The History of Mathematics and Its Applications
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- Опубліковано 12 лип 2024
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Numbers/Counting (00:00)
Logic (00:50)
Euclids Elements/Euclidean Algorithm (2:16)
Cryptography (3:05)
Calculating the Radius of Earth (4:54)
Calculus (5:06)
Graph Theory (6:20)
Topology (7:51)
Fourier Analysis (9:17)
Group Theory (10:15)
Boolean Algebra (12:21)
Set Theory (12:45)
Markov Chains (15:40)
Game Theory (17:05)
Chaos Theory (18:17)
Geodesics (19:51)
Fermat's Last Theorem (20:08)
Millenium Prize Problems (20:40)
You can maybe go back to doing that homework you're procastinating (21:17)
Not everything in the video is exactly in chronological order but most of them are. I know I didn't include everything of course but there was constant back and forth of should I go over more topics in less detail, or less topics in more detail...I hoped this would be a happy medium.
lol I clicked the last timestamp and felt guilty
That last timestamp is so relatable
bruh that last time stamp.... how did you know lmao
Where is zero ?
....the truth is that math is math ...shit is shit ....
What a fantastic video ?
Math without zero....🤣🤣🤣
long division 3➗111= ＼(^^)／
Does anybody else love Math but are currently terrible at the subject?
I love math, and i am making a fast and solid progress to improve it.
Tomorrow is my mathematics paper, and i am confident.
@@wuhski good luck
All it takes is practice, friend. I already notice an incredible improvement in myself after studying 3+ hours a day. I don't really have to worry about passing anymore. Instead I can worry on getting a 100. I used to keep myself down by telling myself I wasn't a math person, but if you tell yourself you can't do something, you most certainly won't. It's all about self-motivation.
@@SuperSaltyFries I agree.It's also much easier to become a good math person if you enjoy it
I have a bachelor's in math , I'm working on my master's and I have good news for you. Most people who end up doing math feel like they aren't particularly good at it, but they work at it a lot because they like it. Work hard and you can succeed in it too!
Do you guys want one for physics and one for engineering as well?
Yes
MajorPrep Yes please!! I love physics!!
Yes.
Physics first.
YES
So, in 3rd Century BC, Mathematicians calculated to 99% accuracy the radius of the Earth, without any special tools, or equipment.
And today, we have Flat Earthers.
That is because they all are born with the "stupid gene" firmly imbedded in their chromosomes!
Nah, deep inside they know the truth. They just wanna feel special. Just like us, leaving useless comments about some stupid, misled idiots.
The Internet gave an unfiltered voice to everyone and anyone, including stupidly retarded inbred Neanderthals idiotic morons with the I.Q of a refrigerator light bulb.
And then they spreaded their corrupted erroneous views, conjecture, speculation and mere opinions as if irrevocably factual, and a bunch of other low life forms agreed with them, to form that new subset of humanity: Truther, anti vaxer, climate change denier, NWO conspirationnists, reptilian, planet nibiru, creationists, chem trail and flathearter, just to name a few.
@Sunny Shah: I mean the movie "Idiocracy" is becoming reality (Idiocracy is a 2006 satirical film that depicts a future in which humanity has become dumb. The title of the film, a coinage meaning "government by idiots"). What gets me is that the earth being a sphere has been proven time and again beginning most notably with Eratosthenes about 2200 years ago (his rigorous proof depicted in this excellent video). Yet, the Flatearthers will "flat" out tell you that we Globers are wrong. However, their arguments have been disproved and refuted time and again. All of their arguments are based on pseudo-science and voodoo-math. Granted, I have never seen the Earth from space, but every argument I have heard that I live on an oblate spheroid makes sense to me and not just on a "knowing" level, but a deep intuitive understanding level ... and yet the Flatearthers want me to accept their view of the cosmos without rigorous proof ... oy vey ...!!!
@@UTUBESUCK666 How dare you insult Neanderthals by comparing them to flat earthers!
I’ve been in school for about two decades now and this is the most inspiring thing I’ve seen to learn math. When you think about it, it’s kinda weird how we start teaching kids math before telling them what it’s power is. Aside from counting 42 bananas
@@mikem4481 I would assume that it is referring to the use.
I don't think children that can't count past 10 will understand the uses of game theory
Bro.....you must understand how incredibly niave your comment is...
That is why Elon Musk home schools his kids.
@@portagepete1 because school education is suck?
