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2026-08-22 08:55
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Mathematicians Dubbed His Work "Evil". It Broke Mathematics
- Turing 17일 전 2026.08.21 22:03 인기
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Weier you mispronouncing his name?
2026-08-25 03:15
DONATED you yuppie twit
2026-08-25 02:59
Now layer quantum concepts within the fractal.
2026-08-25 02:55
The W is pronounced a V. You bet he's evil he was responsible for real analysis 101.
2026-08-25 02:34
How long will it be before youtube is all commercials?
2026-08-25 01:37
It's not 'wire'-strass, it's 'vire'-strass.
2026-08-25 01:32
“Isolated blemishes” ?????
P.S. Poincaré was a creative retard who adamantly criticized every new and revolutionary idea in mathematics.
2026-08-25 01:04
It's not really a real world function though. It's not even continuously anti analytic, where it always integrates maybe. Given that the past is just as there as the future ... sure, it might do an abstract domain transform and develop to a real solution for something. It's Heisenburg inconsistant.
2026-08-25 00:20
Another fantasy created by infinitists. Functions consist of finite points only folks. We can’t have a completed set of points, that is also incomplete and forever ongoing.
We can always get slope between two successive points since there is always some finite smallest interval between them.
2026-08-24 20:58
The video and the content are ok or even better, but the claim that calculus led to or helped the Industrial Revolution is not correct. The Industrial Revolution is contemporary or parallel with the Scientific Revolution, including Newtonian mathematics chronologically, but it happened as a result of the efforts of pre-modern, trial-and-error engineers and craftsmen without any training or awareness about the revolution happening in math and physics during the invention of steam engines and factory manufacturing.
2026-08-24 16:18
Every time you think you have it all, you are wrong.
Weierstrass didn't break mathematics, he straightened a lot of it out.
Though personally I'm not certain, I like Cauchy sequences and I like their openness, epsilon/delta still tries to close infinite series by induction. IOW we are still really not done perfecting calculus.
2026-08-24 11:39
Hermite the Termite
2026-08-24 11:37
But we don't like Leibnitz, so his name will not be capitalized, eh?
2026-08-24 08:01
Fractal.
2026-08-24 07:10
No curves like in a monastery.
2026-08-24 07:06
Pointyness-Maxxing.
2026-08-24 07:05
And yet, Weierstrass couldn't handle the equally weird results Cantor was coming up with.
2026-08-24 06:52
No "evil function" has "broken mathematics".
Some functions are not differentiable. That's OK. That corresponds to Nature.
2026-08-24 06:45
Nice video ??
2026-08-24 05:46
important concepts, brilliantly explained. The idea of fractals a century before Mandelbrot is not well known.
2026-08-24 05:24
Composite Functions is part of the precalculus curriculum virtually all of us were taught one way or another. I think that the purpose of composite functions is to apply empirical scientific data to mathematical models framed by experimental hypotheses and theories. Over time through trial and error sensory patterns should reveal themselves. I think approximating these interdependent behavioural patterns into algebraic functions should smooth out isolated special points.
2026-08-24 05:21
National character is a social construct, but holy cow this is one of the most hilariously stereotypical yet engrossing (and also least lethal) tales of How Brainy French People Argue with Brainy Germans I've ever seen. And, I mean, just within math and science, there are dozens of them.
2026-08-24 03:34
The function could also be considered fractal-like as any small part of it resembles the whole; much like the plot of the stock market.
2026-08-24 02:56
2:29 Your formatting looks MUCH more like y= 3*sqrt(x). This highlights a huge problem in computer-based mathematics. It’s time for someone and something to move beyond TeX, ASCII and Unicode!!!
2026-08-24 02:36
I'm reminded of the first day of my 1970 freshman calculus class, which I thought would be a "gut" class because I had already studied calculus in an AP high school class.
The professor used a different function, which I'm trying to recall from memory more than 50 years later. It was something along the lines of "Let f(x) be 1 for all rational values of X and -1 for all irrational values of X". The professor asked the class for the value of the integral of f(x) from 0 to 1.
