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Do you need to know math for doing great science?

• noodlio 11y ago
  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.
• Xcelerate 11y ago
  Site seems to be down. Cached version: 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/ http://webcache.googleusercontent.com/search?q=cache:8cobPmg...
• dkural 11y ago
  Yes.
  • andars 11y ago
    Faraday?
    • dkural 11y ago
      I suppose, only if there is no Maxwell yet :)
• dkarapetyan 11y ago
  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".
  • gavazzy 11y ago
    Einstein was hardly the best mathematician at the time, simply because there were people who spent as much time on theoretical math as he did on physics.
    • johnloeber 11y ago
      The parent poster claimed that one of Einstein's strengths was his mathematical prowess. Whether or not Einstein was among the best mathematicians of his day is irrelevant.
  • danharaj 11y ago
    "I admire the elegance of your method of computation; it must be nice to ride through these fields upon the horse of true mathematics while the like of us have to make our way laboriously on foot" - Einstein to Levi-Civita He could grok the math, which was difficult and very new at the time, because he had the best possible teachers.
  • johnloeber 11y ago
    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.
    • deleted 11y ago
      [deleted]
    • logicallee 11y ago
      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.
• Fomite 11y ago
  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.
• ankurdhama 11y ago
  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.
  • bloaf 11y ago
    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.
• dnautics 11y ago
  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 11y ago
    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 11y ago
      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).
• threatofrain 11y ago
  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.
• jupiter90000 11y ago
  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 11y ago
    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.
    • jupiter90000 11y ago
      Cool quote, thanks. Guess I'll want to keep an open mind about it all..
    • vlehto 11y ago
      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.
  • kriro 11y ago
• sandworm101 11y ago
  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.
• deleted 11y ago
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• quanticle 11y ago
  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.
  • stdbrouw 11y ago
    But (1) statistics is really not the kind of math that is being talked about in the article, (2) even if you study statistics in a graduate program, you'll be inundated with hypothesis tests and alpha=0.05 and any deeper insight just kind of has to develop on its own, (3) the only math you need to understand the shortcomings of statistical tests is P(A|B) != P(B|A) and (4) the reproducibility crisis is primarily due to publication bias and null hypothesis significance testing is at most a catalyst.
  • fengwick3 11y ago
    > 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 11y ago
      Reproducibility of results, not reproducibility of thought process on different (even though similar) ground.
  • sprash 11y ago
• thegenius2000 11y ago
  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 11y ago
    > 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.
• deleted 11y ago
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• lutusp 11y ago
  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.
• randomsearch 11y ago
  "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.
• tegeek 11y ago
  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 11y ago
    > 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.
• reallydontknow2 11y ago
  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.
• kriro 11y ago
  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.
  • InclinedPlane 11y ago
    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 11y ago
      >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.
• crncosta 11y ago
  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.
• nsajko 11y ago
  This is an interesting, though quite old example of the importance of math: https://en.wikipedia.org/wiki/Hardy%E2%80%93Weinberg_principle#History https://en.wikipedia.org/wiki/Hardy%E2%80%93Weinberg_princip...