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E O Wilson is a great biologist and author. However, this article is completely wrong. In particular, this > Fortunately, exceptional mathematical fluency is r

E O Wilson is a great biologist and author. However, this article is completely wrong. In particular, this > Fortunately, exceptional mathematical fluency is required in only a few disciplines, such as particle physics, astrophysics and information theory. is embarrassingly incorrect. For one example of why this is wrong, and sticking to E O Wilson's field, consider statistics. No biologist can publish anything nowadays without including some statistical analysis in their paper. So there's a pretty simple choice: either publish statistical stuff you don't understand, or learn enough math to achieve a basic understanding. Integrating probability densities, maximum likelihood estimators, etc etc, you certainly need calculus, and linear algebra will be very helpful too. As a second example, what about theoretical biology? How is a student going to have a hope of understanding theoretical models in behavioral ecology or population genetics without some mathematical training? What E O Wilson is saying is straight out of the bad old days which ended in the 1990s. Back then, at least in the UK, it was much more common to think that students studying biology didn't need math. Those days are over. Everyone recognizes that the statistical, computational, and theoretical parts of biology are essential for students to come to grips with. I'm a little sad to publicly criticize an old biologist who has made great contributions but no young scientist should read that article and come away with the impression that it's anything other than embarrassingly out of touch.

