a partial sequence of a single gene was a Nature paper. Not much math needed then, biology was a different thing.

Now we have systems biology, neuroscience and population biology all moving in a pretty mathy direction. Molecular biology is morphing with biophysics and becoming pretty mathy as well, especially when you talk about drug design and/or large scale data analysis. To wit:

The problem here is that one person, who understands both the math and the biology is the right person to do this job. You can definitely be a biologist these days and not understand math beyond the basics. However, you're more and more likely to be outcompeted by the people who are complete scientists.

posted by overhauser at 11:46 AM on April 8, 2013

Now we have systems biology, neuroscience and population biology all moving in a pretty mathy direction. Molecular biology is morphing with biophysics and becoming pretty mathy as well, especially when you talk about drug design and/or large scale data analysis. To wit:

*Dear god, this. This for an hour. I am currently dealing with an electrical engineer, a guy who has this really complicated method of........*The problem here is that one person, who understands both the math and the biology is the right person to do this job. You can definitely be a biologist these days and not understand math beyond the basics. However, you're more and more likely to be outcompeted by the people who are complete scientists.

posted by overhauser at 11:46 AM on April 8, 2013

**overhauser:**

*The problem here is that one person, who understands both the math and the biology is the right person to do this job. You can definitely be a biologist these days and not understand math beyond the basics. However, you're more and more likely to be outcompeted by the people who are whole scientists.*

I tend to find the idea that scientists should be able to be great at more than one field kind of absurd. It's like telling an athlete that to be a 'whole athlete', they have to be both an amazing marathon runner and baseball pitcher, or some other combination. You might get good at both, but you also risk being surpassed by specialists at either, since you are splitting your time between learning two things. Probably the best you can really hope for is to be great at one and fair at the other - but then you have to wonder if the best strategy would be to just have two different specialists collaborate.

posted by Mitrovarr at 12:10 PM on April 8, 2013 [2 favorites]

*But in all cases the "mathematical method" is logical deduction and argumentation. That's quite distinct from the scientific method; math, as an academic discipline, is not a science.*

Logical deduction and argumentation are pretty universal methods in the sciences.... the difference is that mathematicians make a game of it: we frown on people who use methods other than logical deduction. Although, plenty of prominent people make arguments for experimentation in mathematics.

posted by ennui.bz at 12:12 PM on April 8, 2013

*Relativity is much more difficult on a conceptual level than it is on a mathematical level -- once you figure out what you're trying to solve, the math's usually quite basic;*

That's one way to approach it - the other is to spend a couple of years learning the necessary geometry, and then point and laugh at the people confused by all the "paradoxes".

posted by Dr Dracator at 12:15 PM on April 8, 2013

Mitrovarr, I agree that it's very hard to get deep training in multiple fields, but even if you bring two brilliant people together from different disciplines, you can still end up wasting a lot of time while they speak completely disjunct languages at one another.

But I think that points to the existence of multiple niches within the scientific community: some people are going to advance human knowledge by being a world-class expert on a single technique or topic, while others are going to contribute by synthesizing and combining ideas from disparate regions of science. I'm not sure I have any evidence that one is more valuable than the other.

posted by en forme de poire at 12:21 PM on April 8, 2013

But I think that points to the existence of multiple niches within the scientific community: some people are going to advance human knowledge by being a world-class expert on a single technique or topic, while others are going to contribute by synthesizing and combining ideas from disparate regions of science. I'm not sure I have any evidence that one is more valuable than the other.

posted by en forme de poire at 12:21 PM on April 8, 2013

But getting back to Wilson. The problem with the eusocial darwinists (like Fox) inspired by Wilson is that they are no more aware than the individual competition theorists they are arguing against that the sophisticated equilibrium models they exploit have baked in philosophical/scientific assumptions. When you have a mathematical model that works, there is a terrible pressure to make the interpretation fit the math... which only says you don't really understand your model in the first place.

You can sort of see it here:

posted by ennui.bz at 12:22 PM on April 8, 2013

You can sort of see it here:

Seems to me that the fault often lies with empiricists who stick with their intuitions come hell or high water, and who actively resist the discipline that mathematics imposes on their groundless daydreaming. Intuition is great–as long as it’s only a starting point, and as long as you’re prepared to give it up when it’s proven wrong, even if there’s no better intuition to replace it with. Unfortunately, that’s really hard to do.Fox seems to imply that the mathematics is value neutral, when it never is.