Switched majors from Electrical Engineering to Physics & Mathematics. And as a friend of mine stated, Math might be intimidating but, I definitely understand why Math is beautiful. Even though I don't understand all of it, you see all these zigzags that may seem random, but you know that they hold a meaning for educated people. It's like a unique language, one that is both human and not entirely so.
Why did you switch? Engineering seems to be better.
@@destinyovbiebo8988 no
Actually the reason we have ten fingers is there are ten integers
I did not get it! Can you please explain this more from an Evolutionary point of view?
@@aysoodaagh3167
It was a joke
@@JJean64 oh! I see.
Underrated
Can you believe my boss said "I've never used Algebra in my life"
As a maths grad I love the subject, especially the counter-intuitive stuff where understanding the answer is more important than knowing it.
The biggest problem with Mathematics is that people try to know it rather than understand it.
Nice post... !!! I am not a mathematician, but I do play one on TV ... ;) ... seriously, I will revisit the steps I went through to solve a problem, even if I get it right ... I want to have a deeper understanding of not just the problem or the solution but as to how they fit in the greater scheme of things and if these lead to other problems and solutions. I also think we can never truly know the full impact of the problem or the solution ... I doubt Archimedes realized the full impact of his calculating an accurate estimation of pi and all the math, science and technology that would come from that over the course of 2200+ years ... Archimedes just wanted to understand .... As to your Boss' statement, from what I understand, Algebra is based on solving problems with relationships between things. Whether we do this formally or informally, we solve problems with relationships between things every day. I think all human beings use Algebra every day over their entire life. We just don't stop to think about it or consider it Algebra. Or is this too loose an interpretation of what Algebra is? Someone please help me with this, I am not a mathematician so this is just an observation ...
@@dvd11811 You hit the nail on the head. We use Algebra in everyday life even if we don't write x + y = z we are still intuitively using the concept of algebra.
My bosses comments infuriated me enough to start a educational programme teaching people within the company about algebra as well as other branches of mathematics.
My first module takes a look at what mathematics (and our understanding of the universe ) is without algebra.
The course looks at number theory, mathematical operations, big numbers, infinity and humans inability to comprehend numbers of this magnitude.
If my company enjoy and learn from the course I may make my own UA-cam series.
Thanks for the kind words
@@davidtalbot2061 Thank you for the confirmation. Please let me know if and when you start your UA-cam channel as I would like to subscribe ...
While being interviewed by Bill Moyers for the "Power of Myth" series, Joseph Campbell (one of my favorite authors) said, "Everything we say and do has both good and bad consequences. Our job is to lean toward the good and do what is right.".
David, from what you have written in your post to me, it sounds like you are leaning toward the good and doing what is right. God Bless! ... I also like to reiterate what you said about understanding being more important than knowing and apply it to humans, as Carl Jung once wrote, “Everything that irritates us about others can lead us to an understanding of ourselves.”
BTW, Speaking of BIG numbers, I once used the word googolplexian in a sentence ...
OMT, my name is David as well ... !!!
Your boss is an idiot. Confusing algebra with the notation we use to describe it is an unfortunately common mistake.
@@davidtalbot2061 are you giving talks in the break room??
It's strange, all of my school years I did nothing but try and escape math. I hated it, and I was never good at it because I simply didn't apply myself. Now that I'm 22 and have spent time learning more about it, I find myself so inclined to learn more, and I feel it will help my perception of the world so much. I'm starting college for computer science this summer, and I couldn't be more excited! I never in my life thought I'd pursue something that is math heavy.
Same here
😮❤tfdghhv
This is me with literally all my subjects, math, science, and history. I’m 16, and only recently have I been interested in learning and being fascinated in the world, it’s definitely motivating to see others who are now wanting to learn more about things their weak at rather than not doing anything about it
As a high schooler, about half the stuff went over my head
You are making a good start!
You'll literally, figuratively, and metaphorically reach it if you get to a higher level
I did not understand a single word my guy😂😂
Full of the stuff went over my head 😂😂
@@mickelhayward4617 😂 I was at the same boat during a time
"Now one of the oldest foundations of mathematics WHICH IS LOST ON MANY PEOPLE TODAY IS LOGIC" 0:50...sadly true😣
To research and ask, what counting is this?
Scrolled too far for this
Logic isn't everything dude it may not apply beyond 3 Dimensional World but till some extend you are right
POWER defies logic................for a while ask trump
Did not expect this. As a math major, this is a pleasant surprise.
