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Physicists avoid highly mathematical work despite being trained in advanced mathematics, new research suggests. The study, published in the New Journal of Physics, shows that physicists pay less attention to theories that are crammed with mathematical details. This suggests there are real and widespread barriers to communicating mathematical work, and that this is not because of poor training in mathematical skills, or because there is a social stigma about doing well in mathematics.
Dr Tim Fawcett and Dr Andrew Higginson, from the University of Exeter, found, using statistical analysis of the number of citations to 2000 articles in a leading physics journal, that articles are less likely to be referenced by other physicists if they have lots of mathematical equations on each page. [...] Dr Higginson said: "We have already showed that biologists are put off by equations but we were surprised by these findings, as physicists are generally skilled in mathematics.
"This is an important issue because it shows there could be a disconnection between mathematical theory and experimental work. This presents a potentially enormous barrier to all kinds of scientific progress."
http://phys.org/news/2016-11-physicists-mathematics.html
[Abstract]: Statistical Analysis of the Effect of Equations on Citations
(Score: 4, Informative) by bzipitidoo on Monday November 14 2016, @01:17AM
I'm pretty good at math, but I could be better. Math is poorly taught. Made much harder than it actually is. To add to your complaint about imaginary numbers, the meaning of such words as geometry (earth measure) and trigonometry (triangle measure) and even "tri-angle" is mentioned once or twice, then forgotten. Politicians understand that voters need to hear simple slogans over and over for them to sink in. Math teachers seem to feel that students will just magically understand the big picture if they're buried under technique after technique.
Then they don't even pick the best techniques. My pet peeve is the "slope of the line" formula y=mx+b taught in geometry. It is a terrible representation. Can't handle vertical lines, and is a general pain to work with. The Linear Algebra method of keeping lines decomposed into x and y portions and dropping that miserable 'm' for slope is much superior. Two of Linear Algebra's basic operations, the dot product and the cross product, are awfully handy for geometry problems. Another blunder is going straight to the analytic methods, skipping the more intuitive and visual ways used by such ancient mathematicians as Archimedes. Yes, analytic is more powerful, but visual is easier to understand. Geometry class is "analytic geometry", but too often abbreviated to just "geometry", and the students never get any explanation why that "analytic" part is there and what it means.
I find it hard to believe that high schools can burn up a whole semester on trigonometry, when the essentials can be taught in a few days and fit on a business card. Half of trig is "sine is opposite over hypotenuse, cosine is adjacent over hypotenuse", and it is sometimes useful to remember the law of cosines and the trig version of the Pythagorean Theorem, sin^2 + cos^2 = 1.
Calculus is vewy scawy. Most students never get anywhere near the stuff. Those that do don't come away with a good feel for how to apply it. Students are drilled on meaningless formula, learn how to take the derivative of polynomials, trig functions, logarithms, etc. but not what to do with any of it, and that's a tragedy.
(Score: 0) by Anonymous Coward on Wednesday November 23 2016, @10:47PM
With regard to trig, I really struggled to learn it*. (Math "genius" here, btw.) I later understood more fully why. A lot of the complexity of trig is artificial. It has more to do with history and naming of things than anything else. I understand it extremely deeply today, however, and think it's awful that we force it on kids the way we do. There are alternatives. I particularly like the approach of Norman Wildberger--Rational Trigonometry. I feel this is a "sweet spot" of understandability and insight into the actual mathematics, that is actually something accessible to students, without forcing concepts that are terribly artificial. But I strongly agree that analysis is conflated with trig unnecessarily.
Imaginary numbers are a holdover of misguided assumptions in mathematics, and could also be purged if formalized appropriately. It is somewhat arbitrary what mathematicians have chosen to accept as primitive, and imaginary numbers happen to fit that mold. That's not to say they'd disappear. They'd just have a different representation.
I'm less inclined to agree with you on slope/intercept. Unlike the others I've mentioned, that's less of a reach (much of the complexity is necessary), and more of just a practical considerations problem. Yes, linear algebra is powerful and unifying. But to ask middle schoolers to understand it is too much.
*Fun story: After two days of panic trying to learn trig, I did finally get it. It took three more days.