kiba 14y ago
Wilson said that he simply rely on statisticians as collaborator. Of course, what if you can't find a statistician to help you do your paper?
- tezka 14y ago
  you use R?
- saraid216 14y ago
  Stop living in an academic silo?
anigbrowl 14y ago
But he's not denying that everyone needs basic fluency - indeed, he recounts the embarrassing necessity of learning calculus in early middle age in order to master his own field. He's saying that exceptional fluency is only required in a few fields. You're arguing with a straw man.
- Myrmornis 14y ago
  Why would he write an article in a national newspaper to point out that exceptional mathematical ability is required in only a few fields? That follows almost by definition. No, the effect, and intention, of his article is to make students of biology think that they don't need to worry about difficult-seeming math courses. My rebuttal is entirely appropriate; I would imagine that most people involved in teaching biology at university level would be very disappointed by what he is promoting.
  - rdouble 14y ago
    He's actually taking a dig at "Quantitative Biology" specializations and saying they aren't really producing anything interesting, so are not worth the trouble.
  - epistasis 14y ago
    His motivations are clearly stated in the second paragraph: >During my decades of teaching biology at Harvard, I watched sadly as bright undergraduates turned away from the possibility of a scientific career, fearing that, without strong math skills, they would fail. This mistaken assumption has deprived science of an immeasurable amount of sorely needed talent. It has created a hemorrhage of brain power we need to stanch. He doesn't have to dig on quantitative biology to recognize that there's lots of science that is largely founded on using reasoning that doesn't require lots of symbol manipulation.
continuations 14y ago
The need to understand basic statistics is a far cry from needing to have "exceptional mathematical fluency." The point is that to be a great scientist you don't need to be a math genius. Having the math ability of a von Neumann is not a prerequisite to being a great scientist.
- pfisch 14y ago
  You should really understand more than basic statistics for most science. How are you even defining basic stats?
  - tezka 14y ago
    no you shouldnt. look at any medical science, exercise physiology, psychology etc. papers. All you see is data gathering and basic statistic analysis (anova, t-test etc.). Basic stats is what they teach at the undergraduate level to scientists and engineers.
    - gajomi 14y ago
      pfisch's comment refers to "most" sciences. Here you have listed "medical science, exercise physiology, psychology" as examples of fields for which knowledge of basic statistics is sufficient for publishing work. Of course, you have excluded physics where undergraduates should (at the very least) understand geometry and calculus, topics in modern algebra and probability theory. If we consider electrical and mechanical engineers we have to add linear algebra to the mix, as well as somewhat non-elementary material in odes and pdes. In computer science and (modern) biology there will be an expectation that one can solve linear recurrence relations. This list could be expanded in various directions.
      - deleted 14y ago
        [deleted]
    - ivoflipse 14y ago
      Isn't the reason those fields mostly see usage of basic stats that they were never taught anything more sophiscated. For example in exercise physiology, which studies a lot of phenomena over time, the results get reduced to minimum/maximum/average because those points match the required input of their basic ANOVA's. Instead they could be comparing time series and find more subtle difference in when a rise starts to occur or at which rate. Numbers that often get obscured by the massive data reductions. Sure you can get by without more advanced data analysis and statistics, but its not exactly something to strive for.
jerryhuang100 14y ago
I second this as the article is very wrong, very misleading, and very last-last gen about math and today's biology. There is even no advanced Biology/Medicine programs (under/grad/whatever) in the world without the Biostatistics as the required core course. Oh, by the way, interested in Biological research but with a low Quantitative score in your GRE? Well, good luck with that! And "Think twice, though, about specializing in fields that require ... quantitative analysis....as well as a few specialties in molecular biology." Come on! Even a simple DNA agarose gel requires your careful calculations about the gel percentage and some basic interpolation for DNA sizes. Basically WSJ has been turned into the Rant Mountain and the rants like "Great Scientist ≠ Good at Math" or "To (All) the Colleges That Rejected Me” won't be the last two.
- tezka 14y ago
  He is totally right and I have seen many many examples of it in grad school. The fact is, US's quantitative GRE is a joke even for mid-high school students in other countries. I take it that he says to become a good scientist in many fields, you don't need Tensors, stochastic PDEs, calculus of variations, group and field theory, functional analysis, path integrals etc. You can get by only mastering single variable calculus, statistics and some basic linear algebra.
  - jerryhuang100 14y ago
    If that WSJ book promotion op is not disturbing enough about math, here is what PBS summarized [1]: "Mathematical skill is not essential, and neither is a genius IQ, he says. Of more importance is creativity, deep thinking, confidence, commitment and allegiance to the small, informal experiments." And what EO Wilson said himself: "I found out that advances in science rarely come upstream from the ability to stand at a blackboard and conjure images from unfolding mathematical proposition and equations. They are instead the product of downstream imagination leading to hard work, during which mathematical reasoning may or may not prove to be relevant." There is nothing about Calculus, ODE/PDE, stochastic modeling, or whatever. He explicitly refers to mathematical reasoning and skills. I can't wait to see this book promotion op appears on The Colbert Report. [1] http://www.pbs.org/newshour/rundown/2013/03/post-27.html http://www.pbs.org/newshour/rundown/2013/03/post-27.html
mjs 14y ago
These three things require wildly different levels of ability: incorrectly using a t-test (e.g. using it in the wrong circumstances), correctly using a t-test, inventing the t-test. I think Wilson is saying that whilst scientists need to be able to use mathematical tools effectively, they don't need to be able to come up with them. (Though statistics is probably much easier to use in this way than, say, calculus. Mathematica is very good at differentiation, but I think in many situations where you need to know how to differentiate, rather than just the result?)
a_p 14y ago
Perhaps you haven't heard about the doctor who rediscovered the trapezoid rule and had his article published in a respected, peer reviewed biology journal in 1994.[1] The paper is called "A mathematical model for the determination of total area under glucose tolerance and other metabolic curves" — and it got 75 citations (as of 2007). EDIT: Google Scholar lists 178 citations now [‽]. The abstract: "OBJECTIVE To develop a mathematical model for the determination of total areas under curves from various metabolic studies. RESEARCH DESIGN AND METHODS In Tai's Model, the total area under a curve is computed by dividing the area under the curve between two designated values on the X-axis (abscissas) into small segments (rectangles and triangles) whose areas can be accurately calculated from their respective geometrical formulas. The total sum of these individual areas thus represents the total area under the curve. Validity of the model is established by comparing total areas obtained from this model to these same areas obtained from graphic method Gess than ±0.4%). Other formulas widely applied by researchers under- or overestimated total area under a metabolic curve by a great margin. RESULTS Tai's model proves to be able to 1) determine total area under a curve with precision; 2) calculate area with varied shapes that may or may not intercept on one or both X/Y axes; 3) estimate total area under a curve plotted against varied time intervals (abscissas), whereas other formulas only allow the same time interval; and 4) compare total areas of metabolic curves produced by different studies. CONCLUSIONS The Tai model allows flexibility in experimental conditions, which means, in the case of the glucose-response curve, samples can be taken with differing time intervals and total area under the curve can still be determined with precision." More information about it is available here. [2] EDIT: I just looked at the full article and it is more bizarre than I had anticipated. For one, it says that "three formulas have been developed to calculate the total area under a curve", and then lists the works in which the formulas are given. One of the works listed is Irving Adler's A New Look at Geometry, which is a math book accessible to readers with a high school education (it's good book by the way — the MAA has given it a rating of BLL [3]). But Adler's name is misspelled "Alder" in the article and in the citation. The author also gives credit to a doctor at Yale for "his expert review". How embarrassing. [1] http://care.diabetesjournals.org/content/17/2/152.full.pdf+html http://care.diabetesjournals.org/content/17/2/152.full.pdf+h... [2] https://fliptomato.wordpress.com/2007/03/19/medical-researcher-discovers-integration-gets-75-citations/ https://fliptomato.wordpress.com/2007/03/19/medical-research... [3] http://mathdl.maa.org/mathDL/19/?pa=reviews&sa=viewBook&bookId=72713 http://mathdl.maa.org/mathDL/19/?pa=reviews&sa=viewBook&... [‽]http://scholar.google.com/scholar?q=A+Mathematical+Model+for+the+Determination+of+Total+Area+Under+Glucose+Tolerance+and+Other+Metabolic+Curves&btnG=&hl=en&as_sdt=0%2C33 http://scholar.google.com/scholar?q=A+Mathematical+Model+for...
lvs 14y ago
That's just not true. Perhaps you're in a specific field where your statements are accurate, but the level of statistical analysis exhibited in a large segment -- dare I say the majority -- of current biological literature is still at a very basic level. You wouldn't believe how many biologists and chemists have only a working knowledge of the basic math they need for everyday work. Wilson is entirely correct.

