The Map of Mathematics
ฝัง
- เผยแพร่เมื่อ 3 มิ.ย. 2024
- The entire field of mathematics summarised in a single map! This shows how pure mathematics and applied mathematics relate to each other and all of the sub-topics they are made from.
#mathematics #DomainOfScience
If you would like to buy a poster of this map, they are available here:
North America: store.dftba.com/products/map-...
Everywhere else: www.redbubble.com/people/domin...
French version: www.redbubble.com/people/domi...
Spanish Version: www.redbubble.com/people/domi...
I have also made a version available for educational use which you can find here: www.flickr.com/photos/9586967...
To err is to human, and I human a lot. I always try my best to be as correct as possible, but unfortunately I make mistakes. This is the errata where I correct my silly mistakes. My goal is to one day do a video with no errors!
1. The number one is not a prime number. The definition of a prime number is a number can be divided evenly only by 1, or itself. And it must be a whole number GREATER than 1. (This last bit is the bit I forgot).
2. In the trigonometry section I drew cos(theta) = opposite / adjacent. This is the kind of thing you learn in high school and guess what. I got it wrong! Dummy. It should be cos(theta) = adjacent / hypotenuse.
3. My drawing of dice is slightly wrong. Most dice have their opposite sides adding up to 7, so when I drew 3 and 4 next to each other that is incorrect.
4. I said that the Gödel Incompleteness Theorems implied that mathematics is made up by humans, but that is wrong, just ignore that statement. I have learned more about it now, here is a good video explaining it: • Gödel's Incompleteness...
5. In the animation about imaginary numbers I drew the real axis as vertical and the imaginary axis as horizontal which is opposite to the conventional way it is done.
Thanks so much to my supporters on Patreon. I hope to make money from my videos one day, but I’m not there yet! If you enjoy my videos and would like to help me make more this is the best way and I appreciate it very much. / domainofscience
Here are links to some of the sources I used in this video.
Links:
Summary of mathematics: en.wikipedia.org/wiki/Mathema...
Earliest human counting: mathtimeline.weebly.com/early-...
First use of zero: en.wikipedia.org/wiki/0#History www.livescience.com/27853-who-...
First use of negative numbers: www.quora.com/Who-is-the-inve...
Renaissance science: en.wikipedia.org/wiki/History...
History of complex numbers: rossroessler.tripod.com/ en.wikipedia.org/wiki/Mathema...
Proof that pi is irrational: www.quora.com/How-do-you-prov...
and en.wikipedia.org/wiki/Proof_t...
Also, if you enjoyed this video, you will probably like my science books, available in all good books shops around the work and is printed in 16 languages. Links are below or just search for Professor Astro Cat. They are fun children's books aimed at the age range 7-12. But they are also a hit with adults who want good explanations of science. The books have won awards and the app won a Webby.
Frontiers of Space: nobrow.net/shop/professor-astr...
Atomic Adventure: nobrow.net/shop/professor-astr...
Intergalactic Activity Book: nobrow.net/shop/professor-astr...
Solar System App:
Find me on twitter, instagram, and my website:
dominicwalliman.com
/ dominicwalliman
/ dominicwalliman
/ dominicwalliman - วิทยาศาสตร์และเทคโนโลยี
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“The more you know, the more you know how little you know”
- Someone Smart
"I hate math, but I need it"
-Sun Tzu, the art of hating math
"The human mind isn't like mine, it cannot understand the universe"
- Albert Einstein
@@spec_wasted i cannot believe he ever said it, does he?
Someone smart. Pretty funny name isn't it
"The More You Learn, the Less You think You Know!" ✅
Just realized my current math skills are at the same level as those in 50,000 BCE.
😂
Belief is a beautiful thing my friend. I believe you have the ability to be a good mathematician:)
That's an epiphany in itself! I'm in the same boat.
🤣🤣🤣
I got pretty good at algebra in college, but have forgotten the majority of it. I find these math videos fascinating, even though I don't understand it. For one, I need to understand the notation. That would help.
I am a Physics undergrad student but trust me, there is nothing that can beat the Math. Math is the most interesting subject ever discovered. You will in love with it once you know how things work there.
Teach me 😭
@@nitxbms Linear algebra is great.
Just wish it was easier, some people are too bad at it to appreciate
This is surprising
math is all about asking u ask u get
I got a degree in Applied Math in 1973. If I had seen this video first, I would either have done better and learned and understood more, or I would have changed my major to Bowling. Thank you for a Fantastic Video; I am going to show this to my math & physics anxious nephews, so they have a broader understanding of what math can do to assist their understanding of the physical world. This should be shown to ALL Math and Physics majors in every university, and even to math students in High School. Bravo to You.
hello, i’m currently in school to earn my applied mathematics degree. how was it for you?
@@paulmccharmley I struggle math do you think you could help me 🥺🙏
@@ksofficerofficer7858no
The funny thing is every single item on the map could probably have a full-scale map of its own.
Yes, just as every discrete number has a multitude of numbers between them. 0 to 9 is the most mysterious sequence possible.
@@pamelafrancis4476 Ok almost every single item lol
So perhaps the map is a fractal. I wonder what it's Hausdorff dimension is.
Exactly
@@dcterr1 Yep, because every item on the plane here has an own plane where every item has its own plain and so on until after hundreds of layers its just planes of zeroes and ones, which are finally the only items that dont have an own plane.
When you find solutions for math it called "pure math"
When math find solutions for you it called "applied math"
th-cam.com/channels/9zWut-PVOkVufFtVpQsYlw.html
😆😆 true.
I am in for appplied maths more than pure maths.
