Nowadays, it takes a student at least five years of university

>>7703866
Evolution baby.

no. It will become more like Object Oriented Programming on .NET
You will use an algorithm or a rule that someone else has written or deducted without needing to know how that algorithm works

>>7703866
In the past people were mathematicians, physicists, musicians, politicians and philosophers all at the same time.

Nowadays you can only be one of those, say, mathematician. But you will know geometry, calculus, analysis, topology, graph theory. etc.

In the future there will only be geometrologists, analysists, topologists, graph theorists, etc.

This is the "knowledge event horizon" though other names exist.

Back around 1900 Planck, Einstein Dirac et al were young when they made their breakthroughs. These days you need to cover a lot of their work to reach new grounds. So yes, there will be a leveling out unless someone makes learning a whole lot faster.

Papers have been written on this topic, it is the basis of serious research. I'll see if I can find a paper (I have a copy somewhere) but it will take me a few days.

>>7703889
Would you like to expand on that?

>>7703912
is it not kinda like this already? mathematicians specialize in graph theory or optimization or whateverr

>>7703912
>nerf algebra spec mathematicians
>buff topology

>>7703866
That's a good question I often wonder the same

>>7703866
Before the calculator, students would learn how to compute logarithms and such by hand, technology allows us to skip over stuff that becomes irrelevant with it. One may argue that someday learning how to compute derivatives and integrals and such will be irrelevant with technology such as wolfram alpha, etc. and that will free a lot of study time towards other stuff, that's my take on the matter anyway

Then we will have to either extend the human lifespan, upload ourselves to computers, or start specializing people right from birth.

>>7704192

Yes, it is like this now - people have to specialize, or so I am given to understand as a lowly bachelor's undergrad.

Reading OP's thing and your post reminded me of a passage from a textbook, which identified a definite period when "total historical mathematical knowledge" in individual humans ceased to exist. I quote now from a biographical blurb on Augustin Louis Cauchy, from Contemporary Abstract Algebra, Joesph A. Gallian (6ed), p 119.

"In 1815, at the age of 26, Cauchy was made Professor of Mathematics at the Ecole polytechnique and was recognized as the leading mathematician in France. Cauchy and his contemporary Gauss were among the last mathematicians to know the whole of mathematics as known at their time, and both made important contributions to nearly every branch, both pure and applied, as well as to physics and astronomy."

So according to the textbook-author Gallian here (the sole author of the whole text), real specialization began around the early 19th century.

>>7703919
bumping thread for this

>>7704334
They had tables of logarithms to convert large multiplications into sums. In much the same way we have tables for tricky integrals.

>>7703866
>university
If you try really hard you can learn just about any subject entirely in a month (given that you have learned the preliminary topics). University is LOW density learning so that the lowest common denominator in class can learn too, that's why it takes so long.

>>7705608
Are you talking undergrad level or PhD level here?

Your university sounds like a real outlier and I'd say all the things you need to know to finish a PhD takes way, way more than a month.

File: math education.png (119KB, 1216x970px) Image search: [Google]

119KB, 1216x970px

>>7703866
>research has advanced

No, math education has regressed. We should be starting off at functional analysis in university.

>>7705871
Jesus Christ that's a ton of learning.

And what is that religious class? do they just choose from a set of religions and learn?

>>7703866
LAW OF DEMENISHET RETURNTS

>>7703866
no. CRISPR is now operating within the margin of error of the natural mutation rate. We are going to start germ-line modifying human babies really soon and they will just come out of womb super smart.

>>7703866
>Nowadays, it takes a student at least five years of university to learn enough about Mathematics to engage in research.

Because we're starting off with college algebra since public school educators don't feel like it's useful

>Do you think there will come a time where research has advanced so far that it would take one ten or twenty years to get to the necessary level of knowledge?
>Once there is so much information even in one specific branch of mathematics that it takes a whole lifetime to understand it, progress is no longer possible.

No because the nature of mathematical progress leads to more powerful general abstract methods that simplify solving what came before. In the olden days, the quadratic equations took up pages going over the various case were a, b, c were positive, negative, and zero with a special methods for each. Now we have a one line formula. The cubic equation filled up a whole book with solution methods but now we just need a page. Synthetic geometry required an unique creative solution to each of it's theorems but now they have been reduced to simple turn the crank algebraic manipulations thanks to coordinate geometry. Calculus standardize the diverse methods for finding tangents and squaring curves into very simple rules. Vector Calculus greatly simplified carrying systems of equations around for each dimension. Abstract Algebra saved tremendous time by allowing you to just prove that a given set up has a certain algebraic structure allowing you to use all the theorems true of the algebraic structure for the set up. etc etc

>>7706094
this
Knowledge isn't a homogeneous resource that is steadily increasing, it's dynamic and constantly changing.

