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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: 2) by ledow on Sunday November 13 2016, @07:13PM
Because God forbid we expose children to things that are difficult for them to learn.
(Score: 3, Interesting) by RamiK on Sunday November 13 2016, @08:19PM
Studies show 5-12 y/o have very limited capacity to comprehend math. What they do well at those ages is rote memorization. As such, if one were to optimize the curriculum, those early years could be better spent learning an extra language or two, and maybe a musical instrument if they're so inclined, while following the fashion of religious schools and having the children memorize mathematical tables and identities without any attempt at actually explaining or exercising what they're learning.
Overall, there's plenty of time to teach everything. Much like a good gym routine for novices, it's simply a question of efficiency rather than priority.
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(Score: 1) by Ethanol-fueled on Sunday November 13 2016, @10:12PM
I am now a math retard, but once upon a time I was 2 grades ahead in math and learning imaginary numbers -- and how those were taught remains to this day one of my largest pet-peeves. First of all, they're not "imaginary" because they're used every day (particularly where I work).
Perhaps I'm biased, but I believe that they should be taught alongside electronics where inductive and capacitive reactance represent complex impedances (sounds fancy to the layman but it's a pretty simple concept). And they should stop calling them fucking "imaginary." I believe every student should have to take an electronics class, because it is a practical science and at its most basic levels can be taught with arithmetic and hands-on experience.
My former professor, who had a degree in pure maths, told us that the running joke was that it was 99% pure -- and I believe it. Even in babby's first discrete math class one gets different answers about what zero divides (just itself, or all integers?) depending on which interpretation one subscribes. Some people think zero is one of the natural numbers, others don't. In calculus II here students are taught notation abuse, separating the dx from dy in dx/dy to solve basic differential equations.
(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.
(Score: 2) by RamiK on Monday November 14 2016, @01:32AM
they should be taught alongside electronics where inductive and capacitive reactance represent complex impedances
This will (and does) help address comprehension which reduces antagonism. But when people are complaining about the whole trig \ imaginary(complex) \ (partial) differential equation \ Laplace transforms calculus subject, they're really complaining about the endless memorization of identities at an age when they really shouldn't be learning via memorization.
but once upon a time I was 2 grades ahead in math and learning imaginary numbers
You might have noticed this already, but this is the same with most EE students: They've all been either on an accelerated private school program, come from high achieving families with academics parents (ideally a stay-at-home mother) or from a culture that hasn't stigmatized memorization and repetition for early tuition (Jewish religious schools, private boarding schools and Asian cram schools immediately pop to mind).
There are rare top-of-the-crop exceptions that can still memorize as adults. But those are so few and far between that they're trivial to single out earlier in life and don't need to be considered as part of a standardized program.
So, I stick with my original suggestion: Get those 10 year old sheets of identities and let them hammer at them. They don't need to solve anything or nothing like that. Just cram it all in. When they'll hit ~16ish, you can expose them to circuit solving and physics side-by-side with the actual explanation of the math and solve some problems. Once it's just about applying what they already have in their heads, the process should be fairly painless.
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(Score: 1) by khallow on Monday November 14 2016, @09:59AM
In calculus II here students are taught notation abuse, separating the dx from dy in dx/dy to solve basic differential equations.
Differential forms [wikipedia.org] (what is represented by such things as "dx" and "dy") rocked my world. It isn't just notation abuse, but turns out when applied correctly to be a better way to do calculus over multidimensional spaces (especially when the space is squirrelly, like it's curved, crossed over itself due to some weird embedding in another space, or something). What's interesting is that the basic symbols of modern differential forms were developed by Leibniz back in the 17th century, while the full math itself came around at the beginning of the 20th century.
(Score: 0) by Anonymous Coward on Monday November 14 2016, @10:29AM
Wait, you weren't learning complex numbers, of which the imaginary numbers are a mere subset?
No. That's what they are named, and there's no reason to change the name. Just as we don't stop calling irrational numbers "irrational" despite nothing about them being irrational in the common sense of the word. And we don't stop calling transcendental numbers "transcendental" despite them in no way related to religion or spiritualism.
One of the things you have to learn when you learn mathematics is that the mathematical terms generally do not mean the same as the common terms, even though they may originally have been derived from that term.
Also note that from the common meaning of the term, all numbers are imaginary, even the natural numbers. In nature, you may find five apples or five oranges, but never the number five. The number five is an abstraction that lives purely in our mind.
(Score: 0) by Anonymous Coward on Monday November 14 2016, @02:04PM
I actually don't even agree with how you describe the names.
Imaginary numbers are called such, because they came to be that way: a "value" that was invented because it made the formulas easy to solve. That makes them fairly imaginary, even if we just accept them like we do "normal" numbers (admittedly I am here ignoring your comment about all of them being imaginary which surely is a good point :-) ).
There is a lot of things "irrational" to the human mind about irrational numbers, though I guess it comes rather from "ratio" (fraction), so that is likely just a misunderstanding of a name, and can be easily explained.
Similarly for transcendental, though I am not sure if that is not even a mistake translation, as the texts that started using it were in Latin and German I believe.
Most of these issues with naming really would IMHO be easier to fix by adding a few sentences on where this came from before teaching the details. At reasonably tiny bit of history in their mathematics won't hurt anyone, and actually quite a few people will enjoy it. And even in mathematics one can learn from history (like all the cases where major flaws in proofs that were considered solid went by unnoticed for ages).