Sorry i see them as the same thing where do i learn the math to separate them in to there smaller form of 1x1= all the way to 100 I am dyslexic so only understand thing from a 3-D way but can only half translation it to 123 and abc i am so lost looking for the right way to start math
Well said!!
I struggle with math in school and always have. I just returned to college at 21 and got an 18/100 on my pre-test for college algebra. Probably the lowest score in the class. I wish people knew that I am actually passionate and excited about math. I wish I could learn all these things, and I hope I get to understand at least some of them someday. Trigonometry was actually my favorite class in high school. I got a C lol.
Marks don't really matter, they only show how good are you at the test. If you like maths, learn it and do not let some schooling system destroy it for you. Good luck!
same here. keep going!
If you're passionate about a math subject then you do already understand it in its core. In your case you just haven't found someone who can communicate it (or even really understand it) the way you would receive it. Find someone to teach you or even teach yourself - we got all info online now, you don't have to rely on poorly skilled ppl to teach you. You totally got this.
Dope, 64th like, a number which will always remind me of Minecraft and remind me that math is universally applicable and can make sense while being entertaining if the teaching method is right. I liked Minecraft, and thus I liked the inventory full of numeric patterns as I halved each stack... School has taught me a few more ways to write or dissect the number 64, but it's hard to find a learning platform that offers as much fun as a video game. If you find the right teacher or teaching style and keep going because you like math, as suggested by the 3 other replies, you've got this. I loved math in High School, did terribly, decided I wasn't cut out for math, and now I'm in school for engineering at 23 and have had to entirely reassess my approach to math and studying in general. Neuroplasticity for the win! A Growth Mindset is better than a Fixed Mindset! American school systems are designed a specific way, I might have to struggle in that system to achieve the same success as everyone else, but that's just because my learning system is designed a different way. Find your best learning method, make and keep useful study habits (this is my downfall), and know that you ARE a math person. Keep your head up, fellow nerd (aka a person who is enthusiastic about their interests)!
Don’t give up. Master the basics and the rest isn’t so bad.
When I was learning in school I hated mathematics but now I'm passionately learning mathematics for my competitive exams, I love to learn that what feels hard to me and my respectful regards to those mathematics geniuses
same ngl, idk what changed
JEE aspirant??
Jee 🤨
I've personally always been interested by maths, but it took one good teacher to really spark all this interest I have, now Im upset if I didn't spend a week learning new stuff lol
what da sudeep showing too much cock?
I'm more amazed at the fact that you didn't try to pitch me a brilliant subscription at the end
True😂😂
I used brilliant before all the sponsors, it's genuinly good
@@alexwang982 No one cares, bitch.
Pi did anyone ask?
I think it's better to understand that creators don't necessarily decide to pitch you a 'brilliant ad subscription' for the love of god.
A lot of creators tries to make a living from TH-cam and TH-cam is becoming harder everyday on its regulations. Thus affecting monetization.
Creators find themselves with a lack of revenue. Sponsorships like brilliant is a way for them to get a salary but also a way for you to get those vids right to you.
So if you find yourself at the sponsor session of a video please just double tap on your screen to avoid it.
The more I learn about things, the less I understand.
The more I know, the more I discover that I don't know
@@duzacsp1376 scio nescio
"But knowledge puffs up while love builds up." 1 Corithians 8:1
The more you learn, the more you realise you don't understand.
think about it
I am a writer but a few years ago I discovered my curiosity towards mathematics & this video definitely gave me an idea about what I need to cover. People think mathematics can be boring but Alkhayam was both a mathematician & poet. Lewis Carroll was a mathematician. You can be creative at anything you love.
I have always hated math and have been a huge history nerd, but this video made me interested in math....somehow. good job :/
I dislike math aswell and enjoy history and drawing, math is very important when it comes to drawings aswell.
let's go dive in.
Me too! I’m actually considering studying history and physics in Uni :)
@@julieditzler890 ooh
Are you a grad student ? Which major are you taken?
YOOO SAMEE
“The mathematics we do in school doesn’t quite do the field of mathematics justice.”
So damn true
I didn't even know 90% of these existed!!!
To be fair, most of our schooling is based on Pure Mathematics and within that we are mostly taught the Number Theory and the Changes Section from this video.
The spatial is usually left out in the early stages of education and is slowly brought in after 10th grade.
By engineering, we are mostly taught applied mathematics for about 5 semesters so its not like we are missing out on anything.
@@phs125 There's a very good chance you already know the mathematics behind it if you have completed your 12th grade, but you might not know where it exactly lies in which leads to that very question in school when we ask "WHY DO WE EVEN NEED THIS?!"
Study engineering at uni and you will encounter almost all of it
@@phs125 This doesn't even scratch the surface! Mathematics has been tending to increasing levels of abstraction that it's hard to even describe many of the active areas of mathematics.
I love being a math student and coming back here once a semester and tick off more boxes
Goals
this…..is genius. what a way to keep you motivated.
currently ticking off topology and measure theory
Wow, you sound amazing
Currently studying integration!!
This was just absolutely amazing, I started watching this video 1 second ago and now, 2 seconds later, it has been 11 minutes and no wonder I have lost track of time, this literally blew me away with many new things I did not know, but also with the BEAUTIFUL graphics and the emotional touch in the end.
If all maths teachers were like you, humanity would have reached this Star Trek future and gone way beyond by now.
Thank you dearly for putting this work together, respect!
I learned and taught mathematics at school and college level for over 40 years. My time with my students in the class and outside with them remains my best time ever.Now when I am enjoying my retired life I have the greatest respect from my students who themselves are grandparents. All thanks to mathematics.
