I can't find the citations right now, but there was a recent study done through Elsiver's website. The group got a hold of the servers for Elsiver and took a look at page views. They wanted to know what the rates of papers being read was. It was... disheartening. They found that ~46% (again, not sure here as I can't find the source) of papers will never be looked at outside of the authors, reviewers, and the editors. The articles are not only never downloaded, but the pages are never even loaded. The stats were, to me, confusing, but hey that is what peer review is for. Still, if you take this paper (that I can't find now) to be true, ~half of all papers are effectively lecturing into the void. I admit, I drank a bit after reading that one.
I honestly don't know what to make of it really. I at least bother to look at my papers once, if only to show my family on the Holidays, and I have a lot of so-authors that may be doing the same. Are most researchers so fed-up with their own work as to not even bother looking at it again? What is going through their minds concerning their efforts? It's just ... heartbreaking. At least half of researchers don't seem to care at all, not even the people that put all that time and effort to get their research out there. Like, what are we doing with our lives?
I think many more papers would be read if authors invested more time in learning how to write.
Higgs said he could have not been able to operate in todays academia. Not everyone needs to have John von Neumann performance levels to do valuable work.
The Wikipedia article has a long section of criticism of Elsevier: https://en.wikipedia.org/wiki/Elsevier#Criticism_and_controv...
But that said, I don't know of any author that wouldn't give you a gratis copy, oh, ok, maybe an old 'draft' that is 'close' to the publication.
This seems, at first, to be a problem in academia, but, at further glance, is really a problem with education.
In my view, this wasn't about doing mathematics as an academic career, climbing up the ivory tower, publish or perish, and all that.
Edit: I tend to agree. My intellectual capacity was far improved only after doing first year Engineering Maths & Physics. I did terrible gradewise, but it has helped me visualize, juxtapose mental structures, quickly iterate on different concepts etc.
I should go back to doing something again. Had to do some cartesian products in a data migration the other day, in my dayjob, it was refreshing :).
And as always, this timeless quote from Einstein motivates "Do not worry too much about your difficulties in mathematics, I can assure you that mine are still greater."
Same here, and thanks to the internet just remembering concepts is usually enough these days.
Yesterday I had to quickly guestimate for a project how much space overhead we'd have on the server if we pre-generated an image pyramid of tiles for leaflet.js[0], instead of generating a "PNG" in RAM on the fly each time and serving that. Then I realised the number of pixels shrinks by a quarter every time we zoom out, so the worst case would be the infinite sum of 1/4^n. While I vaguely remember from my first year of physics how to calculate that, it's been over a decade. But we have Wolfram Alpha these days[0], which told me it converges on 4/3. So I knew the upper boundary would be around 4/3 of our original data, plus negligible PNG header overhead, and assuming compression is about the same.
[1] https://www.wolframalpha.com/input/?i=sum+of+1%2F(4%5Ek)
While I can probably count on one hand the times I've used what I learned in the "real" world, I can say I really value my education.
I believe the real value of a math based curriculum or even something like philosophy with an emphasis in logic is that it teaches one how to think in a reasoned, dispassionate and rational way.
>Teaching mathematics shouldn’t be about sending everybody to a Ph.D. program. That’s a very narrow view of what it means to do mathematics.
I know this from personal experience. After I joined industry I thought I'll do physics research in my own time. In fact, I can't even keep myself up to date about current research. Most journal articles require a lot of effort to go through, and I don't have that kind of energy after a work day.
For instance, compute the fibbonacci numbers modulo the square of a prime and compare to modulo a prime. Are there numbers where the first zero appears at the same point? We don't know.
I'm not saying the problem is easy. I'm saying one can make some progress without much theory.
It took mathematics much beyond what was known at the time to get anywhere close to a solution.
Claimed without evidence.
Sure, you can make trivial progress by writing a computer program to search, and the problem is "elementary", but "elementary" doesn't mean "can be solved without studying lots of techniques and theories", it means "can be solved without calculus"
[0] https://mathtourist.blogspot.com.au/2010/06/tiling-with-pent...
... the achievement of human flourishing, a concept the ancient Greeks called eudaimonia, or a life composed of all the highest goods. Su talked of five basic human desires that are met through the pursuit of mathematics: play, beauty, truth, justice and love.
(From TFA.)
In physics these laymen are generally called 'crackpots' for a good reason because the context one needs to understand to generate new results is so huge.
Mathematics is different - all one needs is pen, paper, a mind that's attuned to generating logically whole statements and a problem that just won't let go of ones mind. The results are likely in geometry or some other approachable field and not in some more obscure subject.
(I have a MS in Math, my field was algebraic geometry. I considered a career in math research, but the industry was paying too well for it to be a reasonable)
In fact, in academia, in some fields (and mathematics is certainly among them), in some sense only "the best" contribute to pushing the field forward by working on the cutting edge.
And I think the author's point was that focusing only on that is an overly narrow view, and one can engage in maths in a recreational, joyful way, without aspiring to an academic career in it.
However... being a math major is really different from a career in academia. People really should be encouraged to major in math.
Somewhere in this thread there is a link to Francis's lectures and they are wonderful. The method/enthusiasm be has for teaching is wonderful and makes all the difference to students.
Rather than going through online courses and paying for them (many university classes are mostly online math problems, and proctored during a specific time.)
