

Great Scientist ≠ Good at Math - tokenadult
http://www.wsj.com/article/SB10001424127887323611604578398943650327184.html

======
Myrmornis
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.

~~~
a_p
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+h...](http://care.diabetesjournals.org/content/17/2/152.full.pdf+html)

[2] [https://fliptomato.wordpress.com/2007/03/19/medical-
research...](https://fliptomato.wordpress.com/2007/03/19/medical-researcher-
discovers-integration-gets-75-citations/)

[3]
[http://mathdl.maa.org/mathDL/19/?pa=reviews&sa=viewBook&...](http://mathdl.maa.org/mathDL/19/?pa=reviews&sa=viewBook&bookId=72713)

[‽][http://scholar.google.com/scholar?q=A+Mathematical+Model+for...](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)

~~~
Steuard
It's more like 175 citations now, according to Google Scholar. I've been
tempted for years to do some sort of survey of everyone who has cited the
paper, to find out (among other things) if they ever took calculus and how
this situation could happen.

------
beloch
Wilson's point is not that math/stats aren't necessary for most research. They
_are_. He admits it. Instead, he argues that there is an ample supply of
math/stats researchers to collaborate with, so you can get by in science being
mathematically illiterate. I disagree.

As a grad student, I did work in experimental quantum physics. Emphasis on
experimental. There were only a handful of places on Earth where theorists
could go to test the sort of stuff we could do in the lab. In a very specific
corner of scientific knowledge, we were the choke point. We collaborated with
theorists from all over the world. Many of them could do things on paper that
I could barely understand. I had to understand them to test them though, and
they helped me greatly. I'd be rather disappointed in Wilson if he was happy
to test theories he couldn't understand!

I think the message shouldn't be that "there are people to do math/stats for
you if you want to do science". Perhaps you could get by that way, and perhaps
Wilson has been able to con people into thinking he's good when he's testing
things he doesn't understand. That takes a completely different skillset than
math/stats I suppose, but I don't find it admirable.

Perhaps a better message is that you don't have to be a hardcore theorist to
contribute to scientific research. You need to be able to understand what
you're doing, but you don't need to be a genius who covers every surface
around him in incomprehensible symbols while gibbering to himself gleefully.
(Yes, these people do exist, and they are sometimes _awesome_ to have around.)
Theorists are just one kind of scientist. Experimentalists are every bit as
important, but their skill set is different. Theorists can wave their hands
and make assumptions when solving problems. Experimentalists have to think
things through very pedantically because assumptions usually bite them in the
ass. Theorists can tackle a different problem every day and move between
wildly disparate fields on a whim. Experimenalists have to stick with one
problem for months or years at a time. Experimental work involves a lot of
craft and patience.

So no, you don't need to be a mathematical genius to be a scientist, but I
wouldn't want to be an experimentalist who can't understand what he's doing!

~~~
asafira
I think the fact of the matter is simply this: at some point in one's career
in physics, when you make a decision between being an experimentalist and
theorist, you don't spend nearly as much time focusing on the theory. I don't
think it's wrong, but it's just natural that at some point you won't be as
fluent with the theory as theorists.

I was writing out how I don't agree with the author, but then I took in the
bigger picture and realized that indeed I do think that a lot of the
experimentalists in the field have either forgotten or just aren't that great
at their math skills. I think this shows most in classes, where it's easy for
them to get tripped up over details.

That being said, most of the time it's just simple things. I think there is
still clearly a higher bar (in general) in physics than in other sciences
(i.e., biology) as far as math goes, and it's far too much of a stretch to say
you don't need to know math well to do well. We aren't talking about algebraic
topology here, I think Wilson is commenting even on just multivariable calc
and linear algebra. Quantum Mechanics without linear algebra? At the very
least, it would be very hard to learn (if at all).

If anyone from non-physics fields has some comments, I would be interested to
hear.

------
Permit
E.O. Wilson did an excellent TED talk on this exact subject called "Advice to
young scientists". I'd recommend watching it as it's one of my favorite talks.

[http://www.ted.com/talks/e_o_wilson_advice_to_young_scientis...](http://www.ted.com/talks/e_o_wilson_advice_to_young_scientists.html)

------
kiba
Math isn't that hard to learn, it's just that it requires lot of tutoring and
lot of thinking. The reason why people today don't possess that much
mathematical knowledge is that they don't maintain their knowledge of
mathematics. So, when it comes to learning calculus or other advanced
mathematics, you have a swiss cheese foundation. That swiss cheese foundation
simply means you didn't mastered the previous required materials. So it's hard
to learn.

I did the really elementary to high school materials in the past two years on
and off. Math concepts didn't really get harder to learn. They're easy or hard
to learn at time, but there's no difficulty ramp to speak of. Then what
happens afterward is that you start forgetting about how to do things like
logarithmic operation, how to simplify trig identities, and so on after a week
or two, or sometime days. So you need to continuously review them everyday or
do enough real world problems that you know how to do them for life.

The skills and knowledge that we master requires daily maintenance, or
otherwise you lose your ability to do them. It's just like fitness. A person
who stop long distance running for a while will no longer be able to run as
long.