Mapthematics.
tongue twister
+
mapematics
Mapmatics, with a mute 'p'
mathemapics
I wish this is how they explained mathematics in school, instead of hyper-focusing on some specific part taken out of context, telling you it just works and making you do the same menial task over and over.
And thats why most students cant do maths, they dont understand why. But this is maths, the question of why? And the system called school doenst do a good job in educating so.
@aids I think what he more wants to say it, to focus it on the logic and not tje formulas. Maths isnt formulas, its the logic behind. Mathematiciams of course have to know these formulas, but they have to understand the logic behind and create new ones.
@aids No he probably means he wants to solve questions which actually require critical thinking. When I was in seventh grade , I was taught the formula for Pythagoras theorem and had to do like 20 problems which involved direct application of the formula and the only difference between those questions was the change in numbers. Maths felt easy then, now that I'm in eleventh grade, I don't have enough problem solving abilities required. That's the problem you see. The maths till tenth grade is shit and they expect you to be super smart in eleventh grade out of nowhere
thats what bureacracy does, it takes something wonderful and orderly and destroys it. entropy i guess.
Lol our schools still use an old system taken from prussia. The system was made too make citizens easy to control. One of known myths is "School kills creative thinking" and this myth very true, sadly. Everyone of my classmates hate "english" xd
Btw english ain't my native and didn't learn it from school but from internet. I still don't know all English tense XD
Is it just me or the math being so beautiful that I swear I can enjoy studying this beauty however old I get
Ikrrr
Same
+1
Tbh it's just the education system that has ruined the beauty of math, I enjoy maths only when I'm doing something out of my syllabus and not for the sake of exams.
Imagine chess being a subject...
Its just you
3:01
"Some infinities are bigger then others"
Well it's not the size that matters 😂
Some people think high level maths is just multiplying really big numbers together.
If only it would be as easy as that
@@LuizFernando-ux8yi lol, I rest my case
@@nobody7817 Computers can't do its job. The mathematics part is to develop and prove concepts and in the area of computational science and numerics it is to find ways a computer can either solve or approximate stuff. The mathematicians job is not to actually take the formulars and concepts for calculating real world problems. Thats the part for the computer. A computer can calculate. But calculating is not mathematics
@@Haniel93 The day will come when computers do math. Or the day we change and improve our brains and make math primitive and useless. Just try to imagine that future.
@NPC #369369 1) "High level mathematics is basically just abstract illogical thinking". Did you mean creative/lateral thinking?
2) The way we think is pure consequence of how our brain works. You change that, it changes everything.
3) What computers do now is just a fraction of what them will do with in decades
Back in highschool, my main goal in life was to study all the maths and science to understand the universe I was in. Turns out I was just delusional lmao.
I want to specifically learn classical EM in physics, and in math Topology seems very interesting.
Maybe later in life I'll try to learn as much as I can, if I can, the theory of relativity.
Yes I love mathematics and science too.
Ah yes the dreamer, i am one of them
th-cam.com/video/cEbMLW7K1_c/w-d-xo.html
Ultimate Loser why delusional? How did u know u were delusional?
I graduated with a BSc. Maths major & Physics minor...I really enjoyed watching the video and vividly recalled learning all of and applying some of them at work. Congrats on the effort in producing this video....enjoyed watching it!!!
You should make a poster of this! Great video, such a great way to generate interest in new subjects to learn
0:08 what you learn in class
0:10 *what’s on the test*
That's the beauty of India
haha
yep
WONDERFULLY DIVERSE
wonderfully diverse subject, what's not to understand, it's easy they said
this video is actually incredible when you think about it, even after three years. at first glance it just seems like another cool "wow interesting math video." but if you look through this video and studied all the math subjects covered here it would take you forever, and you would just be that much closer to understanding the universe we live in. math is such an underrated subject, i love math and i barely passed it in high school. i would suggest to everyone who hates math, start studying it a bit.. just take it at your own pace, i started by relearning basic math. its a very incredible subject, really.
Umm did you get better at Math? And if you did, can you please explain to me how I can be better at it too? (I'm just curious because I'm not very good at Math but I really want to learn the subject more)
@@BongRamilBaladjay Practise more, Keep reading, watch videos on topics you struggle with. You need to start with the basics and work your way up. Learning Maths is slow but is very rewarding it just requires hard work.
@@AJMaths Thank you! I will do my best to learn!!!😊😊😊
@@BongRamilBaladjay It's a beautiful subject, if you ever want help just drop me a comment and i'll help :)
@@AJMaths Thank you so much! And sorry for the late replies haha😅✌... actually I think I have "Math Anxiety" that's why the subject is so hard for me, but I'll ask for your help if I need it! Thank you again!!!
Great job buddy. I was having a pretty rough day studying Biology 😭 So came into TH-cam for some refreshments and got your video. Really an interesting video. Made all my fatigues go away.
@@nav6496 depends on the type of biology. biostats and biophysics is hardcore
Aspiring Mathematician here!
Great effort,love it ❤
But as a learner of pure mathematics,i should say that we need atleast another map like this to cover a good amount of it. I'm sure it would be the same for applied people too
It's just fascinating(sometimes overwhelming) to see how much progress humans have made as a species!
I'm only in high school, but I love this map cause it makes me feel like I am in a video game upgrading my skill tree with experience points lol. i am 100% going into something math related in life, no idea what yet, but i find it absolutely fascinating.
Have you thought about becoming a mathematician? Physicist?
Keep going bruh. It fr is brain scratching stuff. Educate yourself finely.