kiba 14y ago

Wilson said that he simply rely on statisticians as collaborator. Of course, what if you can't find a statistician to help you do your paper?

tezka 14y ago
you use R?
saraid216 14y ago
Stop living in an academic silo?

anigbrowl 14y ago

But he's not denying that everyone needs basic fluency - indeed, he recounts the embarrassing necessity of learning calculus in early middle age in order to master his own field. He's saying that exceptional fluency is only required in a few fields. You're arguing with a straw man.

Myrmornis 14y ago
Why would he write an article in a national newspaper to point out that exceptional mathematical ability is required in only a few fields? That follows almost by definition. No, the effect, and intention, of his article is to make students of biology think that they don't need to worry about difficult-seeming math courses. My rebuttal is entirely appropriate; I would imagine that most people involved in teaching biology at university level would be very disappointed by what he is promoting.
- rdouble 14y ago
  He's actually taking a dig at "Quantitative Biology" specializations and saying they aren't really producing anything interesting, so are not worth the trouble.
- epistasis 14y ago
  His motivations are clearly stated in the second paragraph: >During my decades of teaching biology at Harvard, I watched sadly as bright undergraduates turned away from the possibility of a scientific career, fearing that, without strong math skills, they would fail. This mistaken assumption has deprived science of an immeasurable amount of sorely needed talent. It has created a hemorrhage of brain power we need to stanch. He doesn't have to dig on quantitative biology to recognize that there's lots of science that is largely founded on using reasoning that doesn't require lots of symbol manipulation.

continuations 14y ago

The need to understand basic statistics is a far cry from needing to have "exceptional mathematical fluency." The point is that to be a great scientist you don't need to be a math genius. Having the math ability of a von Neumann is not a prerequisite to being a great scientist.

pfisch 14y ago
You should really understand more than basic statistics for most science. How are you even defining basic stats?
- tezka 14y ago
  no you shouldnt. look at any medical science, exercise physiology, psychology etc. papers. All you see is data gathering and basic statistic analysis (anova, t-test etc.). Basic stats is what they teach at the undergraduate level to scientists and engineers.
  - gajomi 14y ago
    pfisch's comment refers to "most" sciences. Here you have listed "medical science, exercise physiology, psychology" as examples of fields for which knowledge of basic statistics is sufficient for publishing work. Of course, you have excluded physics where undergraduates should (at the very least) understand geometry and calculus, topics in modern algebra and probability theory. If we consider electrical and mechanical engineers we have to add linear algebra to the mix, as well as somewhat non-elementary material in odes and pdes. In computer science and (modern) biology there will be an expectation that one can solve linear recurrence relations. This list could be expanded in various directions.
    - deleted 14y ago
      [deleted]
  - ivoflipse 14y ago
    Isn't the reason those fields mostly see usage of basic stats that they were never taught anything more sophiscated. For example in exercise physiology, which studies a lot of phenomena over time, the results get reduced to minimum/maximum/average because those points match the required input of their basic ANOVA's. Instead they could be comparing time series and find more subtle difference in when a rise starts to occur or at which rate. Numbers that often get obscured by the massive data reductions. Sure you can get by without more advanced data analysis and statistics, but its not exactly something to strive for.

jerryhuang100 14y ago

I second this as the article is very wrong, very misleading, and very last-last gen about math and today's biology. There is even no advanced Biology/Medicine programs (under/grad/whatever) in the world without the Biostatistics as the required core course. Oh, by the way, interested in Biological research but with a low Quantitative score in your GRE? Well, good luck with that! And "Think twice, though, about specializing in fields that require ... quantitative analysis....as well as a few specialties in molecular biology." Come on! Even a simple DNA agarose gel requires your careful calculations about the gel percentage and some basic interpolation for DNA sizes. Basically WSJ has been turned into the Rant Mountain and the rants like "Great Scientist ≠ Good at Math" or "To (All) the Colleges That Rejected Me” won't be the last two.

