This is true, but you have to understand that there is a difference in Applied Math vs Pure Math, what you are describing is Applied Math, they learn very well known methods of optimization, modelling etc. But Pure Math is research focused, it’s about grasping the philosophy behind it in the very deep level. Some of our disciplines are separated with tests with non trivial questions focused. To have a consistent 9,8 average score in Pure Math is a big deal.
People who does pure math are people getting an education for a future PHD grade, because otherwhise it alone is literaly useless and applied is much more useful.
Yes that’s the exact problem. People are able to think faster but the cost of that is that it cuts out the higher order thought processes which are too slow. So it short circuits your fast thinking processes to have complete control over your actions. In other words it puts your brain into a state where your reflexes are in complete control.
The study I linked to shows that this creates a reduction in the “stop signal” metric, meaning it definitely hinders the conscious brain’s ability to control the though processes and utilize higher order thought. In other words it makes you faster but dumber.
My question is this: how can a university or organization even teach unexplored areas of math? They’d have to understand them first. At best they could say, “here is the problem where our current maths fall short” but beyond that what can they do? How do you score a student when you don’t know the right answers yourself? How do you teach your student the steps when the steps haven’t been established? How do you teach them the creative process, when by feeding them the answers you undercut that process entirely?
That’s not what I mean, what I mean by non trivial tests are questions that still requires the books knowledge but at the same time isn’t teached direcly by it. And it involves some “out of the box” thinking.
Right and my point is that the established math has limitations. The creative process is supposed to go beyond those limitations. But the schools foster a certain thought process, which is deeply entangled with and that was used to derive the established math. So they train students using these thought processes and then act surprised when these students aren’t able to do anything creative that pushes it forward. And that’s how we are stuck with an understanding of math that has existed since 1600’s. They still teach math with pen and paper rather than a keyboard and mouse, for example.
Computing integrals is a heck of a lot easier using a Riemann sum, and with computers it only takes a few minutes, and is less error prone, but they frown upon “short-cuts” like that that aren’t the “proper” way of computing an integral. Basically they are sticking like glue to old methods that are inferior because those methods are hundreds of years old and are the “right” way to do it. Translation: they have zero creativity and stick to methods they know work because they can’t forge out into new territory since they lack the creativity to do so. They can only re-apply the math that they already know and love.
This is why Universities should not have a monopoly on knowledge and education. Hopefully YouTube + certification programs eventually replace the traditional modes of education, since they are holding humanity back.
Well you may be right since there is a severe teacher shortage. I’ve always thought watching an episode of Modern Marvels would be better than any history class out there.
So here’s a good example of what I am talking about. Suppose you are writing a program in C. C is a language that was designed to solve certain problems, so it is designed to be sufficient for those problems. A class teaching C will teach the reasoning of C and how it can be used to solve all the problems C was designed to solve.
What happens when a problem comes about that C doesn’t have the features needed to model it? Well you can’t solve it with C, you have to create a whole new language, and that’s how C++ was born. C++ is constantly being revised since limitations are always being found. Being able to extend the toolkit is a very different and much more complicated task than simply using the toolkit. 99.99% of people only know how to use the toolkit.
Well the universities are still using virtually the same language/tools that were invented hundreds of years ago. How are you supposed to solve new and modern problems with an outdated toolset? You have to create a new toolset and leave the old one behind, and you have to constantly revise the toolkit itself.
When was the last time maths updated the toolset for calculating integrals? Basically never - it’s done the same way Newton did it back in 1600’s. They are stuck in a perpetual cycle of trying to apply the same old toolkit to new problems that the toolkit was never designed to be able to solve.
And his theory was superseded by Einstein’s relativity because Newton’s theory couldn’t explain certain observations. That’s where relativity is currently. There are loads of things it struggles to explain. It basically deals with the curvature of spacetime on a large scale. However it can’t explain many effects on a VERY large scale, the small scale. Some of these observations can be explained with small scale space-time curvature. For example some theories think that there may be micro-dimensions that fold back in on themselves on a small scale which has the potential to explain why galaxies spin so fast without adding new particles. But there are literally an infinite potential ways to fold spacetime on that scale which is why it’s basically impossible to find the correct folding pattern. This is the problem that string theory struggles with. Basically there is a discontinuity in how gravity behaves at certain scales so there must be something that scales it. If the shape of space/time is different on a small scale it can explain why gravity doesn’t scale well in 3 dimensions.