EDIT: The way math is currently taught really forces people to dislike math and think they suck at it. (in general)
Starting in primary school with basic arithmetik. (I help a young boy with his homework) They don't really teach them Math, how to solve thing, they tech them to memorize different algorithms, which they can handle after a while, but don't know what they are doing at all ...
So the best mathematicians there are not the ones who can think best, but who can memorize and follow orders the best.
I met a woman from South Korea who was taught all drill and no concepts. She was solving differential equations in high school but had no intuitive concept of derivative and integral or what they were used for. In fact, she had no interest in math. She was just a diligent student focused on getting into the top university. She was obviously trained the way you describe.
I have also personally, in the United States, been in math classes where many students suffered because they couldn't string together correct calculations consistently enough to validate and reward their high-level understanding. They learned a lot of the words and pictures, could explain what an integral was for, and could listen to a lecture and feel like they got it, but if you asked them to apply what they knew to a real problem, they responded with a kind of rueful helplessness. To them, mathematics was like magic in the Harry Potter universe: anybody could explain it, but it worked for some people and not for others, for reasons that seemed to them to be innate.
Each system stressed one aspect at the expense of the other, and in each system, there were many students who picked up both, but also many students who only learned the part that was stressed by their teachers. It was certainly the case in my classes that a student who only learned the concepts, without the mechanics, was unlikely to progress much farther in the math curriculum.
A balanced method treats the two aspects as complementary, each enabling the other. Treating one as the hero and the other as the villain might make sense locally as a response to a warped system, but it can easily become a warped approach in itself.
Of course, most students do just memorize equations and follow orders. But in my experience the most successful students are always the ones who understand the material on a fundamental level and memorize very little (on some level, memorization is all but required by even the best).
Later on, things get better, yes, but not much.
Common Core in the US is supposed to solve this. I've seen some common core math homework for myself and despite the odd outrage most people have towards it, I think both the idea and execution are at least decent, and an improvement.
^ THIS.^
If math education could only be more like: https://betterexplained.com
On the one hand, academia has become rather harsh and intimidating and there is room for all kinds of improvement.
On the other hand... there is no world where whoever just wants to study math can just go study whatever they want for as long as they want, regardless of how well they do it. Of course, when I spell it out, that probably seems obvious, but I suspect this may be the unexamined assumption in a lot of people's heads.
"There is really no point in doing any exercise unless you're aiming for Olympics level performance. Yes, it's somewhat harsh and intimidating. But there is no world where whoever just wants to can just go do sports and exercise what they want as long as they want, regardless of how well they do it."
I think that was the point of the article - doing maths as a way of life (like exercise), not just for your career with the aspiration of being the best.
I'm speaking in a context where we're talking about academic life and academic life being harder than it needs to be. I think that's the only way to read this context, because nobody is making self-study "harder than it needs to be", so reading this thread as being about "life in general" doesn't make any sense to me.
I think the article is precisely not about professional mathematicians in academia. To quote: "If mathematics is a medium for human flourishing, it stands to reason that everyone should have a chance to participate in it." (my emphasis).
I solve Project Euler problems for fun. The article presents an argument that more people should do something similar, and more mathematicians and maths teachers should support it.
Plus I suspect you missed my "regardless of how well they do it" clause. I doubt that you can flunk every math class over and over and just keep attending. Loopholes that big get noticed, exploited, and closed very quickly.
In recent times, the pressure to finish or drop out has increased, and studies have become more rigorously structured (or infantilised...), particularly with the introduction of the Bachelor/Master system.
Certainly in Sweden, once you're in, you're basically free to hang around at University and study for as long as you want. It's not like they're going to kick you off campus.
"You should expect to invest years of your life into making progress on some meaningful game with little encouragement in the meantime...sometimes even after you release a game that took a lot out of you, it may take many years before people appreciate, let alone play, your game, and the vast majority of games aren't going to be played." "To compensate for this you basically play the popularity game and give as many interviews and talk up your game when you meet people, so there's a lot of salesmanship involved there as well."
"The career path is so twisted you have to either be insanely good or just hate yourself enough to sacrifice your best years working essentially in the metaphorical darkness well outside the spotlight and most likely alone and poorly paid." <- My experience working in the game industry, except I wasn't completely alone, I did have coworkers. However I did feel like I never had time for a relationship.
Su isn't as concerned with the amount of full-time mathematicians doing research work as he is the people who drop out far before that becomes an option. We should teach it better in high schools, and encourage more math undergraduates.
Su isn't saying math is a great field free of problems, but he's arguing we should focus more on getting people further along that path, regardless of the stage where they drop out. I also think the problem you're referring to exists in most academic fields, and that the solution (if there is one) will probably have to be more general than just relate to math.
this is true throughout the sciences.
it's a big issue.
From my own experience I think it's the latter. Jumping off the edge of human knowledge and hoping there was a result to catch my fall was very mentally taxing. Not many other careers force you to grabble with the uncertainty of creating knowledge, and I think it takes a toll.
The former is a thrill to many, and the latter is at best a chore for all.
Feedback needn't be a necessity in a work. Assessments and criticism will come if the work is essential, perhaps many years in the future.
In an ideal world I might have continued in academia but the career path is so twisted you have to either be insanely good (at math and at managing time) or just hate yourself enough to sacrifice your best years working essentially in the metaphorical darkness well outside the spotlight and most likely alone and poorly paid.