
Do you need to know math for doing great science? - Immortalin
http://blogs.scientificamerican.com/the-curious-wavefunction/do-you-need-to-know-math-for-doing-great-science/
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dkarapetyan
I stopped reading as soon as the article said Einstein's strength was his
physical intuition and not his mathematical prowess. Try explaining tensor
calculus to someone that doesn't have proper understanding of Riemanian
geometry. Einstein was indeed a very good mathematician and not just a
physicist with "great physical intuition".

~~~
johnloeber
Einstein was an exceptionally strong mathematician. He mastered integral and
differential calculus by age 15, and gained ample knowledge in more advanced
topics (topology, geometry, etc.) in the following years. Note that this was
much more impressive back then than it is today. That being said, he did also
command impressive intuition and observational skills.

By the way, the _exact same_ can be said for Feynman, with the exception that
Feynman was a stronger mathematician yet.

~~~
logicallee
why do you say this was more impressive back then than it is today? I thought
all the areas you mentioned were well-understood. if anything I'd think this
kind of math is more daunting today because it just takes 1 click to get to a
wall of text on wikipedia in impenetrable notation. I'd think back then any
kid who picked up a text could just read it without potentially diving into
100 years of abstract math.

~~~
johnloeber
A normal school curriculum back then did not go so far as to teach calculus.
When Einstein taught himself vector calculus, he used the textbook written by
the guy who invented it because it was the _only_ textbook. Then he personally
wrote to the guy to clear up his misconceptions.

Today, you can learn this material in open university courses, and if you have
a question, consult a plethora of freely available resources on the internet.

Accessibility of information matters.

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Fomite
My take (working scientist):

\- You need to know _some_ math to do great science. How much math depends
very much on your field, and what you're looking into (even within my field,
'great science' can range from things that only need long division to things
that need serious calculus or simulation chops).

\- Knowing math does _not_ mean you can do great science. The mathematically
inclined occasionally fall susceptible to the stack fallacy, and assume that
once the math is known, everything else falls into place. Some of the worst
science I've seen in my field stems from that assumption.

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thegenius2000
In the sciences, mathematics serves as nothing less than a convenient notation
for expressing (and manipulating) certain principles: it is an invaluable
tool, both for analysis and exposition.

That being said, in my opinion, _great_ science is largely about insight, and
this does not necessarily depend on maths. For example, consider the
contributions Faraday made to our understanding of electromagnetism. Although
he never mastered maths, he broke the ground for many that followed him, most
notably Maxwell. With Maxwell, you have almost the opposite situation, as he
was a highly skilled mathematician: his insights were largely borne of
mathematical abstraction.

So I think the best answer to the question is sometimes. Faraday's insights
were not (directly) dependent on advanced knowledge of mathematics, but
Maxwell's were. We needed the genius of both these men, but mathematics was
only required of the second.

What should we do, then? Definitely require hard science majors to learn
mathematics, even more so then currently. Encourage mathematicians to think
about science problems, and vice-versa. But let us not make the mistake of
closing the scientific doors on the so-called 'mathematically illiterate.' For
all we know, they carry the solutions to some of our most difficult problems.

 _Edit: changed 'where' to 'were'_

~~~
lutusp
> But let us not make the mistake of closing the scientific doors on the so-
> called 'mathematically illiterate.'

Fair enough, but it can lead to a very serious problem -- how do we compare
the results of different studies? Day-to-day experimental results can be
collected with only a little math, but any theories that might be shaped on
the basis of those results, that might end up defining new fields, usually
have a mathematical form that summarizes the experimental work and creates new
principles and paradigms. Those theories that last the longest and have the
largest effect on science, tend to be more mathematical than anecdotal.

> Faraday's insights were not (directly) dependent on advanced knowledge of
> mathematics, but Maxwell's were. We needed the genius of both these men, but
> mathematics was only required of the second.

This example supports the role of mathematics in science. Faraday _described_
some results that arose in laboratory experiments, then Maxwell _explained_
those results using mathematics. Faraday's results were fascinating, but
Maxwell's results were portable and later served as a foundation for
relativity -- which was also very mathematical.

~~~
forgetsusername
> _Faraday described some results that arose in laboratory experiments, then
> Maxwell explained those results using mathematics._

The issue is with expecting a single person to be able to do both; people with
incredible insight who are also great at mathematics are inherently rare. If
you require the latter you're going to miss out on much of the world's stock
of the former. I think the future of science rests on the coordination of
both.

~~~
lutusp
I agree completely, but by 1915, Einstein had reshaped himself into exactly
the multidisciplinary person required to write the general theory.

The real tragedy in science are those with only physical intuition and little
mathematical foundation, like Nicola Tesla, who wasted much time on notions
that flatly contradicted the mathematical underpinnings of physical theory.

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sandworm101
Note the author taught biology. I think we would all agree that there are a
variety of sciences, some of which rely heavily on advanced maths (particle
physics) while in others (biology) it's really optional and there is plenty
that can be done without a deep understanding of numbers theory.