tezka 14y ago
He is totally right and I have seen many many examples of it in grad school. The fact is, US's quantitative GRE is a joke even for mid-high school students in other countries. I take it that he says to become a good scientist in many fields, you don't need Tensors, stochastic PDEs, calculus of variations, group and field theory, functional analysis, path integrals etc. You can get by only mastering single variable calculus, statistics and some basic linear algebra.
- jerryhuang100 14y ago
  If that WSJ book promotion op is not disturbing enough about math, here is what PBS summarized [1]: "Mathematical skill is not essential, and neither is a genius IQ, he says. Of more importance is creativity, deep thinking, confidence, commitment and allegiance to the small, informal experiments." And what EO Wilson said himself: "I found out that advances in science rarely come upstream from the ability to stand at a blackboard and conjure images from unfolding mathematical proposition and equations. They are instead the product of downstream imagination leading to hard work, during which mathematical reasoning may or may not prove to be relevant." There is nothing about Calculus, ODE/PDE, stochastic modeling, or whatever. He explicitly refers to mathematical reasoning and skills. I can't wait to see this book promotion op appears on The Colbert Report. [1] http://www.pbs.org/newshour/rundown/2013/03/post-27.html http://www.pbs.org/newshour/rundown/2013/03/post-27.html

mjs 14y ago

These three things require wildly different levels of ability: incorrectly using a t-test (e.g. using it in the wrong circumstances), correctly using a t-test, inventing the t-test. I think Wilson is saying that whilst scientists need to be able to use mathematical tools effectively, they don't need to be able to come up with them. (Though statistics is probably much easier to use in this way than, say, calculus. Mathematica is very good at differentiation, but I think in many situations where you need to know how to differentiate, rather than just the result?)

a_p 14y ago

Perhaps you haven't heard about the doctor who rediscovered the trapezoid rule and had his article published in a respected, peer reviewed biology journal in 1994.[1] The paper is called "A mathematical model for the determination of total area under glucose tolerance and other metabolic curves" — and it got 75 citations (as of 2007). EDIT: Google Scholar lists 178 citations now [‽]. The abstract: "OBJECTIVE To develop a mathematical model for the determination of total areas under curves from various metabolic studies. RESEARCH DESIGN AND METHODS In Tai's Model, the total area under a curve is computed by dividing the area under the curve between two designated values on the X-axis (abscissas) into small segments (rectangles and triangles) whose areas can be accurately calculated from their respective geometrical formulas. The total sum of these individual areas thus represents the total area under the curve. Validity of the model is established by comparing total areas obtained from this model to these same areas obtained from graphic method Gess than ±0.4%). Other formulas widely applied by researchers under- or overestimated total area under a metabolic curve by a great margin. RESULTS Tai's model proves to be able to 1) determine total area under a curve with precision; 2) calculate area with varied shapes that may or may not intercept on one or both X/Y axes; 3) estimate total area under a curve plotted against varied time intervals (abscissas), whereas other formulas only allow the same time interval; and 4) compare total areas of metabolic curves produced by different studies. CONCLUSIONS The Tai model allows flexibility in experimental conditions, which means, in the case of the glucose-response curve, samples can be taken with differing time intervals and total area under the curve can still be determined with precision." More information about it is available here. [2] EDIT: I just looked at the full article and it is more bizarre than I had anticipated. For one, it says that "three formulas have been developed to calculate the total area under a curve", and then lists the works in which the formulas are given. One of the works listed is Irving Adler's A New Look at Geometry, which is a math book accessible to readers with a high school education (it's good book by the way — the MAA has given it a rating of BLL [3]). But Adler's name is misspelled "Alder" in the article and in the citation. The author also gives credit to a doctor at Yale for "his expert review". How embarrassing. [1] http://care.diabetesjournals.org/content/17/2/152.full.pdf+html http://care.diabetesjournals.org/content/17/2/152.full.pdf+h... [2] https://fliptomato.wordpress.com/2007/03/19/medical-researcher-discovers-integration-gets-75-citations/ https://fliptomato.wordpress.com/2007/03/19/medical-research... [3] http://mathdl.maa.org/mathDL/19/?pa=reviews&sa=viewBook&bookId=72713 http://mathdl.maa.org/mathDL/19/?pa=reviews&sa=viewBook&... [‽]http://scholar.google.com/scholar?q=A+Mathematical+Model+for+the+Determination+of+Total+Area+Under+Glucose+Tolerance+and+Other+Metabolic+Curves&btnG=&hl=en&as_sdt=0%2C33 http://scholar.google.com/scholar?q=A+Mathematical+Model+for...

lvs 14y ago

That's just not true. Perhaps you're in a specific field where your statements are accurate, but the level of statistical analysis exhibited in a large segment -- dare I say the majority -- of current biological literature is still at a very basic level. You wouldn't believe how many biologists and chemists have only a working knowledge of the basic math they need for everyday work. Wilson is entirely correct.