~~~
Xcelerate
> Math isn't that hard to learn [...] calculus or other advanced mathematics

Most people's concept of what "math" is, isn't advanced math. Advanced math is
incredibly complex. (I honestly kind of chuckle when people tell me they are
"really good at math".) Read Wiles' proof of Fermat's Last Theorem
(<http://www.cs.berkeley.edu/~anindya/fermat.pdf>), or Godel's incompleteness
theorem and tell me if you understand _any_ of that.

Math much easier than his proof, yet vastly more difficult than calculus, is
used in many areas of physics and chemistry. And I think it is this kind of
math to which the original article was referring.

People like to quip that Einstein wasn't good at math, because he had
mathematicians helping him with his work. What they don't understand is that
Einstein's skills in math blows everyone else's out of the water; it's just
that they weren't up to the level of an actual mathematician.

~~~
kiba
_it's just that they weren't up to the level of an actual mathematician._

I guess what I am doing and learning is really elementary. But I like to think
my point about having foundational knowledge and the willingness to practice
everyday still stand.

I know what I am doing and learning isn't what mathematican really do day to
day. They make up new stuff, prove things, and solve problems in creative
ways.

I just commit to memory or practice steps on how to solve exercise sets,
although the way I do is way smarter and time efficient than what people do
when I was in high school. I don't know if all that practice will eventually
pay off in some way, but I know that I just really hate forgetting stuff that
I learned in high school math class. ( Yes, I really do "incredibly boring"
math homework everyday despite finishing high school three years ago)

------
erichocean
In my opinion, the problem with math is actual mathematical notation, which
is, frankly, terrible. Ridiculously bad. Especially given the advances that
have been made in CS in that regard.

Early programming languages created by mathematicians? They were terrible (for
the most part). Then CS people started formalizing stuff, grammars were
invented, and finally, the situation began to improve in the late 60s.

But not math. Nope, it's the same archaic, imprecise, terrible notation that's
been around for centuries. AFAIK there's nothing in math comparable to the
development of programming languages in CS. It simply doesn't improve. Imagine
if the first language ever created in CS was also the last. That's math.

In CS, we've kept inventing new, better programming languages and conceptual
foundations. Not math. There, they have a bad foundation, but they just keep
building up and up and up, each paper even more hand-wavy and imprecise than
the next.

It's to the point where things that are actually trivial mathematical concepts
to understand are _damn near impossible_ to learn by actually reading a math
paper about the topic -- all because of the notation, implied rules, etc.

IN my experience, mathematical objects and concepts are simple, at the same
level of difficulty as, say, quicksort or an AVL tree. All of math is that
way. What's hard about math is the notation, not the concepts or mathematical
objects that are presented.

And because the notation is so bad, it's very hard for people to make use of
math in an _À la carte_ manner. You either spend years of drudgery with little
payoff, or you don't use math at all.

Contrast that with open source software (the CS equivalent, I would argue, to
reading math papers), which is easy to use, because, hey, consistent notation,
no hidden rules, no assumed set of knowledge or information. Everything has a
definition. There is an answer for everything _in the source code itself_.

Math papers are the opposite, including the math articles on Wikipedia. Math
is damn near unusable for that reason by anyone but mathematicians who can
intuit the implicit rules, notational deviations, etc. after a lifetime of
study.

It doesn't have to be this way.

~~~
jpallen
Can you give an example of a piece of math notation that you think could be
improved?

Maths is more like a human language - the writing necessarily does not contain
a complete picture, just like a book can never unambiguously describe a scene.
This is what sets it apart from the computer programs you have compared it
with since a computer program is a complete, unambiguous definition of the
thing it is describing.

All that math notation does is give us a language that sits somewhere between
description and precision to let us talk about concepts that are very hard to
formulate in natural language.