As I recall, this function is continuous and NOT "well-behaved". If I recall correctly, there is an irrational number "between" every rational number, no matter how small the epsilon between one rational X and the next.
Like so many of my college texts, I leave the derivation of the answer to the reader. :)
This single question opened my 18 year old mind to the marvels of mathematics for the rest of my life.
2026-08-24 01:37
Weird how long it takes people to realise: Common sense is always wrong. It's just that for a narrow band of applications, it's usually right enough for current practical needs, and we don't realise how narrow that band it.
2026-08-23 23:29
this video as internet as casa is a continous dick or cock analysing a baby//// you really fuck it slow and nice al9ahba::: tu ne recules devant que dalle salope de pute nawal l9ahba et tute chose qui te suit salope//// tabbounak fih lakhra otramtek fiha lahwa nti et les femmes qui te suivent; devine pour naima!!!!! Internet est un ami à hammouda et ils se rencontrent:::: amazing crasse////
2026-08-22 18:36
3/ what is the relation between 'calculus' and bipeds?????calculus has no emotions and bipdes to have emotion: who serves who then???? bulllllshiiiit your story; everyone's stuck on their ways.......///// things have always happened first from a 'present free and god" and you have always drawn a line from past to futur with a clock inside talking numbers you call hours//// you are the ancient 'devils' and believe it or not: after you falling from heavens you managed to fall from your ancient "devils forms" by incompetence to be that also//// -1/20 is your final test result//// try to find emotionless creation to rule if you feel ' godlike ' today or an emotionless 'godlike' slut torule you if you go by bipeds yesterday//// tomorrow is closed the big one and tomorrow is the 23rd of August 2026 the same tomorrow until XXX your rendez-vous//// putin says miaaaaaw
2026-08-22 18:31
2/ when you know that by zooming on any line you'll see how discontinued you are calculus why did you introduce 'continuity' for science? there is symbollically 1 real-atom for 1024 atoms molecule or structure meaning less than 0,1% matter in the void//// the rest is what you wanted to see as you pretended to grow in size until things hide the empty spaces in betweens and become apparently solid continous and pragmatic//// and so happened in all levels of 'conception': material moral cultural spiritual; matter ideas thinking faiths; all illusions from empty terms pronounced by a first speaking throat and as illusions they do not exist in reality even if projected when the budget allows it and still have a real influence on any innocence who does not know what the lie is//// empty yous and the offer for the atom among 1024 has expiredin the position 1984//// you are your last very brillant sexy ugly emanation of yours after explosion//// tell'em why you put them in a scenario where the source of life -the sun- is also its ending process; all the Universe is IN Earth under the sun wherever you go//// the horizons are the furthest you can go in a picture when pushing the fake 3D far behind: under arrest guessss by who/////
2026-08-22 18:20
1/ you were meant to sit down and find your creator as humans or homo; you opted to become stupidly knowers or homo-sapiens; then you went more in suicide by pretending to double knowers or homo-sapiens-sapiens///// calculus? there has never been any brain except that who was pulled out from a sheep's crane on a day casawa ( people of casablanca-morocco ) assassinated a friend as a ritual sacrifice for something they call 'lah' then ask them who they talk about//// first: as homo you started feeling more powerful until sex and food were not that delicious then you started willing to get to the 'core' of things ( fatiha bent reddad was there loving herself before everyone promising a hidden wisdon that was ' hidden' from you!!!! and no one said for exemple " hey sluts do you want paradise or do you wat the throne itself!!!! " but you all went on higher hopes//// second: by homo-sapiens you failed; a species who was eating fruits from trees and starts standing on its feet it could have been homo-ready to know or homo-willing to know: NO; you made it atthe start homo-who-knows!!!! from there you were above your creator forever since you defined also what is high low smart stupid good evil legal necessary and your 'culture' of bites///// third: with homo-knower-knower all logics abandonned your 'world' to let you with machines smarter than you still your slaves//// the end of your show////
2026-08-22 18:05
Great video! But the applicability of fractals to real life has its limits, literally;-)
2026-08-22 09:57
In my opinion, the most significant result of Karl Weierstrass is his Theorem of the Dominating Majorant for series of functions.