Traditional math with NEVER solve these problems. They are only problems modern toolkits can solve using computer science.
This is true, but not as you think it is, of course math has it’s limitations, that’s why researches exists, but it’s very rare that someone without an PHD that can contribute to it, it’s not like 1500 anymore and math fields extends beyond non educated human creativity, if you want to contribute you need to understand the theorems.
School kids are not supposed to push math foward. What kids gonna do? Invent some revolutionary philosophy? We should be teaching them math as a language, just like C++ like you said, C++ or even Python are being updated by professionals, but the difference is that math is being updated for thousands of years. There is a method, it is solid, not everyone will like it, so it’s a problem of the teachers themselves or their method, not the content.
They who? I don’t understand this criticism. If you are talking about mathematicians, it is important to develop other methods, Riemann integration is itself a method and he is a mathematician. If you are criticising math teachers on how they teach calculus, well if you want to use a calculator you gotta know what is the concept of “sum, subtraction, multiplication and division” first, same for calculus, if you wanna use Wolfram Alpha you gotta know what an integral is.
Lmao to that. I understand some criticism that Universities and academic spaces are sometimes too “antisocial” to the general public, but it’s not like scientific divulgation is very popular or profitable. Now, if you wanna take a full grad course on youtube and take the exams godspeed man, I can speak for my courses, I cannot take those classes alone, not use only one book as reference, I myself resort to mutiple sources, I have to talk to multiple people, before the pandemic I used to ask PHDs for some help to harder nuances that I couldn’t understand by my own, for me it’s important to see how professors think and how they approaches subjects I don’t have a clue how to approach myself.
The reason Universities have a monopoly on knowledge is because they came up with their stuff and for others to come and misrepresent even the smallest data/theory that took years to develop very easely results in misinformation. My point is, Youtube should not be considered as a good source for science as academic source because a problem comes when the desinformation sources becomes profitable/popular.
I strongly disagree with you, it’s not rejecting years of science you’ll come up with a better one. Science is a building block, each person slowly and methodicaly contributes with it, even Gauss (aka the best mathematician that ever lived) that invented entire fields (yes, plural) did it with previous knowledge. Modern problems absolutely is solved by millenar knowledge, this is the case in every single field. This quote “If I have seen farther than others, it’s by standing on the shoulders of giants” is literaly science summirized.
That’s never how I approached problem solving. I always look for real problems in life and dive head first into solving them. You pick up the necessary skills. You think you are going to be able to consult smarter or more educated people when you’re diving into a completely unexplored area? Good luck. They will only discourage you and tell you you are wrong at every turn, because it doesn’t fit with their conventional knowledge. If it did, it wouldn’t be an unexplored area.
I don’t think that’s true at all. Some of the greatest minds of our time were not college educated. If you want an example, look no further than George Dantzig. There were TWO unsolved problems in statistics. He showed up late to class and saw them on the board. He thought they were homework. He proceeded to go home and solve BOTH. He went on to invent the Simplex algorithm, an algorithm that heavily impacts everyday life behind the scenes.
People think that it’s their education that makes them smart and allows them to do great things. This utterly untrue - it’s usually the barriers of entry like the cost of research that prevents non educated people from contributing. But, those barriers are coming down.
I’ve seen highly educated people publish the most insane BS I’ve ever read. There was a paper claiming humans could see the future. Yep, she had a PhD, yet she was literally dumb as rock. There are countless such examples. Meanwhile people like George Dantzig can revolutionize statistics entirely by accident because he showed up late to class (had he heard they were unsolved, he may not have even tried to solve them - instead choosing to lean on conventional wisdom which says they are unsolvable). The point is, having an education DOES NOT make you smart and DOES NOT mean you will contribute to society, and the reverse is also true: many smart people are uneducated and they go on to do great things.
In fact it is exactly these kinds of people who go against the grain who revolutionize industries and set the standards that are then taught in school. The reason they are able to do that is because they have not been fully engulfed into the hive-mind of robots who think in lockstep, which allows them to think outside the box. Humans are social creatures and they USUALLY prefer having a popular opinion over being correct, and don’t want to suffer the penalties of challenging the established framework which at most casts doubt on their superiors and at worst threaten reputations and careers.