There's many different career choices you could choose from with a math background. Hard work pays off. It's even better if you enjoy what your doing. The best of luck.
High school?? 10th?
same
MATH ---- YES
EXAM ---- NO
Totally agree with that
Yup
😂🤣👆🖕😂🤣😂🤣😂😃😂🤣😅😊🤣😂🤣
Projects > Exams
Change me mind.
@@sergioandresbenitezhernand2542 the projects or researchs (about your interests or about the subject that you want to work on when you grow up) that you have done lately,are the things that will bring succses in your carrier
Math is one of those things that continually fascinate me. Mostly because I try so hard to grasp and understand it, whether it be geometry or algebra(I’m scared to even try learning about calculus) but my brain can’t seem to grasp and understand it. I applaud those who have the talent and ability to learn the ‘language’ of mathematics, in any of its forms. (Probability, statistics, algebra, calculus, geometry, etc.)
This is incredible! Great explanation for such a wide coverage of mathematics.
I wanna learn all of this.
Ruslan Zarifov let him do it lmao who are you to tell him what to do . He could discover another type of math
Ruslan Zarifov actually the hard work involved in it is what gets me excited.
Ruslan Zarifov o.o...I’m sorry man. Your point is correct, I was just talking about me and my love for the painful hardships of drawing
r/im14andthisisdeep
@@raggedclawstarcraft6562
I agree with you wholeheartedly. I have my own example. 5 years ago my friends used to read "Popular Science books" because they wanted to become Physicist or Mathematicians while I used to study Dummit and Foote( a rigorous math book). Now most of them have long left the idea of becoming a mathematician because they romanticised the idea of being a mathematician rather than the idea of studying hard every day . I loved studying it and kept on doing it even if things were difficult now I'm doing pretty good maybe 5-6 years down the line I might actually become a professional mathematician. The crux here is loving the work and being continuous with it.
Math was, still is and forever will be one of my favourite subjects to study. I feel in love with both its simplicity and complexity; the way it never makes sense when you go through it, but at the end everything fits together with such ease to form an answer. Some of the best memories of my school days were formed in the math class, and everytime I come back to it it astounds me all over again. I feel extremely privileged and lucky to be able to enjoy such a wonderful subject, and I hope our education system can improve enough to spark interest in more and more students. 😊
I wish i coul express my feelings like you, haha ..for the Ielts test
@@fariarahman9444 treat them like a puzzle. It’s hard at first but once you are familiar with that topic it would be interesting to solve them. Especially for geometry and trigonometry, they are really just IQ question at some point when you grind them enough.
@@fariarahman9444 It's simple, forget all what you know or think about maths, lose your inhibitions, act like you don't have any idea about what is it about and try to "discover" it at some point, especially, understand the essence of it, why is 1+1 always equal to 2 ? Why does Pi have this value ? Why are things like this and not otherwise ? And to answer this you gotta look beyond what the horizon shows you, don't focus on the surface of the ocean, go deeper than that and find the treasure it hides
So well said. I grew up thinking I hated math and realized at the age of nearly 30 that I love it for all the reasons you mentioned. Part of me is angry at the teachers who made it so hard for me to comprehend and never seemed to care when some of us whose brains work differently (I have ADHD) needed more guidance. However, another part of me is just so happy that I discovered my love for it while I’m still young. I can’t wait to learn more and teach it to my children in a way that’s fun and easy to absorb. I want them to love and embrace math as well, because it’s extraordinary, how it’s like this one language that unites all of us.
I hope it becomes more accessible in the future and that more people realize just how fun and interesting it actually is. Because way too many kids like myself feel like it’s not “for them” when the beauty of it, is that it truly is for all of us.
@@yuumir1072 Yes! Great advice. I used khan academy and just relearned the basics starting from the ground up. I always wanted to know the answers to those questions growing up and was always told “it just is!” but being able to learn at my own pace, thanks to the internet, has made math so much fun haha
if you know in india NCERT is the main book of mathematics from class VI-XII. The structure of pure mathematics you described in this video is followed by NCERT such as
IN class - IX and X
chapter 1 - Number System
chapter 2 - Polynomials
and so on......
This show how brilliantly NCERT books are made
man love the way you explained everything in brief!!!!
By watching this, I learned that I know nothing
you're at a good level bro, i still haven't learned that
th-cam.com/channels/9zWut-PVOkVufFtVpQsYlw.html
That's a great thing about learning! :D I'm a physicist, which means I'm constantly confronted with my own lack of understanding in the face of a strange and wonderful universe, and my life's goal is to understand slightly more than I do now :)
so there' s room to learn something :)
My Mathematics teacher used to say "Without mathematics the world would be zero, and that also belongs to Mathematics".
How would the world be zero can u elaborate ?
The world would be the same
@@covermaiden no it wouldn't, Math is literally the most important thing you are taught in school
@@ishaqali9347 It would be 0 since the world needs math in order to function
@@boganborn I agree with you, but you are talking about OUR WORLD MADE OUT OF LANGUAGE, not the real world: shamans survived without math and the world was better back then.
I've been watching that video probably six years ago. It was "okay" or "kinda nice". Now as I'm taking courses for the second and fourth semester (weird situation) I decided to rewatch this video and it was so so exciting! You really nailed it! I started making a sort of "to-do list" for myself to get an overview of what I actually know in order to make a proper scedule. This video was really helpful. it matches my internet research - except it's beeing a little bit better.