2026-08-22 05:58
Is this related to the Bolzano-Weierstrass theorem?
2026-08-22 05:37
Wow. What a technical beauty.
2026-08-22 05:36
RE: “y = 3 x Cube Root of X”; Not differential at the origin as a vertical line (“y axis”). Further, The Derivative cannot be estimated at the origin, and is therefore termed “undefined”. The slope reappears as the function heads immediately north from the origin. ? 2:56
2026-08-22 03:24
Why does "Leibniz" start with a lowercase letter?
2026-08-22 01:06
Great video, I learned about calculus & Physics of Astronomy
2026-08-22 00:57
What I found even weirder in calculus was how you could make a function that was continuous at only one point and nowhere else
2026-08-22 00:57
Great video, I learned about calculus & Physics of Astronomy ❤
2026-08-22 00:56
Great video, I learned about calculus & Physics of Astronomy ❤
2026-08-22 00:55
Great video, I learned about calculus & Physics of Astronomy ❤
2026-08-22 00:55
I think college profs should start Real Analysis, formal defn of limits, continuity & differentiability after telling this story. It would lay the motivation behind constructing these definition.
But college maths seems so dull, boring, less motivated. Without proper history to the subject, how it evolved..
Where does those definitions came from?
Like why the definitions of Groups, Vector Spaces, Cosets - Factor grp - Normal subgrp are defined this way?
This video somewhat helped. But someone more expert in the subject pls help me with my questions.
And tell where to learn more of such historical stories and mathematical developments over the years.
I am too curious to know.
2026-08-22 00:27
The real first different pathological function created by Weierstrass!
2026-08-22 00:01
The real first was the genius Pierre de Fermat!!!
2026-08-21 23:58
nice video
2026-08-21 23:46
I am a nowhere differentiable continuous man. I see the Weierstrass shitty function, I press like.
2026-08-21 23:19
?????
2026-08-25 16:40
It's interesting that in explaining fractals we are forced to draw pictures like is done in the video. But the piont is they can not really be drawn , only an approximation shown. Fortunately we can imagine them. I think Turing is far too hard on the the Great Mathematicians of old. I am sure they understood that things are only 'true' within their domain of applicability. They must for example have had some idea that water was not actually a continuum , but none the less did pretty well with fluid mechanics. As for me certainly I think I understand that mathematically self similarity exists . But do I think that an infinitely dagger line exists. To be honest I can only imagine it but would be clueless as to how such a thing could be drawn.
2026-08-25 15:09
Charles Hermite is pronounced like “sharl ermeet”; not Charles Hermite like termite.
2026-08-25 14:18
Rubbish the universe is infinitely jagged, every recursive description outside of pure mathematics brakes down at some level.
2026-08-25 12:27
Good presentation
2026-08-25 12:08
Background music ruins informative videos.?
2026-08-25 10:56
LOVE this
2026-08-25 09:45
My father taught me cartesian coordinates, sines and cosines when I was 10. I taught myself calculus the next year. I worked out the formula for the volume of an n-sphere (in any dimension) in the 10th grade. I breezed through an undergraduate degree in Pure Mathematics with a 3.97 GPA by the age of 17. So, this material is not new to me. I am watching it to the end, to appreciate your pedagogy.
2026-08-25 08:34
Brownian motion paths are similar as well, nowhere differentiable and fractals?
2026-08-25 08:05
It seems kind of like cheating when an infinite number of iterations is needed to make the function undifferentiable - they're defining a function that can never be evaluated because computation will take infinite time and being surprised it has other properties that can't be defined either.
2026-08-26 02:17
I suspect that the existence of such functions is somehow related to noncomputability of the halting problem in computer science. I have no idea what the relationship is; but my intuition tells me there is likely some relationship.