If it was made completely precise too much would be lost. Context is
everything, and sometimes that requires you to understand the previous work in
the field. I don't see a way around that.

~~~
erichocean
Please see my reply to tome below.

------
poof131
I agree with the article, I think?

<TLDR> The only difference between math and English, or any other language, is
a degree of precision. In math, the symbols and connotations are more refined,
but the results are still interpreted. There is no absolute truth.
Mathematical truth is still defined by agreement among leading scholars that
something is correct. Physical truth in the sciences also depends upon
agreement. In the ephemeral world of communication, words and their meanings
are relevant only to our own perception. We can try to better agree upon the
starting ground, the definitions, but definitions still depend upon the flimsy
symbols and what they signify in each person’s mind. There is no perfect line.

I enjoy math as a dilettante communicator. And while math can greatly enhance
the precision of our communications, it can also be used to deceive. My non-
schizoid self agrees that the probability of pulling the “Ace of Spades” from
a deck of cards is 1 in 52, but this depends upon our understanding of the
definitions, our belief that the logic of probability is reasonable, and our
intuition that the results agree with the world we perceive. My skeptic self,
however, disbelieves that the esoteric formulas of macroeconomics accurately
predict the world around us. How much "advanced math" is being conducted at
banks, universities, and government institutions in pursuit of the illusory
goal of modeling the economy? This math serves the purpose of providing the
illusion of understanding, appropriate for politicians justifying desired
actions, bankers selling products, and economics professors advancing careers.
In my perception of reality, this math too often blows up when events it
describes as one in a trillion come to fruition on a much more frequent basis.

While I believe understanding math can prove beneficial to any endeavor that
is trying to more precisely communicate a perception of the world, that
mathematical understanding does not trump the necessity of generating
agreement upon the definitions and the results. With little math but plenty of
logic, Darwin was able to generate an insight into the world with which many
people agree (including myself). Yet with plenty of math and very little
logic, many areas of "science" travel down rabbit hole after rabbit hole where
the community coalesces in complicated group think, with insights that fail to
agree with most peoples' perception of reality, but results that are
nonetheless justified as correct based upon the "math." In the end, math is a
method of communication, often more precise than other languages, but still
transitory in its ability to convey meaning and generate agreement. It is a
helpful tool but not an indispensable instrument to science. But I guess this
all depends upon the definition of science. </QED>

~~~
saraid216
It's profoundly unfair to lump mathematics in with economics. Economics has
massive, massive problems that are only really being mildly addressed today:
namely that its numerical differences with psych/sociology come from an Intro
to Physics textbook rather than being derived independently.

The mathematics is correct. 10 divided by 5 really is 2. The problem looks
something more like 10 kg divided by 5 lb isn't 2 kg. It's 2 kg/lb. It's not
the mathematics' fault that you got your translation into reality wrong.

------
stiff
Just compare what has been achieved in science in, say, 2000 years before the
invention of calculus, with just the 100 years after its invention. As almost
always, the author is extrapolating what is true in his field (biology) to
"the world as the whole". Biology hasn't historically often used mathematics
because it was and to a large extent still is a descriptive science. With
molecular biology now being the hottest stream in biology the need for
mathematics is much stronger than before even in this discipline.

Instead of denying the obvious, it would be better to think of ways to not
scare people away from mathematics - he makes it seem like some people simply
do not have the mathematical ability and there is nothing to do about it
except finding a field that doesn't need it.

------
kaptain
My manager once asked me to finish out a statistical problem to better analyze
the results I was getting from my code changes that were intended to speed up
an API. I looked at the whiteboard for about 5 seconds and grinned: "Who needs
math? That's what computers are for!" Then I went to lunch.

Of course I went back and finished the analysis after lunch.

------
rodrigoavie
Last year I entered CS school and found myself embarrassingly weak at Math.
I've been studying really hard since them and I don't really believe I'll be a
very good Computer Scientist if I do not learn Math (Linear Algebra, Discrete
Math, Graph Theory, Game Theory, Calculus, Statistics).

------
michaell2
there is math, and then there is math. In Russia they have a saying "beat a
rabbit long enough and it will eventually learn to take derivatives, but
integrals are another matter". For many people areas involving spatial
reasoning like college physics for engineers is that "another matter", while
(simple) integrals are still no biggie.

As for the original article, the implication that somebody having trouble with
basic algebra can be "great scientist" sounds dubious to say the least. Like I
said, there is math, and then there is math... there is stuff that anybody
claiming any meaningful level of intelligence should be able to handle.

~~~
thaumasiotes
I find that saying bizarre. In high school, I found derivatives significantly
more difficult to learn than I did integrals. Then, in multivariable calc, I
found derivatives significantly more difficult, again. Integrals follow your
intuition in a way that derivatives just don't.

~~~
dsrguru
Derivatives are formulaic. Integrals, like proofs, require thinking backwards,
i.e. creativity and/or luck. For the vast majority of people, cultivating that
intuition is a lot harder than plugging numbers into formulas...

~~~
zerr
Formally speaking, solving integrals requires brute force. It is only after
many such brute force samples your starting to get an intuition. But I won't
call this creativity.