Step 1: Be really good at math.
Step 2: Solve all the Millenium Questions.
Step 3: Profit???
That's 6 million in your pocket
Gotta get learning then haha Or rather
MrLappis + A lot of learning = 6 million
(More realistically)
MrLappis + a lot of learning = Satisfaction of trying, but no 6 million.
Both would be pretty great, to be honest.
Cards Against Humanity?
If you solve any millenium problem you could most likely have any job in the relevant academic world
I would predict that to solve any of the remaining problems you would have to create a new branch of mathematics
So nice to hear Maths getting some well deserved love and with clear explanation! Well done!
A truly whirlwind flight through mathematics - thanks!! A few additional remarks I hope might interest some viewers:
• Numbers/Counting - that a rational number is a ratio of two integers (the 2nd of which ≠ 0) is their actual *definition.* That they all have terminating or repeating decimal (or any other fixed-base!) representations, is a *consequence* of that definition, not the definition.
• What an algorithm actually is, is a well-defined, finite sequence of steps that is guaranteed to produce a solution to a given problem.
• The Euclidean Algorithm is closely related to a method of "best" rational approximations, known as "continued fractions."
• The measurement of Earth's radius about 2200 years ago, was done by Eratosthenes (ancient Greece). His final error was about 10%, quite good for the time.
• Calculus was co-invented by Gottfried Wilhelm von Leibnitz (Germany) and Isaac Newton (England), using different notations, both of which are useful in different contexts. Many of the ideas behind it go back centuries, including to Archimedes, but it was only formalized starting in the 17th century AD.
• Group theory was invented by Évariste Galois (France). As the story goes, he scribbled his findings down feverishly the night before a duel, in case he would be killed. He was. At 20.
• Game Theory was not the only thing John von Neumann gave us - in the 1940's he developed one of the earliest electronic, stored-program, digital computers (nicknamed the "Johniac" [sp?]), which was at the IAS in Princeton. He also did some important work in quantum physics.
• Chaos Theory - you can thank Ed Lorenz for explaining why the weather forecast will never be perfectly reliable, and why it will always be worthless beyond some finite time horizon, no matter how advanced computation and physical models of the atmosphere, and the density, frequency, and precision of observations, become.
• Geodesics and non-Euclidean geometry in general, were invented by Lobachevsky, Bolyai, and Riemann (the latter, on prompting by Gauss).
• Around the turn of the 20th century, -British- German mathematician David Hilbert gave a talk in which he outlined the then-most prominent unsolved problems in mathematics. I believe that among them were the Poincaré Conjecture, Fermat's Last Theorem, and the classification of all finite groups, and of all 4-dimensional manifolds (which, among other things, constrains the possible solutions of Einstein's Equations of General Relativity).
Thanks again!
Fred
With each of the Concepts going a Level-Up is the beauty of this Video-Explanation. Thanks for such a Beautiful and unique effort.
As someone who is horrible at math, but finds it really interesting- it always amazes me how people back then even figured it all out, and to some degree, created it with nothing but their brains and eyes
If you have all day and no 9-5 job with overtime, then yeah, you're bound to figure something out. These people were also part of the wealthy elite, so they didn't have to worry about basic needs, plus had some schooling.
@@Shvetsario still, it takes amazing concentration to get to these conclusions, regardless of privillage. Also, they didn't have youtube and other dopamine hackers to distract them. We have the access to the information but minimal focus :(
This video is so great. This is something that I have been looking for. I tried so hard to understand the areas of mathematics I could go and things I can do but could grasp during my 4 years of undergraduate but this video just sums up everything. Loved it !!!! Thank you so much
your present in youtube is a grace
amazing content man ! I have been waiting for so long for a good educational mathematics channel !
yes! yes! more math related videos!
really interesting! the graphics made everything really easy to understand :) also congrats on 100k!!!
Thank you!
@@zachstar Just a sidenote: I think that arithmetic would be easier if we had SIX digits.
Me being a math major and a really huge math fanatic, I really want to take a class in each of these topics even though most of them would probably kill my gpa.
Me being a high schooler who wants to be a math major and also a huge math fanatic, I really want to take a class in each of this topics xD
@@alexiafejer1344 you can watch a lecture series in the meantime
Nobody gives a hoot about gpa.