posted by ennui.bz at 12:22 PM on April 8, 2013

One more thing regarding Wilson, I find his attitude that he doesn't need to know math because he can always find someone else to do it for him very strange. I am a researcher who publishes with collaborators, but I would never dream of putting my name on a paper with significant chunks that I don't understand. Certainly the point for collaborating with others is that they bring knowledge and ideas that you don't have, but taking things on faith is bad practice and a recipe for trouble. Actually, to me one of the great joys of collaborating with others is that I learn something new about a different field each time.

posted by epimorph at 12:42 PM on April 8, 2013

posted by epimorph at 12:42 PM on April 8, 2013

*...even if you bring two brilliant people together from different disciplines, you can still end up wasting a lot of time while they speak completely disjunct languages at one another.*

My favorite example of that is that a neurobiologist's dendrite is part of a cell whereas an immunologist's dendrite is an entirely different cell. At least as someone in neither discipline, I find that quite confusing.

Then there's my math friends discussing sequences in cellular homology, while I try to unprocess what "sequence", "cellular", and "homology" mean to me.

posted by maryr at 12:43 PM on April 8, 2013 [2 favorites]

This is why biologists aren't real scientists

Actually, this is why mathematicians aren't really scientists. (IAMAMathematician)

posted by benito.strauss at 1:42 PM on April 8, 2013 [2 favorites]

Actually, this is why mathematicians aren't really scientists. (IAMAMathematician)

posted by benito.strauss at 1:42 PM on April 8, 2013 [2 favorites]

Yet every time I go a restaurant with friends, who is that can calculate the tip without whipping out a smart phone? It's not the particle physicists, I'll tell you that much.

The rule at a certain west-coast technical school was that the restaurant bill should be totalled, tipped, and divided by the youngest math major at the table. "Math major" means they have some facility with numbers, "youngest" means they still believe that numbers really exist.

posted by benito.strauss at 1:47 PM on April 8, 2013 [6 favorites]

The rule at a certain west-coast technical school was that the restaurant bill should be totalled, tipped, and divided by the youngest math major at the table. "Math major" means they have some facility with numbers, "youngest" means they still believe that numbers really exist.

posted by benito.strauss at 1:47 PM on April 8, 2013 [6 favorites]

*Often, those questions are quantitative. 'What are the time constants associated with metabolism and excretion of this amino acid? What is the steady-state condition? What are the gradients across the blood-brain barrier?*

cromagnon beat me to it, but you really have to appreciate just how messy and variable biological systems are. It's not that biomed researchers don't care about quantitative questions, it's that the answers tend to have very limited reliability and specificity. The values you get depend not only on the experimental model and the analytic technique used, but also on the time of the day, the temperature, the Dow Jones Industrial Average, and the alignment of Jupiter. And for practical and economic reasons, you're generally stuck with an

*n*of two or three digits, so you can't just brute force it.

Big Data is certainly blowing up in the biomed world, and over the long-term I expect good things from it. In the short-term, however, I don't trust it worth a damn. It's Garbage In, Garbage Out more often than not.

posted by dephlogisticated at 1:55 PM on April 8, 2013 [1 favorite]

I think that part of the problem you're encountering, OnceUponATime, is that most physicians are not scientists.

Edit: Corrected typo.

posted by wintermind at 2:01 PM on April 8, 2013 [1 favorite]

Edit: Corrected typo.

posted by wintermind at 2:01 PM on April 8, 2013 [1 favorite]

General Relativity and Quantum Mechanics? What... they are not even really "Science" as far as I'm concerned. Its more like Applied Mathematics. And I have done a course on General Relativity - it was run by the Maths department at my uni.

However, I think that there are some problems with bio/medicine science people not really understanding the maths behind a lot of the Statistics and regression stuff that they do - producing work that really doesn't hold up.

posted by mary8nne at 2:18 PM on April 8, 2013

However, I think that there are some problems with bio/medicine science people not really understanding the maths behind a lot of the Statistics and regression stuff that they do - producing work that really doesn't hold up.

posted by mary8nne at 2:18 PM on April 8, 2013

*I tend to find the idea that scientists should be able to be great at more than one field kind of absurd.*

You don't have to be stellar at math. You just have to speak it. Three semesters of calculus and one each of linear algebra and differential equations will get you through 99% of the math needed to do modern biology, including the data analysis live frogs was talking about. Just about anyone can do that. Just don't run screaming when you see a matrix and you can handle systems biology. Don't try to act like you need two PhDs to understand it, that's just not true. All you need is those five undergraduate math courses.

The problem is that undergraduate biology programs haven't caught up with the idea that math is no longer optional. I suspect this is mostly driven by fear of blowback from the hordes of premed biology majors, who will quite likely riot if forced to take calculus.

posted by overhauser at 2:29 PM on April 8, 2013

I don't care if they don't have predicate calculus, but they need to be able to use and understand stats. Actually, I take that back, they do need calculus because they need to understand differential equations too.