(Score: 0) by Anonymous Coward on Wednesday November 23 2016, @10:15PM
I am a mathematician, but hardly a mainstream one. To my knowledge the abuse of notation you refer to could probably be justified rigorously under a framework like non-standard analysis. In other words, it may not be strictly valid using the axioms the student has been provided, but it is probably still justifiable under a similar, albeit more technically precise framework.
(Score: 3, Interesting) by ledow on Monday November 14 2016, @08:10AM
Math nerd here.
At 12 I was writing computer programs to calculate pi, from a formula based on a Taylor-series expansion.
My primary school teachers had said I was all-but useless at maths because I didn't sit down and learn the timetable and - at their demand - recite each perfectly without error in front of the entire class. Literally, by the end of the year, everyone else had their 12 stars for doing so and I think I'd done the 1's and 2's.
In secondary school, on the first day there, a teacher grabbed me (kindly, but immediately upon seeing me). That teacher INSISTED he was my only maths teacher until age 18. Why? Because he taught the top-set.
I was soon top of that school, of about 1000 kids. I now have a maths degree.
The reason - teaching by rote in primary school is a lot of shit, especially for maths. That's not maths. That's arithmetic at best. It's an awful way to learn. Just because you/your parents learned that way means nothing. It's an awful way to learn, still, and an awful way to teach maths.
If you are memorising, you are not doing maths.
If you do not derive, you're not doing maths.
If you do not work out from first principles, you're not doing maths.
If you do not tie it into areas that you learned yesterday, a year ago, 2 years ago, etc. all at the same time, you're not doing maths.
To this day, my arithmetic is average. I can do any sum or multiplication or division, but I do it by going back to first principles, not rote. I can do it from first principles in my head often faster than people can do it any other way. Fortunately, I'm surrounded by machines which can do arithmetic much better than I can - and that would have been true 200+ years ago too.
But my maths? I work in a private school - as an IT guy, my degree is maths and computer science - and I have embarrassed the maths teachers more than once. I like to walk up and correct their formulae on the board while they're teaching. I've had to sit and explain public-key encryption properly when teachers could only skip over it and say it was "something to do with primes". And I did it at a level that 10-year-olds got it. When you're an IT guy, people don't expect you to know maths inside-out.
And, actually, my strength is midway between maths and computer-science. I love graph theory, coding theory and others that are basically mathematics applied to computing principles. I can't program a game without finding the optimal mathematical algorithm for things. I just enjoy doing it.
The reason my teacher chose me from the crowd? I was doing maths FOR FUN at that age, 10, having come from a school where that kind of independent thought was all but openly discouraged and they had "generic" teachers who did not teach subjects but the whole class for the whole year. And because maths is what I did when I was bored.
To this day, I wonder what could have happened if that teacher had worked in my primary school too.
Every time I see "maths is too difficult", I mentally append "for me." You're not the only one in the school. And not teaching maths by rote helps immensely for understanding. I still encounter maths graduates who have NO IDEA where sine, cosine, etc. actually comes from - it's just a magic "by-rote" function for them that does something useful.
(Score: 3, Interesting) by RamiK on Monday November 14 2016, @11:46AM
How is your anecdotal exceptionalism relevant to the general population? How's having a teacher singling you out as a prodigy and mentoring you applies to everyone's curriculum?
This is the same mistake every novice athlete makes: They look at routines of exceptionally talented, advanced and often juiced athletes and mimic their routines. Ask any music prodigy that's successfully teaches music for a living and they'll confirm the same: While they didn't need nearly as much drilling and memorization, the vast majority of their students do.
This is exactly what's wrong here. People look at high achieving youth that are being schooled privately by excellent teachers and think this should somehow apply to their children. Worse, those youth later reach positions in academia that deprive them of the experience of teaching normal people and influence the curricula based on their anecdotal evidence.
And let be clear, we're talking about engineers, not theoretical physicist and mathematicians. People who actually do end up using calculus to design high-power infrastructure and machines on a daily basis NEED to know those identities. Programmers making algorithmic choices need to have all that "arithmetic at best" linear algebra and combinatorics as second nature so when they work on the code they be able to shift between representations on the fly like a musician switches keys reading sheet music.
Keeping it closer to home, pick up Zed Shaw's books and look up his essays. He's discussing these very same issues as relevant to teaching programming. It's elementary stuff. But so is high-school.
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(Score: 1) by Ethanol-fueled on Sunday November 13 2016, @10:21PM
The problem with younger people is that they don't understand why learning that stuff is so important, and it is a tedious grind in the context of passing a math class. Sometimes people just have to wait until they're ready to learn on their own terms. It doesn't help that a lot of math teachers are monotone Ben Stein-tier autists.
I spent my entire algebra II class in high school ditching when I wasn't pinching my girlfriend's braless nipples and playing Led Zeppelin on my guitar in class, and the teacher let me get away with it because he was one of those guys who didn't bother to motivate such blatantly unmotivated students.
Well, when I actually decided I wanted to learn math around college age, I had to start from -- no joke -- introductory plane geometry because I sucked at math so bad. If there was anything I could say to any math newbie it's to learn the fucking symbolic manipulation of intermediate algebra, because that's all math fucking is all the way to quantum physics and beyond. "Calculus" is just a fancy way to introduce new algebra techniques. It's all fucking algebra, and if you blow your algebra class you're gonna be set at least 5 years back and be in a world of shit should you decide you want a degree that will make you some money.