@@Michael-vf2mw I mean grad school does lol. If it wasn’t for a decent gpa, I wouldn’t be in grad school nor a TA
@@edswalkthroughs Fair point. It says a lot about the brokenness of higher ed that they still rely so heavily on a metric as unrepresentative as gpa. I'm very happy with my decision not to pursue any advanced degree.
Great overview. Maybe the incompleteness of mathematics and the work of Gödel and Turing deserved to be mentioned.
Okay, it's decided, I like this and am subbing.
4:00 I was expecting a VPN sponsor
I just found you, I know only basic math, but your videos are interesting, informative and understandable and It makes me want to understand math just a little bit better in my middle age.
do you now understand math?
I'm mathematician I teach calculus, linear algebra, differential equations but sometimes I feel so sad because only few students desire to learn, although I love maths many students are lazy and dont want to work
Im currently not the greatest at math, but i found love in the subject. I think the problem is, to many teachers do a disservice to teaching mathematics.
I love math. I’m going to school to teach it. Everyone thinks I’m crazy, but we all have our things. I may not always get it, I took calc twice, but I just passed with a B+, so it just takes a little blood, sweat, and tears
hi, althoough my major is in environmental sciences (yeah i hated math in school) but i want to learn math on my own. Where should i start. I know basic math and concepts but need to refresh them as well. I am always fascinated by the universe of mathematics but never took interest in learning because my school did a bad job of presenting math as a fun or interesting subject
It’s the way it’s being taught in schools and colleges that is the problem.
@@Capitan_Chaos there are many factors to take into consideration, not only the way of teaching, cultural factors are critical for instance
You've got a new like here! This video has so much information!
Simply fabulous video!
So interesting
You have a gift for this. Great presentation.
Please make a part 2 of this. It was a very informative video 💜
This was so good do a history of physics next!
Edit: and it's applications
yup
Damn I at first felt that I was a fucking nerd for being familiar with the work of every person name dropped in this video but then I remembered I am a third year math major.
If they teach you these, then I wish i was a bloody third year math major too!
I could watch these all day! Love it
Great video Zach!
Thanks
Taking a digital logic course now. I absolutely love boolean algebra. Especially once I realized the use of it. As an electrical eng. student its so exciting to make a truth table of a simplified expression, then make a double NAND or NOR gate realization and have the same output. So frickin cool.
SuperSaltyFries I had the exact same feeling when I connected the components on a breadboard for the first time 😂😂😂😂
My dude make a truth table of his statement at 1:16. A little surprise for ya.
Loved this video man! Please do more! I would love it if you could do a history of specific mathematical subjects like “The History of Calculus,” or Algebra, Geometry, Topology, etc... and physics and engineering subjects like fluid mechanics, engineering mechanics, quantum field theory, and so on. Just an idea, I think you have a wealth of potential and material for this “A History of...” type of video.
Love that idea! Yeah I’ll see where I want to go with that but you’re right, lots of potential ideas.
Zachy, You Rock !
Dude, I didn't realize just how important math is! Just thanks, it gives me so much motivation for studying it :)
Holy crap we literally just learned Euclid's algorithm in my maths class and at the same day this? Are you a prophet
😱
not the video i thought i needed but the video i needed all along
I find it amazing how much of calculus comes from algebra and geometry and then influences every subsequent field.
Also, i appreciate the your time and effort which you invested in this video.
God I've been looking for this, your videos are amazing
The symbols for 10 and 11 in base 12 (duodecimal system) are: upside down "2" and "3" respectively.
Thank you so much for making this video! Math is awesome
This is a very interesting video! Thank you!
I completely lost track of time watching this, well done
Wonderful video
Excellent video
Great job!
8:42 Got me laughing hard. Nicely done.
May you make a video about the “aptitude tests” engineers take before getting accepted in college? I googled some and there are a lot of tests, but it would be nice to hear from your experience during the application process involving tests.
(I know it depends on the college, but if someone knows about practice test or what to expect it would be nice to hear some advice).
This is Gold, Subscribed!!!!
Wow! At last! Something worth watching on UA-cam.
YOO MAKE THIS A SERIES I want more detail
I am an amateur programmer and you were definitely right on the algebra in computer science. In machine learning, all you need to know is math pretty much such as linear algebra, calculus, and some other stuff. Good video.
the discovery of pi was a glorious day for bakers everywhere
Lol
Mind expanding. Thanks for sharing.
Oh. My. God. I came across this channel as I was looking for some info on the meaning of eigenvectors/eigenvalues for a statistics class, and I spent half of my Monday watching other videos of this guy. And I am not even that interested in math. I simply could not stop... What a brilliant way of talking about complex things in such understandable language. Thank you!