It's not enough to hide in your lab or your field camp and claim to be an experimentalist. Nor has it ever been. There are a lot of stamp collectors in science. Don't get me wrong, data gathering can be a lot of fun, and I do a great deal myself, but it's only one part of the whole.

You need to design experiments: that needs stats. You need to hypothesize, either from new data or old. That needs both stats and math. You need to conduct your measurements with some sort of QA/QC, stats again. You need to test the hypothesis, again with stats.

What Wilson calls intuition has to ultimately lead to model formulation. It's true that this is often done collaboratively, but even the most ardent stamp collector needs to be able to talk to the biometrician.

That's where I think his argument falls apart. A feel for one's subject is an essential part of a researcher's intuition, but not being able to translate that into quantifiable terms is like being a composer who can't write their own music. Mozart didn't compose by humming to his librettist. A naked intuition is almost impossible to test---it has to be formulated into a hypothesis. The way hypotheses are formed and tested fundamentally relies on mathematics, like it or not.

posted by bonehead at 3:00 PM on April 8, 2013

It's not enough to hide in your lab or your field camp and claim to be an experimentalist. Nor has it ever been. There are a lot of stamp collectors in science. Don't get me wrong, data gathering can be a lot of fun, and I do a great deal myself, but it's only one part of the whole.

You need to design experiments: that needs stats. You need to hypothesize, either from new data or old. That needs both stats and math. You need to conduct your measurements with some sort of QA/QC, stats again. You need to test the hypothesis, again with stats.

What Wilson calls intuition has to ultimately lead to model formulation. It's true that this is often done collaboratively, but even the most ardent stamp collector needs to be able to talk to the biometrician.

That's where I think his argument falls apart. A feel for one's subject is an essential part of a researcher's intuition, but not being able to translate that into quantifiable terms is like being a composer who can't write their own music. Mozart didn't compose by humming to his librettist. A naked intuition is almost impossible to test---it has to be formulated into a hypothesis. The way hypotheses are formed and tested fundamentally relies on mathematics, like it or not.

posted by bonehead at 3:00 PM on April 8, 2013

*The way hypotheses are formed and tested fundamentally relies on mathematics, like it or not.*

Again, though, this is not true in molecular biology, which got along fine for decades with very little reliance on mathematics. Most "models" of cellular mechanisms in this field are summarized as arrow diagrams. You could argue that these models can be mathematized, and that would be true (as well as being one major aim of systems biology, I think), but that still would have very little relevance to how these models have been used or understood in the field. Even statistics has historically not played a particularly major role in interpreting, say, Western blots or gel shift assays.

posted by en forme de poire at 4:41 PM on April 8, 2013

(Pedantic epistemological tangent:

Perhaps I should have said "deductive proof" instead: while logical deduction informs the generation of hypotheses in the scientific method, science doesn't/can't

posted by eviemath at 4:44 PM on April 8, 2013 [1 favorite]

*Logical deduction and argumentation are pretty universal methods in the sciences.... the difference is that mathematicians make a game of it: we frown on people who use methods other than logical deduction. Although, plenty of prominent people make arguments for experimentation in mathematics.*Perhaps I should have said "deductive proof" instead: while logical deduction informs the generation of hypotheses in the scientific method, science doesn't/can't

*prove*it's results in the way that math does. And experiments are used a bit differently in (experimental) math - more as a tool in the generation of conjectures, in fact, in a nice little reversal of roles from the situation in scientific inquiry.)posted by eviemath at 4:44 PM on April 8, 2013 [1 favorite]

*I don't care if they don't have predicate calculus, but they need to be able to use and understand stats. Actually, I take that back, they do need calculus because they need to understand differential equations too.*

Predicate calculus is not the kind of calculus that deals with differential equations.

posted by jjwiseman at 5:05 PM on April 8, 2013 [1 favorite]

This seems like

One thing is that being really good at math helps you come up with concepts. You can visualize things, and then you can figure out how to

Is it really possible for a grad student to find stats and math people to help get papers published?

posted by delmoi at 6:29 PM on April 8, 2013

*really*terrible advice. Sure, you might be able to find mathematical collaborators if you're a tenured prof at Harvard, but good luck doing that as a grad student.One thing is that being really good at math helps you come up with concepts. You can visualize things, and then you can figure out how to

*encode*what you see in mathematical equations, which in turn can help you figure out how what you visualized in one situation might change in other situations that you can't visualize (so for example, if you can imagine populations changing on a 2D grid, if you work out the math you can much more easily figure out what might happen in 3D, or with more variables added in)Well, that's great if you have the money to hire a mathematician. But how exactly do youYes; it's not specious at all. I've been hired for just that reason, in the past. It's simply collaboration; it's analogous to a musician hiring a brass player,

*get*to that point without being able to do so?Is it really possible for a grad student to find stats and math people to help get papers published?

that's because sports is aI tend to find the idea that scientists should be able to be great at more than one field kind of absurd. It's like telling an athlete that to be a 'whole athlete', they have to be both an amazing marathon runner and baseball pitcher, or some other combination.