>>7705994
You can get back 4 years by reverting to how things were done in the 1700s. Then it was common to start undergraduate at 14 or 15.

>>7705861
No no. I meant that a single semester long course could be learned in a month where usually they take about 3. I base that on how long it takes to go through a coursebook devoting 1-3 hours of intense study per day and while doing more than one subject at a time. Granted, you won't be able to ask a professor for the answers but you will have the internet (which in my opinion is better, just slower)

>>7703919
this+probably less breadth coverage but more depth

Broad foundations will be replaced by relevant theory in your interest area, that said I am getting out of pure math as an undergrad as my interpretation is that it is a dead field, the low hanging food used in applications have been answered, its gotten to the point you can sped a couple years fucking around with some pre with a specific set of initial conditions.

So go applied, pure is dead.

OK, I am back from here: >>7703919

The paper is titled "Age and Great Invention" and is authored by Benjamin F. Jones. The PDF is found many places on the net and runs at 52 pages on my PDF viewer. Oh and it is very clearly written in (La)TeX and the font is Computer Modern.

It is a good read though I am a bit unsure about a few points such as the relationship between acquiring new knowledge per unit time vs. loss of knowledge per same unit time.

File: aristotle_excellence.jpg (239KB, 1067x1479px) Image search: [Google]

239KB, 1067x1479px

>>7707996
Thank you kind sir!
I have been waiting for this!
Please take with you this bust of Aristotle, as a token of my appreciation.

Bumping for justice.

>>7708293
>appreciation
Much appreciated dear colleague. While I had to leave the world of research as my field dried up I still have an interest.

You may also be interested in some closely related papers such as those at the bottom of this page: http://www.nber.org/papers/w11359

Then comes the question of what to do. People will always expect the next big thing in tech and continuously improved healthcare, medicine and more. yet all this takes a lot of work from nameless scientists.

>>7708293
>We are what we repeatedly do
So I'm a mastrubation? I don't get this.

Well get more and more specialized. Instead of getting a math degree or a physics degree, you'll get a degree in Non-adiabatic Quantum dynamics, or Sherrington-Kikpatrick spin glasses

>>7705871
I agree the standards should be raised but that's way too much. in 10th grade quadratics nearly brought me to tears. also, 0.01% of people who pass 8th grade ever go on to need to know vector calculus. maybe if by the 4th grade a child decided they want to specialize in math, then they could be put in a stream like that, but normies would not be able to handle that at such a young age.

>>7708736

There's no reason to make all the grades required.

>>7703866
In a way we are already there, I use Eureqa to find correlations in data, I have a idea on how the computer does this, but it is strictly not necessary to know to be able to use it. And it might end up with some empirical answer that I can not easily explain, but which might still be used.

>>7708699
>Well get more and more specialized.
That is one approach. There are limitations since you risk overspecialisation where there is no contact between adjacent research fields.

A more reasonable approach is just to drop the garbage from schools and just get on with it. If someone wants to learn stuff then let them. Instead everything is geared towards the lowest common denominator and that is real low.

If you are into sports then elitism is OK. If your pursuits are more academic then it is baaad. And the people who make these rules still want all the latest gadgets and medicines.

>>7703919
We should decide at birth a persons role in society and only teach them things pertaining to that in school. They can learn whatever else in their free time.

>>7703899
Functional programming > OOP

>>7712539
then you wouldn't have went to school, because you don't need an education to dig ditches

>>7712530
Humanities classes should be cut to. Soft sciences are cancer.

>>7710279
This desu. Get kids working at 15.

>>7712582
A major problem with some of the humanities is that they get research funding for weird womens studies and more, money that would be better spent on real research into, say, pharmaceutics. That would improve life.

>>7703866
more like three years. going to uni involved taking a bunch of other shit like humanities and spending way more time on a text than is needed by going at a snails pace.

>>7714522
Really?? Having done my undergrad and PhD at a British university I did not have to take humanities. Still, I think 3 years sounds unrealistic unless you are talking about the next Einstein.

>>7712650
You're ironic but that's true. There's nothing wrong with youths of age 15 put 16 working. Why does anyone need to learn till 18 or 25 just to wipe tabletops, make coffee or work in factory?

>>7703866
> it takes a student at least five years of university to learn enough about Mathematics to engage in research
False premise. Only certain fields require super
advanced mathematics.
>Do you think that will ever happen?
No. Not in a general sense.

>>7715649
Absoulutely this. I mean those are the kids bitching on facebook about "hurr high-school didn't teach me how to open a bank account :("

They are the retarded double digit half of the population and whichever way you cut it they are destined for service and labour jobs.

We should accommodate them instead of forcing them to learn math they will never use.

>>7712568
Procedural >>>