Do you need to know math for doing great science?

He could grok the math, which was difficult and very new at the time, because he had the best possible teachers.

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

But including Feynman in that list is an egregious joke. Richard Feynman was one of the top mathematical talents to grace physics. He was a lightning fast calculator. I know of two math competitions that he was in (one from NYU, the other the Putnam). He won both by wide margins. He was the only student ever to get a perfect score on both the math and physics sections of the Princeton graduate entrance exams. He invented a whole series of mathematical techniques, Feynman diagrams being only the most famous.

Einstein was merely extremely good at math. Feynman was phenomenal. Neither is a good example of physicists not needing to be good at math.

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. Einstein's strength was to imagine thought experiments, Fermi's was to do rough back-of-the-envelope calculations. So while mathematics is definitely key to making advances in fields like particle physics, even in those fields what really matters is the ability to imagine physical phenomena and make sense of them. The history of physics presents very few examples – Paul Dirac’s work in quantum mechanics and Hermann Weyl's work in group theory come to mind – where mathematical beauty and ability alone served to bring about important scientific progress.

There is nothing there that attempts to imply in any way at all that Einstein was bad at math. Infact, it matches your characterization of him ("Einstein was indeed a very good mathematician" ~= "mathematics is definitely key to making advances in fields like particle physics") quite well.

I think what it is trying to say is that it is quite rare for a break through in Physics to require new maths. While we can all think of exceptions (and indeed the article mentions them) I think it's a reasonable point to make.

I actually think this is a pretty good article, and attempts to make subtle points. Dismissing it like this by mischaracterizing what it is saying does it a dis-service IMHO.

I think Einstein himself wrote that to move to general relativity he had to go to great lengths in studing fields of mathematics he didn't know - not least because the were just being discovered at the time.

This lends credence to the idea that is genius was foremost guided by physical (I would say also philosophical) intuition, though of course you can' t discount the role of math in GE.

https://en.wikipedia.org/wiki/Relativity_priority_dispute

In other words, his contributions to science arose from his exceptional physical insights, and not his mathematical brilliance.

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.

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.

If you treat math as a blackbox the best case scientific contribution you can make will be reduced to measuring numbers. New numbers might lead to some new major insight, however this new insight will most certainly not be delivered by you but by someone who uses your numbers to actually "do the math" hence develops a mathematical theory capable of delivering quantifiable predictions for a more general case including the new data.

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.

"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.

However, these small, incremental changes are going to pile up and amount to what ends up being a qualitative change.

Also: I'd not fear a new dark age. Chinese or other East-Asians are bound to get to the business of modifying embryos for higher mathematical intelligence before 2060. That's going to induce quite a jolt for the sciences, even if 3/4 of those kids end up doing something else.

Yes. The problem is not a lack of excellent scientific results, the problem is the sheer number of mediocre people in the field and the amount of trash that's published as though it was either significant or science. These mediocre results tend to hide the high-quality work.

My theory is that there are just as many original thinkers as ever lived, but the noise level is much higher now, and scientific publications tend to publish page fillers with little or no significance or that are simply wrong:

http://www.nature.com/news/over-half-of-psychology-studies-f...

In my opinion, the problem is not that science is over, the problem is that it's become to a large extent a business instead of an exploration of nature for the sake of exploration.

> "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?

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.