That’s exactly the snobbish attitude that professors use to discredit good ideas because they go outside the realm of what the professor thinks is “right” and “established”. And they are probably right. They probably are bad ideas. But that’s part of the process. You will have a thousand bad ideas for every right one. Such people completely miss the point when they cast stones from their ivory towers at people who are thinking outside of the box. In fact it shows their lack of creativity, since they are CLEARLY unaware of how the creative process works.
The creative process is quite literally about breaking rules and going outside what is conventional, and the conventional purists will ALWAYS resist this change. Yet history shows time and time again, that conventions are always wrong and meant to be broken.
They’re teaching kids to use a stone hammer built with a rock and a stick and some leather twine. Mathematics are outdated. People solved problems using these methods not because they are good methods, but because it is the only thing you had access to in the 1600’s. You don’t build houses using stone hammers but somehow we still use 400 year old math with a pen and a paper.
It wasn’t a mathematician scribbling on a chalkboard who solved the protein folding problem - it was a team of software engineers working on an artificial intelligence. Traditional mathematics are as equipped to solve modern problems as a stone hammer is equipped to build a skyscraper.
Do you want to know a common problem in an area of math that plagues everything from fluid dynamics to Einstein’s theory of relativity? It’s that vector fields don’t conserve energy. You can create fluid simulations with infinite velocity and space-time curves with infinite curvature. Yet, these are repulsive absurdities that don’t exist in reality but rather are a quirk of old mathematical tool sets.
One of the greatest revolutions in mathematics will come about as a solution to this very problem - mark my words.
I have never read weirder BS in my entire life. I mean, I never meet a math denier in my life lmao.
This is the guy who is trying to prove Protoss is op by the way.
Literaly a math PHD and he was in college at the time. Still rare individual.
It literaly was mathematicians, Machine Learning is literaly applied math, you can even say it’s applied statistics for the most part. ML is literaly a math field of research.
That proves how unfamiliared with calculus you are, there absolutely are conservative vector fields, specialy in fluid dynamics, I doubt you even know wtf a field even is.
I said that it was outdated, that better toolsets exist, yet they cling to outdated methods. If you have to lie about what I said, then you’ve admitted my argument is too strong to address honestly.
Exactly my point. There are much better tool sets than traditional math, such as machine learning. Yet you called me a “math denier” for pointing that out. Now you’re accidentally agreeing with me. Lmao.
They are winning 6x more tournaments than Zerg, but go ahead and keep using terms such as “trying” to try to prove your point (hint: it won’t work).
Exactly. He was punching well above his weight. He hadn’t graduated and yet he solved problems NONE of the entire industry’s experts were able to solve, despite their degrees, tenure, and work experience. How can such a VAST pool of intellect be outdone by one man, unless that vast pool of intellect is nothing except a hive-mind of politically correct right-thinkers? It’s basically a slightly more intelligent version of CNN.
Oh really? You can plug a continuous function into a discrete vector field and you can guarantee that it conserves energy? You have no clue what you are talking about. The moment you discretize a quantity it no longer conserves energy, PERIOD. You ALWAYS lose or gain energy in the rounding, PERIOD.
Whether or not that gain/loss of energy is impactful is another matter. When calculating how far a ball will go when thrown, it probably doesn’t matter. However, in any kind of math that involves iterations, e.g. the output is fed back into the input of the algorithm repeatedly, the errors compound so the rounding issue of discretization is a HUGE unsolved problem. Even if you increase the accuracy of weather simulations by 1,000,000x you only increase their duration of stability by a factor of 3.
Mathematicians can’t find the last digit of pie but let’s pretend the rounding problem exists only in computer science. Nice “logic”.
Thanks for the confirmation that everything I was saying is true. I debate with actual math graduates all the time and they can easily retort with formidable arguments. You didn’t even know that discretization causes rounding which by definition violates conservation of energy.
Now that we’ve established that I was right on that point, let’s argue the point that discretization errors only exist in computer science. Please explain to me how you intend to have no rounding errors in any computation involving PI. Thanks. I am sure this will be TRULY an enlightening conversation. /s
???
A transcendent number (pie is one of them) can’t be expressed with a finite number of digits. What you are asking is precisely the “Squaring the Circle”.
For every practical application enough digits can be used: for 99.999% of the applications 5-15 digits are enough.
You like to rail about “mathematic is stuck in 16 Century” (which by the way is a big BS), and then make such affirmations?