7
8
Dude this is something that everyone needed
i think that if schools explained and showed us the beauty behind math like this, more people would appreciate and love it
Maths unplugged is also good 👍 for those who are starting from beginning or to even to go advanced level
I don't think so. It may sound nice to learn the scope of maths, but trust me, as a person who studies physics, very few people would actually enjoy learning it. This guy also pretty much says incorrect information about a lot of topics here. For instance, saying that group theory studies groups is really retarded way of saying it, even if it is somewhat true, he doesn't say what a group is, which if you actually delve into it, you'd find that group theory and abstract algebra in general is one of the harder math subjects. I didn't like this video, because it is clear that this guy had very little experience with math, which makes sense because he studied biology, but it really doesn't feel good to listen to him talk about stuff he know nothing about.
Maths are cool
But alike other subjects, school makes it suck
Bull
You can make maths fun, by
1. Learn on your own
*Google exist*
2. practice even when you don't have exams
3. Stop blaming others, and stop blaming yourself, only thing you should blame is the lack of practice or study
Khan Academy is the best!!!!
@@clipit4503 Khan academy taught and is still teaching me Mathematics. Teachers can't teach you everything because of the stagnant, caged, School curriculum that has a time limit. I like to have fun while doing Mathematics and khan academy offers great content that is not limited due to age or grade.
@@clipit4503 True!!
Such an excellent, visual and practical map... thanks for sharing mate!
Amazing summary of so much complexity. This is what we non-experts need in order to strive to learn more.
“Math is a beautiful field”
*camera pan to every college student screaming in Cal B*
They are pursuing marks and they arent really learning for the sake of it
They usually get stressed because they cannot keep up with tge syllabus due to various factors
@@kuntalmukhrjee3993 so true, all information compressed into three years is too much to retain. Not enjoyable and stressful
what cal b tho?
@@thetrickster9885 I would assume the University of California Berkeley?
@@lipstickcardigan he could also be referring to Calculus II since some schools call it “Calc B”
What are the odds you'd be willing to print up posters of your map? I'd surely buy one :)
The description links to where you can buy them!
What if I recreate this and sell?
Instead of just taking someone's hard work you appreciate and finding a way to get it free show your appreciation by purchasing the poster legit.
Lakey Hinson don’t be a sucker😂
i would buy to
Math is so confusing and interesting at the same time. It facinates me how everything fits perfectly like a puzzle.
Fantastic ! Thank you so much for this wonderful presentation. I believe such a map should be hanging on the wall of each and every classroom all over the world.
Much to often the kids are taught maths without seeing the bigger picture. I am convinced this kind of tool is absolutely useful to help on this matter.
Normal person: so....Why'd you choose to get a degree in maths?
Me: "to get an edge and win all those fat stacks"
watch my maths tricks and videos.
Haha, humans...
@@JesusChrist-lx4vm says the axiomatic human of the west
@@JesusChrist-lx4vm
You don't exist. Gods don't exist. Hence you did not make that comment. And I did not make my comment. Boom
Jakhighermsthematics
I love the way he pauses for a second after he says " some infinity are bigger than others " 3:02
He gives us some time to think about it 😯
All are equal. But some are more equal.
@@android12921 Why does that makes sense?
@@XxAlexanderProxx Animal farm by George Orwell.
@@android12921 We say two sets have the same size if we can create a function from one to the other that is invertible. You could make such a function between all of the natural numbers and the even natural numbers by doubling each number. Then every element basically had a unique counterpart in the other set. So there are as many natural numbers as there are even natural numbers.
However, you can show that it's impossible to do this between the natural numbers and the real numbers, proving that the infinity of real numbers is bigger than that of natural numbers.
This is such a wonderful video. Thanks for making it
Amazing video. Thanks a lot for the video!
keep up the great job, you should do one for chemistry some day
+ Biology, History, programming/Ict , ... C:
We need a chemistry one
Yeah , it would be the best !
nikolas doubourhydes we dont need chemistry.. chemistry is leech
We definetly need chemistry. Its fundamental
As a math major this really helped me get a glimpse of what I actually know and have built over so many years
Where you from, by the way?
Thank you for the maps - they are extremely helpful.❤️
Congratulations! this is a great video! thank you very much for having created it!
I remember watching this about two years ago and everything just flew over my head. watching this vid again just made me realize how much I've learned :)
poker0001 year?
Same
Same!
Same
Can’t wait for that to happen to me :)
"Education is a kindle of a flame, not a filling of the vessel"
Don't be stressed lel
So educating is dark souls and not hollow knight?
Noted
YES YES YES!!!
Can't imagine this video was made 6 years ago ! Perfect work ! Thank you for showing Mathematics by this beautiful map 🎉
I have no idea how you created this. What an amazing map. Fascinating! Thank you
College: Applied Mathematics
Business: MS Excel
I ♥ spreadsheets
th-cam.com/video/y_XwQkchwrE/w-d-xo.html
deep
@@himanshu7103 learning
@@chrissmith1152 ?? sorry i don't get it ? what r u suggesting
I love everything about maths except maths exams
🗣🤣🤣🤣🤣
I love EVERYTHING about maths even maths exams.
I’ve have never agreed more in my life until now
👏👏👏
Thank you for all the effort it took to make this video so shortcut!
Man this was awesome!!! Wish you could do more videos like this
I m amazed to know that I have studied almost every section of Pure Mathematics in either School or College and still I don't remember anything
My thoughts exactly..
This is a pretty bad overview of pure math. Matrices and vectors are a fundamental part of linear algebra, but linear transformations, and, well, linear algebras themselves are quite fundamental. The theory of rings and fields goes unmentioned, as does Galois theory. Topology here is made out to seem like a small subfield of geometry, but it is far more complex. Really, topology should itself be a large branch of the map, containing point-set, algebraic topology, etc. Algebraic geometry is unmentioned too. "Number systems" is not a field of mathematics - it is at most the object of study of some parts of NT, which should be divided into algebraic and analytic number theory. There is no mention at all of probability in the pure side. I could go on, but this is a pretty surface level understanding of what pure math entails.