*game*with specifically defined rules. The person who's best at X get to be the "winner" but that doesn't advance the human condition. The "rules" in science are stuff pretty much everyone can do: don't do unethical experiments, don't plagiarize, don't make stuff up. Beyond that, the point of science is to do things that no one's ever done before.posted by delmoi at 6:29 PM on April 8, 2013

*Maths is an awfully huge umbrella.*

Amen to that.

Pick an area of mathematics, it's likely that even a full-fledged capital-M Mathematician working in it is going to need assistance from another one at some point if they're doing any significant let alone groundbreaking work.

When the totality of the knowledge in your field no longer fits inside the brain of one person any longer, there really shouldn't be any shame in relying on others.

OTOH, where we're not necessarily talking about the totality or even significant subfields, but rather a subset of math/stats that's vastly useful across the sciences, I think there's a case to be made that everybody working in any science should know that better. Wilson seems to agree.

posted by weston at 6:50 PM on April 8, 2013

Both of these articles are really interesting to me. First because I worshipped Wilson in undergrad and am typing this with Consilience beside me on the book shelf, but also because my current supervisor is the biotatistician in the department and ANY time the question of statistical analysis comes up anywhere, the standard answer is "Ask [my supervisor]."

That said, one thing I think is neat about this post is the evolution of scientific discussion, with the older Wilson publishing in the Wall Street Journal and the younger Fox making a blog post with both pieces getting equal exposure (at least here) and credulity.

posted by Midnight Rambler at 7:23 PM on April 8, 2013

That said, one thing I think is neat about this post is the evolution of scientific discussion, with the older Wilson publishing in the Wall Street Journal and the younger Fox making a blog post with both pieces getting equal exposure (at least here) and credulity.

posted by Midnight Rambler at 7:23 PM on April 8, 2013

*The way hypotheses are formed and tested fundamentally relies on mathematics, like it or not.*

No it doesn't.

You formulate hypotheses by thinking about what the world (or whatever chunk of it is relevant) would be like if your theory were true. In some circumstances you can use mathematics to make very precise hypotheses, but imprecise ones aren't unscientific. Just imprecise.

You test hypotheses by comparing your hypotheses with observed empirical reality. If you're willing to make whatever series of heroic assumptions are required, you can use mathematics to determine what the bounds of uncertainty around your results are. Or at least what they would be if those assumptions were true, which they never are.

tl;dr: there is such a thing as qualitative science.

posted by ROU_Xenophobe at 7:34 PM on April 8, 2013 [2 favorites]

There's a culture difference for you then. In my field, papers which would have been accepted with qualitative hypotheses even a decade ago are not getting past review now. I'm not sure how I feel about that to be honest, but it's a thing.

Right now, stats literacy is hugely important. Wilson's comments reflect his own history, but there's no way I could recommend his approach to a grad student in population ecology in good conscience now.

posted by bonehead at 8:12 PM on April 8, 2013

Right now, stats literacy is hugely important. Wilson's comments reflect his own history, but there's no way I could recommend his approach to a grad student in population ecology in good conscience now.

posted by bonehead at 8:12 PM on April 8, 2013

**delmoi:**

*Is it really possible for a grad student to find stats and math people to help get papers published?*

Well, like I mentioned, my university has a statistician on staff for that exact purpose. But even if not, anyone with a project that includes a difficult statistical component should have at least one person who can do statistics on their graduate committee. And if you don't, you can still try asking the appropriate professors.

*that's because sports is a game with specifically defined rules. The person who's best at X get to be the "winner" but that doesn't advance the human condition. The "rules" in science are stuff pretty much everyone can do: don't do unethical experiments, don't plagiarize, don't make stuff up. Beyond that, the point of science is to do things that no one's ever done before.*

I understand what you are saying, but it's still true that someone who splits their effort between multiple things can't spend as much time on any of them individually as someone who focuses on one. Having basic mathematical literacy is good; it's a basic component of any graduate biology degree. However, taking the time necessary to be a great statistician would cripple you as a biologist.