My undergrad (UBC) used math (calc 101) as a weeding-out course. They needed
50% of students to fail. When computerized teaching was tested and pass rates
went up, it was a problem. So they eliminated the computer-aided option (early
90s, probably different now). Math was a weapon for dissuading students. It
worked. I probably would have given up had I not completed calc in a
highschool with a teacher who actually cared.

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randomsearch
"but even the greatest theoretical physicists of the twentieth century
including Einstein, Fermi, Feynman and Bohr were really known for their
physical intuition than for formidable mathematical prowess"

Nonsense. Feynman, for example, was famous for his ability to formulate and to
solve mathematical problems in hours that his colleagues had spent months
working on.

How is this in Scientific American?

Not worth reading.

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quanticle
I would say that the answer is trivially yes. You need to know math to do
great science.

Why?

Science is all about reproducibility. Without a strong grasp of statistics,
you do not know whether you've actually discovered an effect, or whether you
just got (un)lucky with your data. And far from being a theoretical problem,
numerous scientific disciplines, especially those in biology and medicine, are
currently dealing with a "reproducibility crisis", as they find that prominent
results don't recur when replication experiments are run.

Far from there being too much math in science, I think there's currently too
_little_ math. If researchers knew more about the limits of the statistical
tests they were using, rather than focusing on the magic p=0.05 level, we'd
have much higher quality science, with a much higher level of confidence that
the results being reported were real results, rather than statistical
abberations.

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fengwick3
> Science is all about reproducibility

Can this really be said in all fairness? What of the flashes of brilliance,
the striking insights into understanding seemingly inexplicable phenomena? The
discovery of the structure of benzene, the creation of the periodic table
comes to mind.

~~~
dozzie
Reproducibility of results, not reproducibility of thought process on
different (even though similar) ground.

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ankurdhama
There are two versions of "being good at mathematics". 1\. You are good in
solving mathematical problems like solving complex equations using various
techniques. In this case you are working inside mathematics. 2\. You are good
at modeling systems using mathematics. Using mathematics as a language and
create a mapping between the system you are researching and mathematical
concepts.

I think the article point is that you can do good science if you have the
second skill.

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bloaf
I would add some nuance, to make the list look more like:

1A) Ability to _create_ new mathematical ways of talking about your systems.
This means things like inventing new notations, conventions, or combinations
of mathematical methods from disparate mathematical disciplines.

1B) Ability to _recognize_ when a mathematical finding applies to your system.
You may not be able to come up with it on your own, but you know it when you
see it.

2) Ability to implement conventional methods quickly to your problem, even a
complex one.

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kriro
I find it troubling that students are put off by the notion that knowing
mathematics is required to do X. Mathematics needs a PR campaign (and maybe
better teachers?).

I've noticed that a large number of our students are scarred of taking any
courses that could possibly be related to math.

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InclinedPlane
Both. I'm worried that the way education is being conducted is increasingly
turning people off of math, science, and literature. These are all wonderful
and highly useful subjects of study and even recreation, but the school
systems have turned then into drudgery, and have been using them for aversion
therapy for years. It's a wonder society functions at all.

~~~
Ntrails
>I'm worried that the way education is being conducted is increasingly turning
people off of math, science, and literature.

I disagree. Looking globally (and to some extent historically) I don't see
evidence that more successful education systems were taught in more engaging
ways by insightful teachers. I do see cultural differences, I see modern
children believing they are there to be entertained and not to simply learn
and do as they are told.

Blaming the teachers and the schools is easy. Blaming the parents and the
society that we have created is more honest though _imo_.

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jupiter90000
Is great science done anymore? It seems like there were prolific scientists
making incredible advances directly impacting the standard of living of humans
for a period, and now we're coasting and making small incremental changes. I'm
sure some folks here have examples of amazing things being done in science
now, but I don't seem to be noticing the discoveries impacting the same way
that seemed to be happening in 1900-2000 era. We're moving into another dark
age. Kidding about that last part, and I actually do love science.

It just seems like before people were making amazing discoveries and now it's
like "let's make facebook work better and get everyone addicted to smartphones
and track 'em so we can sell stuff. Starbucks and iPhones. Donald Trump."

In terms of the article, I don't see how knowing math could be anything but
helpful for doing great science. Maybe one doesn't have to be an expert, but
to pretend it couldn't be helpful seems silly. Maybe I don't need to know how
to spell words to do great science either, but conveying ideas in a clear
manner is so important. Hence math.

~~~
papapra
I don't agree...

"The more important fundamental laws and facts of physical science have all
been discovered, and these are now so firmly established that the possibility
of their ever being supplanted in consequence of new discoveries is
exceedingly remote... Our future discoveries must be looked for in the sixth
place of decimals." Albert A. Michelson, speech given in 1894 at the
dedication of Ryerson Physics Lab, University of Chicago.

~~~
vlehto
Death years of these guys: Maxwell (1879), Darwin (1882), Newton (1727),
Mendeleev (1907). So it seems he was right. We have been just applying the
science of the giants for the past 122 years.

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dnautics
In general: there's an appreciation for basic logic that is necessary.