Worst of all is that real analysis, functional analysis, etc, goes more or less completely unmentioned, when its basically the largest field in pure math in terms of number of people working on it? It's kind of baffling.
@@danielbelkin4652 Also, out of all abstract algebra sections he took only permutation group which itself only a chunk of group theory.
@@Arkan1986 The Langlands program also goes totally unmentioned, as does category theory, and formal logic is missing too... it's pretty bad.
Arkady Zhelezniak
*Cayley’s Theorem enters the chat*
Even though mathematics are part of my life as an engineer, this video is something I've been searching for a very long time, to help ease my mind. At this age and experience, I can understand why so many people hate or afraid of mathematics. Teaching maths should not be a collection of problem solving steps. There is more than that! And the first thing that should be said, is the content of exactly this video. Thank you so much. And I thank for the technology that provides means to communicate and share knowledge and opinions. Things were a lot different back in my studying days.
I also have always loved math, and have genuinely considered becoming a mathematician just for fun.
I love just considering the concepts of it, and how creative it can be (i was made up, discovered, and happened to be useful, or the concept that you can take something infinitely close to something else and it's so genius in its simplicity but so useful!). It's like all these concepts come out of thin air, they feel like they're describing something important (the concept of 0 is a useful and important concept), but its really just another language that allows us to describe what we already know to be true in a much deeper way.
Mathematics is a universe of its own and this whiz mapped it out for use, kinda like how scientists recently presented the world with a "map of the universe." Maybe they're overlays of each other..they certainly relate!
This is AWESOME. GREAT WORK. 👏
Well certainly I'm no good at mathematics, but this gave me a new perspective on mathematics. A perspective from a psychologist which certainly still uses mathematics in research mostly statistics (Applied Mathematics) makes me want to appreciate the complexity and the importance of mathematics in every field of science.
As someone that has seen the incompleteness theorems in class, incompleteness doesnt make math purely made up, it simply means that no system will answer every possible question in the system. A great example is the continuum hypothesis. Current math doesnt know whether there is an infinity between the size of the natural numbers and the size of the real numbers (the infinities you mentioned). It was in fact shown that there is no way to answer it, meaning our axioms are ok with either possibility. The continuum hypothesis suggests there are no middleground infinities. But once that axiom is put in place, there must be some other unresolved question according to the incompleteness theorem.
Thank you! Wanted to make this comment, but could not give an example, of course!
Its not natural numbers. Its integers.
@@karthikeyavishwanatham4261 Well yes and no. Yes in the sense that the integers and the natural numbers are the same size, so it doesn’t technically matter which you choose. However when discussing cardinality, we term a set to be countable if there exists a bijection between that set and a subset of the natural numbers. So a set is generally termed countably infinite when it is infinite and bijective to the naturals, not integers.
It makes no sense that one infinity is bigger than another, infinity is a symbol that represents something that has no end. You can’t have “more” no end or “less” no end. So the most reasonable answer is that both natural and real numbers have infinite numbers, or “the same amount of numbers”. You cannot divide infinity by 2 etc… infinity is not a number it only symbolises a never ending amount of numbers
Kind of like how 3 times 0 and 9 times 0 are the same number
Brilliant overview. Thank you so much!
I would like a T-shirt with all the map ;)
th-cam.com/video/y_XwQkchwrE/w-d-xo.html
@@kumarupendra LOL
I thought the link would take me to a T-Shirt.
again, lolololol
@@chewinggum5550 u r real baklol in this world
7
kumar upendra umm what does that mean
When in math class: I hate this
1 AM in youtube recommended feed: Pog Math
I like the pauses between topics! amazing video :D
This map was displayed on the wall of a classroom in our highschool. I love your work!
Each sentence he says is what I spent 1 semester in Uni learning
th-cam.com/video/klGi_WZ17U0/w-d-xo.html
You put 1 as a prime number?
Feather Pillows
Oh god! He actually did :O
To be fair, it's not a composite number, so it's not too bad
And missed 2...
And he missed 7, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883 and 887.
You always hop on the one bad thing instead of the many positive huh?
Unfortunately... It's a bit sad that in general it's much easier to point out specific "bad" thing than good things. :( That might be because if everything is good but one thing, that one thing is much easier to notice; although in this video he didn't claim to start a list of primes from the start, which was my enterpretation so nothing is wrong here. I commented a bit to fast...
This was a very nice video to be honest. :)
Thanks this was wonderful, my first epiphany moment where I fell in love with Math is when I understood what a Limit was it gave me permission to explore Calculus and changed my life.
The introduction and the origin make a critical point quite well before we begin to know and understand the map, or anything aside from mathematics. Like everyone else, however, he made this map out of his love for maths. I hope as well that we all do what we love and love what we do.
Brilliant! I now know what it is that I so love about mathematics in a nutshell! I would have loved to have had this insight when I was teaching maths for 30 years. Some of my pupils got it and many went on to study maths in some form and have had successful careers, including professorships. At 83, I'd like to believe that kids will always remain curious about the mathematical world.
What is it that you love, your insight, about mathematics?
I wish i can feel like that,like my thoughts are always like “whats the point of all this whatever math languages and stuff,you wont even use it in real life”,all you need to learn is basic math,i rlly wish i can feel what it actually feels like on liking math,because im sooo interested in math,but my brain cant comprehend it
Segway: if maths hurts your brain, then take a break. Chill out.