I kind of think my thesis suffered from this a little bit, actually. I did a molecular phylogeny of a group of fungi (it's submitted but not approved yet, we'll see how that goes. The first chapter is already published.) One part of the project involved a lot of molecular biology, gene sequencing, and phylogenetics. The other was a huge lit review and discussion of the morphology within the group. Honestly, I think it would have been better if the lit review and mycology component could have been offloaded to someone who has practice at that sort of thing - I didn't have enough time to get really comfortable with that aspect. I could have used that six months to improve the phylogenetics and maybe get more genes, or perhaps just to graduate on time.

posted by Mitrovarr at 9:44 PM on April 8, 2013 [1 favorite]

This isn't really a discussion about 'knowing math or not'. There

The other major point is the converse - knowledge of math does not lead to an understanding (or even interest) in science. I mean seriously...engineers, you know?

posted by grajohnt at 11:27 PM on April 8, 2013 [2 favorites]

*is*a threshold, but good luck getting anyone to agree on exactly what that threshold is, whether broadly in science or even in a specific discipline. That threshold is probably lower than you think (I'm with overhauser, and as a geologist, I'd put it at diff-e and some applied math - you don't necessarily have to be able to apply these, but you*should*understand them).The other major point is the converse - knowledge of math does not lead to an understanding (or even interest) in science. I mean seriously...engineers, you know?

posted by grajohnt at 11:27 PM on April 8, 2013 [2 favorites]

I certainly think thatYou formulate hypotheses by thinking about what the world (or whatever chunk of it is relevant) would be like if your theory were true. In some circumstances you can use mathematics to make very precise hypotheses, but imprecise ones aren't unscientific. Just imprecise.

*in the past*there lots of experiments where the results were incredibly obvious, and you didn't need statistics to see if you were right. Like "will this burn if there's no oxygen." It either does or it doesn't. You can think of some famous physics experiments, like the oil drop experiment to show that charge came in discrete units or the double slit experiment.

Certainly lots of early genetics could have been done by altering one gene and seeing what happens.

But, I wonder

*this point*how many experiments with unambiguous answers there are out there. If you look at the large hadron collider, for example they got a ton of data and had do a lot of analysis to identify the signal they were looking for.

I think it's less a question of knowing every stats trick in the book in order to precisely specify exactly how right your hypothesis was given the data you got after you've done your experiment, but rather having a lot of mathematical knowledge that you can use toI understand what you are saying, but it's still true that someone who splits their effort between multiple things can't spend as much time on any of them individually as someone who focuses on one. Having basic mathematical literacy is good; it's a basic component of any graduate biology degree. However, taking the time necessary to be a great statistician would cripple you as a biologist.

*draw inspiration from*when trying to figure something out. I'm obviously not a biologist, and most of the basic biology I know doesn't rely on a lot of math. But if you look at evolution for example I think there are some examples of ideas that came up because people looked the mathematical properties of how mutations would spread through groups, you can predict things like evolutionary basis for sex ratios or whether how

*much*evolutionary pressure it requires to preserve interacting networks of genes based on their complexity (i.e. if a single mutation is more likely to break it's less likely to be preserved compared to something that provides less fitness but is less likely to break from one mutation).

Of course I don't know the actual formulas you would use, they might only require basic algebra/calculus and seem pretty obvious to a real biologist :P. Then of course there are much more complicated things like the physics of protein folding, how quantum interactions come into play, the mathematical issues involved in morphogenesis. (Actually I just looked that up got reminded that

*Alen Turing*of all people came up with some of the key ideas)

I do think you can get to a point where math kind of goes off into it's own totally abstract space where it starts to become less and less likely to have any real-world applications, so there probably is a point of diminishing returns.

posted by delmoi at 9:26 PM on April 10, 2013

*I do think you can get to a point where math kind of goes off into it's own totally abstract space where it starts to become less and less likely to have any real-world applications, so there probably is a point of diminishing returns.*

It is uncanny how often these detours off into totally abstract space turn out to have very important applications (see,

*e.g.*, general and special relativity, string theory, quantum mechanics).

posted by Mental Wimp at 9:50 AM on April 11, 2013 [1 favorite]

J.B.S. Haldane is a good example of how mathematical knowledge is important in biological science. He was a professor of genetics and the first Weldon professor of biometry at University College London. His mathematical abilities were key to his enormous contributions to genetics and biology and to other scientific contributions he made. There are many other notable examples, such as G. E. Briggs, Leonor Michaelis and Maud Menten. The need for mathematical rigor is only going to get greater as biology progresses.

posted by Mental Wimp at 1:44 PM on April 23, 2013

posted by Mental Wimp at 1:44 PM on April 23, 2013

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