Really glad you enjoyed and thanks for the comment!
How am I just getting to like math? I've wasted so much of my grade school years not realizing how beautiful it is
Thanks for making great videos!
thank you so much for this video
Omg this video almost made me wanna be a mathematician! Well done. This channel deserves millions of subscribers.
right now I feel a lot less smart than a proportion of the world and a bit more in relation to another. I'm a computer programmer so I work with logic, I wasn't good at math growing up, but logic and philosophy & working with this has made me able to see and understand maths much better. Holy shit were those guys good at abstracting
Fantastic.. Excellent.. 🙏🙏🙏
This makes me so warm and fuzzy on the inside.
4:22 There's no date given for when pi was pinpointed exactly. (I was not aware that that had been done.)
I love this.. can you recommend me books so that I could get wider knowledge of this subject rather the ways and formulas to solve the problems?
Yess pleaasee i NEED this!
awesome video, it covers every topic of mathematics.
This was unexpected.
Loved the video!
Thanks!
For the first, it'll be useful to name the exact terminology, like contrapositives, inverse, converse etc.
feeling proud of studying maths ^^^
I did my msc math in one nine seven zero having syllabus of abstract algebra linear algebra measure theory vector and quotient spaces differential geometry geodesic curves spherical coordinates and astronomy plus plus .I salute today to this presentation and u tube
Nice job,good summary🍻
OMG this was unexpected!
Hope you enjoyed!
Why didn't you talk about khawarizmi
Thanks for sharing this with the world man.
Best video I've seen in 2021, thus far.
I LOVE MATH!
Same!
It does not really wotk that way every time , for instance:
If a function is properly increasing it is a one to one function.
If a function is not properly increasing it could be a one to one function.
I know this is an old comment, but no, given the first statement, the contrapositive is actually "If a function is not one to one, it is not properly increasing". A implies B means not B implies not A, it doesn't (necessarily) mean not A implies not B.
Some opportunity was lost not mentioning the sumerian counting system was sexagesimal (base 60). The reason we have 60 min/sec and 12 hours.
en.wikipedia.org/wiki/Sexagesimal
Amazing video!
Major prep, I have been teaching myself anti-derivation. My question is, is the integral and the anti-derivative the same???
Yes, when someone says the antiderivative of a function is... and another says the integral of a function is..., they are saying the same thing.
Usually the one saying anti derivative is the math student and the one saying integral is the physics one
Sometimes logic is beautiful than mathematics...🔥
Very cool video ... thank you!
Great video, like it.
Great video, but where's the probability and statistics? Stochastic processes, linear algebra? Regardless I enjoyed your video a lot.
Thank you! There was a lot I wanted to throw into the video that I just had to take out unfortunately. But I kept in markov chains so there was something related to stochastic processes at least.
6:38 I was trying for a while, assuming you were showing how to do it, then it turns out to be impossible haha.
Same.. but I was doing it for fun because I am dumb and would not really understand it
Wow! Thanks for the brief history of math in 20 min❤
If you have any interest in talking a little more about set theory, you could go into Cantor’s theorem and the power of continuum. I absolutely loved this video. One of the best math overviews I’ve ever seen.
Hey Zach, i'd recommend you look up Quantum Linguistics. It is part of the structure of language taught at Master Practitioners level in NLP.
Why start with the Greeks? The Babylonians found the square root of 2 to 15 decimal places and were using the Pythagoras theorem 1,000 years before Pythagoras was born.
Awesome video!
Road to 100k subscribers, congratulation !
Thanks!
I've read and enjoyed Euclid's book on geometry. My math isn't really advanced, being somewhere in the realm of precalculus. Do you recommend any canonical works that might be reasonably understandable? I don't mean a textbook. Rather, a canonical piece of mathematical literature, like Euclid's Elements.
Khwarezmi's algebra
I have the most wonderful proof of the Riemann Hypothesis but i do not have enough room in the margins of this post to contain the answer.
Lol if you get the joke then your a math nerd like me.
Those damn narrow margins!
the rain/ground example contains equivocations that render it incorrect. It can only be correct for true dichotomies - and rain vs wet ground is not a true dichotomy.
Oh my God finally!!!!!! I paused the video to write the truth tables and everything. The arrogance too. 1:16. "Everyone who has learn even basic geography can answer this in a second". Bruh chill.
Great work!