2026-08-26 00:45
Fascinating
2026-08-26 00:39
Mathematics defies our intuition by introducing the concept of a “dimensionless point.” Draw your own conclusions. Gödel is here to help.
2026-08-25 21:18
This video is a demonstration of how ephemeral both math and science real are. Their reality is dependent on the focus and criteria given to the goal by the subject. Both the finite and the infinite are fairly useless except as a temporary concept. In the human world, criteria will set the reality and make it useful for the job at hand. And that focus is typically somewhere between the static and the dynamic. A microscope is no less useful then a telescope but it all depends on your goal and whether or not the criteria has been properly set for the goal. This confuses a lot of people as to what is reality. Reality is a giant tool box, use it as needed, but first learn its principles for a successful endeavor.
2026-08-25 21:07
В функции Вейерштрасса нет ровным счетом ничего загадочного или необычного. Она всего лишь выявляет фундаментальный изъян современной математики, которая не умеет работать с трансфинитными множествами.
2026-08-25 20:02
I saw a thumbnail with the title and clicked in over here just to denounce the title. "It Broke Mathematics". I clicked to denounce the sensationalism. It's yet another example of "All the great profound work in mathematics and science will destroy the way your mind works now. It's all so weird. It's all so strange. It defies what you thought you knew. Watch this video to learn the mysteries, which will make you one of the cool kids who is superior to accepting everyday experience. You will be awed". Everyone today wants to destroy the idea that science uncovers explanations that are quite rational (and therefore, dull, and often tedious) and REMOVES mystery, rather than creating it.
2026-08-25 07:05
In 1872 Poincare was just 18 years old. I never ever heard that he was disgusted by the Weierstrass function, where did you take that? Also the name Hermite is not pronounced as "Hermait" but as "Ermit"
2026-08-26 16:27
People don't realise if you take the inverse of differentials - then you get different multiples of infinity.
2026-08-26 13:58
Fantastic. Lovely.
2026-08-26 11:20
I used to just glaze over the epsilon-delta definition, but then (much later) I became more interested in it. I have figured out that what the definition says is that for there to be a differentiable function, at some point of finite amount of zooming in, there are no humps except for the case of a critical point, where there is a single hump. Weierstrass's monster is simply a function in which no finite amount of zooming in that dispenses with the humps.
2026-08-26 08:09
It wasn't until Kurt Goedel proved that all logic systems are fundamentally incomplete that we actually have a way to reason about this difference between the French and German views of mathematics.
2026-08-26 06:12
2500 years before Indian mathematicians invented all these
2026-08-27 00:02
Things just don’t add up for me, but I’ll figure it out.
2026-08-26 23:16
І це той самий Пуанкаре, котрий згодом прийшов до ідеї розривності всього на світі!!!
2026-08-26 19:47
invented by Leibnizt, and newton has stolen his work
2026-08-27 16:53
Le nom de Weierstrass doit se prononcer à l'allemande, le W se prononce comme un V en français.
2026-08-27 15:45
Common sense is a tool of compliance. No wonder they hated this function.
2026-08-27 15:20
Today we have Norman Wildberger's critique of the foundation of math (in particular calculus), by presenting a rational foundation: Rational Trigonometry, which makes rational numbers the foundation of math, instead of the real numbers that include the irrational numbers.
2026-08-27 14:05
the Koch curve actually is the Bolzano curve
2026-08-27 13:52
I was very pleased to watch a video where all those complex concepts of math flow continuously to a continuous ending...yet, by no means, a differentiable one. I really enjoyed the trip from smooth curves to fractals. You really can convey the beauty of math in simple terms.
2026-08-27 08:29
When I was a math major, my professors provided proper motivation for all those topics you mentioned.
2026-08-27 23:13
Because the capacity of multiplication is finite, the continuity of the number line cannot be definitively guaranteed.
https://www.youtube.com/watch?v=dksj4ikvgJM&t=3s
2026-08-28 12:47