In Curious Wavefunction's field, chemistry (which is something I am, uh,
somewhat familiar with), graph theory could _probably_ be useful, but useful
graph theoretic construction for retrosynthetic analysis seems to be
persistently elusive since at least E. J. Corey's era.

But sometimes just being able to do math is important. Today I got into a
minor dispute with someone who is running a sequencing/diagnostics startup.
Their sequencing technique is, reported as of late 2015, getting an 8% error
rate for an 8x coverage sequence. Asked him what the error would have been for
a 1x coverage, and he couldn't answer. I would think that if you're going to
be using sequencing to do diagnostics, being able to rapidly figure out things
like this is important.

~~~
wobbleblob
The article makes this claim:

> "Most top chemists and biomedical researchers have little use for
> mathematics per se, except in terms of using statistical software or basic
> calculus. "

Now I never ended up working in the field, but I remember my organic chemistry
Msc. being fairly math heavy. Solving the Schroedinger equation for a complex
molecule or refining a stochastic simulation model involved a bit more than
basic calculus. The whole course was more math than lab work.

Was this article written by someone who never took an advanced science class,
or by a mathematician to whom all the math used in natural sciences is trite
and simple?

~~~
dnautics
I think Curious Wavefunction was a practicing chemist. Nobody really solves
schroedinger equations (actually you can't really solve it for anything
besides hydrogen) and first-pass "gut" understanding of kinetics is usually
good enough to get most things done. As for kinetics: in practice, just do it
five times at five temperatures to find the best yield where it goes fast and
doesn't degrade.

This would be for organic synthesis.

Biochemists use kinetics more, one time my boss yelled at her grad students
for using 1 uL pipettes because they have poor resolution for kinetic studies,
but even so they're not necessary for many studies (for example, for my
biochemistry pretty much everything was pushed to the saturating rate and we
had linear kinetics).

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lutusp
Quote: "The other thing to keep in mind is that an over-reliance on math can
also seriously hinder progress in certain fields and even lead to great
financial and personal losses. Finance is a great example; the highly
sophisticated models developed by physicists on Wall Street caused more harm
than good."

This is very misleading -- it tries to hold mathematics responsible for what
in fact was a mixture of superficial mathematical reasoning and an inability
to grasp that the mathematical models had little to do with reality. It was an
example of using mathematics to conceal rather than reveal.

If the mathematical model doesn't accurately model reality, don't blame the
math, blame the mathematician.

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reallydontknow2
As I see mathematics as somewhat like the act of traversing, exploring, and
constructing a hypergraph built fundamentally of pointers where the cliques
and common paths are named simply for economical reasons for quick addressing,
it clearly can increase the probability of doing great science no matter what
field you are.

I'd still say that you can still do great science although you do not know the
formal language of mathematics, but the probability of getting to the position
of doing the science today is harder because we have more aggressive naked
alpha monkeys protecting their turfs from those they see less worthy of
joining the adventure.

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threatofrain
You don't necessarily need great math to do productive science, but even if
you are working in a "soft" field like psychology, strong math is a strong
asset, such as in the field of causal learning, where it was found that
mathematical models of associative learning doesn't sufficiently account for
rats learning (can you do that without math?), or in behavioral variability.

Otherwise you're going to be stuck plugging in numbers into a model you don't
understand.

Also, I think strong intuition is much harder to develop than a strong math
foundation. I don't know if you can hard work your way into strong intuition.

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tegeek
Mathematics is a fundamental tool to convey your imaginations to others in a
way they can test it for approval or disapproval. IMO if you take away
mathematics from Science, the only thing left are novel ideas (which you can
also find in sci-fi novels).

Of course a person can have deep imaginations and solutions to the great
science problems, but if she can't express the ideas then how to prove them
right or wrong??

~~~
alephnil
> IMO if you take away mathematics from Science, the only thing left are novel
> ideas (which you can also find in sci-fi novels).

Math is an important part of nearly all scientific fields, but to say that
there is nothing left but ideas when the math is taken away is too broad.
There are many fields of science that traditionally have been developed
without a lot of need for math, like for example biology and earth sciences.
These days mathematics is a large part of these fields too, but in some
subfields, like in ecology, many researchers use little math even today.

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noodlio
Interesting question. Spontaneously I would say that it depends on the field.
Best researchers seem to me the ones that are not only good in math.

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Xcelerate
Site seems to be down. Cached version:
[http://webcache.googleusercontent.com/search?q=cache:8cobPmg...](http://webcache.googleusercontent.com/search?q=cache:8cobPmgMV-
MJ:blogs.scientificamerican.com/the-curious-wavefunction/do-you-need-to-know-
math-for-doing-great-science/)

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nsajko
This is an interesting, though quite old example of the importance of math:
[https://en.wikipedia.org/wiki/Hardy%E2%80%93Weinberg_princip...](https://en.wikipedia.org/wiki/Hardy%E2%80%93Weinberg_principle#History)

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crncosta
No, you don't need!

But if you want to publish in a respectful magazine and you don't know how to
formalize (in maths) your accomplishment, you will not get accept.

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dkural
Yes.

~~~
andars
Faraday?

~~~
dkural
I suppose, only if there is no Maxwell yet :)