#/Relax. Look up:
Party with Justin's Turkey
The Chill Bah
Cabello Camello
International Beach Holiday
So Summertime
6th graders: i understand enough to be an adult!
university graduates: proceeds to show this graph*
Ignorance is a position of comfort.
I have done master in mathematics but i loved 😍 the way you are explained i have read all the things you explain and you explain all the things so easily
these type of maps opens my mind. Great video.
I have just started learning maths from scratch and am incredibly impressed with this Map. It must have taken much thought, time, and patience to complete, even though you are expert!
From where did you start? I'm intersted in learning it (sorry for my english)
@@sidrum1010 Math Antics for starters. Great for any level to build a foundation.
@@pamelafrancis4476 thank you very much
@@pamelafrancis4476 can u send a link of the playlist plzz
Critical?
What a great video Dominic, Can you make a computer science map?
Just make sure to reserve a large area for all the hot new JS frameworks that will come out in 2017. Standards are great, lets just keep making more of them :p
Jaxteller I would like to see one of those. if you find one please post a link.
+Dan Ross No need for that. JS will die in 5 years. This is just a flaw that has to be buried along with ECMA and other unpredictable, slow languages.
Just cause I am pretty immersed in JS and WASM, I feel suitable to reply to Green Screen.
JavaScript was invented way back in the day, and since then, it was a mere piece of death. In 2007-08, there came jQuery came out and changed the way to use JavaScript. Since then, a lot of frameworks have been created on top of it.
When NodeJS came into the scene, JavaScript was opened to the endless world of possibilities. Currently, JavaScript is used to create apps, operating systems, websites, games and more. Let's keep all that aside and come to the latest state of JS.
WebAssembly, a project that all the huge internet companies took seriously, is future of JS. This means JS will no longer be a slow programming language.
I guess I wrote quite too much. Sorry about that. If you made it to end, I bet you JS will not be vanished until WWW is present.
but all the complex/fun stuff of C.S. is just math...
Plz make more videos. One of the best channels on youtube appreciate your work 🙏🙏
Such a great idea.. and implementation. The most fascinating thing is that it helped me realize I learnt a bucketload of *stuff*... and a lot of my main 'maths-related' interests lie in the areas we weren't actively taught about in school/uni: game theory, chaos theory, dynamic systems, and others)... and ya, I understand that as a Civil Engineer, a lot of those things aren't (weren't) 'in scope' (in the '70s and '80s)... but the 'oneness of everything' (and that some people now understand that) means we can continue to see new applications of any and every form of maths in almost everything 💚
That bruh moment when your math skill is on the same level as that of a bird
I've been watching this video since the start of my journey. I come back here maybe once a year .
It feels so good to have covered up some parts of this map. A dream I had when first seeing this
How it is going?
I started my own journey in mathematics some days ago, I started from zero even if I know a bit of mathematics. I will do the same every single year, I will come back and check my progress insha'a Allah. 🦾🌌
Thank u for this video! Truly enjoyed!
I love this form of content. The only thing is that you should make a much longer video, to fully, in depth, explain everything.
ah yes, a list of things that lower my GPA
Too real.
a map*
you lower your own GPA. lol. noone but you has any effect on it. maybe that kind of thinking is why you cant understand basic human concepts.
r/iamverysmart
@@sameerachaganti8137 Only a few will get that (y) :D
My teacher : ~Explaining...
Me : I can't take this anymore :C
TH-cam : *Recommend this*
Me : It's that simple? :D...
"simple"
maybe u r the kind who needs to see the big picture first before the details
though there r others who need to see the details first before the big picture
@@topaznico3414
indeed, people who don't have a preference for either a top down view or a bottom up view are rare. People who are aware both are valid ways to get to the truth and as such prefer to know about and are able to understand both are even more rare. Most people are quite reluctant to changes being made in their model of reality.
BlacksmithTWD oh but i never knew what i prefer or which one i am so i read abt both of them yet i agree with both :/ hence, i took a test to find out which suits me better so that i can study more efficiently
i ended up with 49:51 for detail oriented vs big picture
i consider myself rather common and average though
and also bcos i dont hav one that suits me very well idt i can excel lol cos both suits me moderately only
how do u know it’s rare?
@@topaznico3414
I don't know about the test you took, perhaps my concept differs from the concept the test intends to convey. In my concept bottom up approach starts with quantum physics, top down approach starts with god. I doubt the test took it to such extremes. The human experience tends to start somewhere in between, that's why I consider those who have no preference rare, since most humans seem to pick either one or the other, but seldom both. I don't have any formal statistical data on this, just my personal experience.
Thank you very much for sharing this map of mathematics.
"Mathematics is the closest thing to perfection we will have as humans."
- Fenil B
Some small-ish inaccuracies that I found (feel free to correct me):
2:39 - irrational numbers like pi aren't special because they "go on to infinite decimal points" (more accurately “have a non-ending decimal expansion"), 1/3 (0.33333...) does so just fine. They do have a non-repeating infinite decimal expansion, but that is hardly the most interesting property of them nor the best way to define them.
2:43 - the word "number" isn't really defined. If you want numbers to have addition and multiplication that play nicely (e.g. having commutativity, a*b = b*a, and associativity, (a*b)*c = a*(b*c)) then you're out of luck - quaternion multiplication isn't commutative and octonion multiplication isn't associative.
2:50 - the "exponential" isn't the name of the number you're referencing, it is 'e' (~2.72). The "exponential" is the name of a related function (exp(x) = e^x whenever x is a real number).
3:10 - the study of structures more commonly relates to the way operations interact with sets and is confusingly also named "algebra" (or abstract algebra).
3:46 - group theory, ring theory, field theory and many more iare sub-categories of abstract algebra. The explanation you're giving for what group theory is isn’t very informative at all.
4:29 - fractals aren't always self similar, they are shapes with non-integer dimension. There are shapes that are scale invariant that are not fractals, like the sqare - you can take four copies of a square which are half its size and make another square. With fractals, the amount of smaller shapes you need is not an integer power of their size.
4:43 - the fact that the mobius strip is "one surface" doesn't mean anything. It does, however, have only only one side, a property called "inorientability".
4:51 - coffee cups are not the same thing as donuts, they are just homeomorphic, meaning they can be transformed continuously into one another.
5:18 - I think you mean "derivatives" and not "differentials". The differential is a type of operator from vector calculus.
5:51 - compelx analysis is much closer to real analysis than to dynamical systems and to chaos theory (which are related to differential equations and vector calculus), assuming distance indicates closeness.
7:37 - probability, as opposed to statistics (the science of making models from data), is much closer to pure math than to applied math.
9:06 - there is no need to "prove" there is a fundamental set of axioms - each such set will give rise to different, interesting fields of math that are used to study different subjects. The results you get from picking different axioms are so varied that there are areas of math that deal just with the consequences of picking different axioms (universal algebra). Most of modern mathematics is however derived from one set of axioms called ZFC (Zermelo-Frankel + the axiom of choice).
9:11 + 9:25 - Godel proved that a strong enough axiomatic system wouldn't be able to prove it is complete (meaning every theorem has either proof or a disproof) unless it inconsistent (it has contradictions). This means that in any set of axioms free of contradictions, there are unprovable statements. Ex: in ZFC, the continuum hypothesis isn’t decidable. If we assume ZFC is consistent, then both ZFC + CH and ZFC - CH (ZFC plus the assumption that CH is false) are consistent.
9:33 - everything is made up. The fact that mathematics can be used to model the universe doesn't contradict that. This is not a consequence of Godel's incompleteness theorems.
The philosophical talk about Godel's incompleteness theorems triggers me to no end, but otherwise - the video is fantastic with outstanding visuals. I Love the way parts of the map get colored light and dark as you go through them.
Addendum: many if you are asking me for tips and resources for learning more math.
First, I’m incredibly flattered you think I know a lot of math :) in fact, I probably know less than the average math undergraduate. I mostly know the type of rigor that is “this is almost correct, but not quite accurate/rigorous/general enough”. This lack of mathematical rigor was very apparent in this video since it tried to address an average audience.
Second, all of the math I know i learned on the the internet! Resources like: Quora (Alon Amit, Senia Sheydvasser, the space “Mathematical Pedantry”), blogposts (mostly Hebrew, sadly) and TH-cam videos (3blue1brown, mathologer, numberphile). Also, as my friends often shame me for, I read Wikipedia articles on mathematical topics on my spare time. Reading about math is very much like browsing social media for me, in a procrastination-y way ;)
I hope it helps all of you to make your dreams of knowing math come true :))
Gold
Thanks for this. It's a great video but his misunderstanding of Godel's incompleteness theorem really bugged me
This comment is great and was badly needed. It should be the top comment to this video. I shall jump at the invitation of adding stuff.
Concerning the topology remarks: this whole one surface thing is really a problem of "embedded understanding"! Topology doesn't require the structures to be embedded in some higher dimensional space! That's why the above comment on "inorientability" is important. In order to understand the Möbius strip one should consider line bundle topology as a special case of fibre bundle topology. I don't think that the cup "=" doughnut is technically wrong because he adds a vague "topologically speaking" which implies just what the above comment clearified, that is "homeomorphic". For topologists "being homeomorphic" is precisely "being (basically) the same", although this is clearly only obvious to people familiar with the concept so... maybe this helps shedding some light on this matter ^^
Finally, I would like to add to the whole "why does nature use maths?" subject because I think it is outrageously interesting and somewhat underrated a topic! I highly recommend the article "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" by Eugene Wigner - it does what it says and is totally worth your time. It's available here:
www.maths.ed.ac.uk/~v1ranick/papers/wigner.pdf
Edit: I came back add that, in fact, physics (as the first example of applied maths) does provide insights for mathematicians as well. So there's things to be learned about pure maths from physics, which is neat. This is happily touched upon in a fun talk by David Tong; a talk, he slyly named "The Unreasonable Effectiveness of Physics in Maths" and that is available here:
th-cam.com/video/UVuKyZ4pBzg/w-d-xo.html
Also , he completely failed to mention Clifford Algebra (Geometric Algebra) which is critical to the study of vector spaces and can be seen as the fundamental mathematical language of physics.
Yeah no doubt all very valid points perhaps there's a way to make them understandable to a general audience and fit them in a short video summarising the whole field of mathematics?
This made me want to study math in school even more!
then you start studying and question 1 already messes you up.💔😪
@@kelisiwe444 then quarantine hits
@@_carrbgamingjr then vaccine hits
@@retrofilmwork then corona virus mutation hits
Pineapple Head XD Then mutated people hits aka x-men aPCka x-people.
This is the most exciting video I’ve seen about mathematics, I don’t think anything can top it 😭👏🏼
Change my mind !
Loved this - thanks so much!
This helped me so much, my friend who is a genius when it comes to school education and he used this to get a basic foundation of where I am so we know where to start, thanks so much, you gained another sub! Keep up the great work! (:
I know it’s a lot of work but I would love to make a very in depth video, one for each of the subjects you mentioned in this video!