The Map of Mathematics 9,485,231 viewsFeb 1, 2017

#mathematics #DomainOfScience The Map of Mathematics 9,485,231 viewsFeb 1, 2017 DoS - Domain of Science 985K subscribers 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: https://store.dftba.com/products/map-... Everywhere else: http://www.redbubble.com/people/domin... French version: https://www.redbubble.com/people/domi... Spanish Version: https://www.redbubble.com/people/domi... I have also made a version available for educational use which you can find here: https://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: https://youtu.be/O4ndIDcDSGc 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. https://www.patreon.com/domainofscience Here are links to some of the sources I used in this video. Links: Summary of mathematics: https://en.wikipedia.org/wiki/Mathema... Earliest human counting: http://mathtimeline.weebly.com/early-... First use of zero: https://en.wikipedia.org/wiki/0#History http://www.livescience.com/27853-who-... First use of negative numbers: https://www.quora.com/Who-is-the-inve... Renaissance science: https://en.wikipedia.org/wiki/History... History of complex numbers: http://rossroessler.tripod.com/ https://en.wikipedia.org/wiki/Mathema... Proof that pi is irrational: https://www.quora.com/How-do-you-prov... and https://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: http://nobrow.net/shop/professor-astr... Atomic Adventure: http://nobrow.net/shop/professor-astr... Intergalactic Activity Book: http://nobrow.net/shop/professor-astr... Solar System App: http://www.minilabstudios.com/apps/pr... Find me on twitter, instagram, and my website: http://dominicwalliman.com https://twitter.com/DominicWalliman https://www.instagram.com/dominicwall... https://www.facebook.com/dominicwalliman 10,323 Comments rongmaw lin Add a comment... Huss Farsani Huss Farsani 2 years ago Just realized my current math skills are at the same level as those in 50,000 BCE. 16K DoS - Domain of Science Eric Zhan Eric Zhan 1 year ago (edited) The funny thing is every single item on the map could probably have a full-scale map of its own. 7.1K DoS - Domain of Science Thishiro KH Thishiro KH 1 year ago When you find solutions for math it called "pure math" When math find solutions for you it called "applied math" 7.4K nono nono 11 months ago (edited) I love being a math student and coming back here once a semester and tick off more boxes 1.7K Pranav Pandey Pranav Pandey 8 months ago Nice illustrations!👍 192 Ananya Akruwala Ananya Akruwala 5 months ago 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. 😊 326 WGF inc. WGF inc. 1 year ago “The more you know, the more you know how little you know” - Someone Smart 5.3K Pamela Francis Pamela Francis 1 year ago 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! 108 Yuzuru Yamai Yuzuru Yamai 1 year ago 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. 190 Sasuri Sasuri 11 months ago 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. 76 Aref Eshghi Aref Eshghi 1 year ago While studying math in high school, we had different subjects related to math, including linear algebra, geometry., calculus, differentials and integrals, etc. I always thought these are very related, why doesn't our teachers start by telling us about the relation of these topics and then start lecturing us?! I went to the university, having the same question until I drew a semi-map in my mind for myself while I was doing my Masters! By the end of my PhD, I had a relatively good map in my mind! :))) But I'm glad that finally someone answered my question, almost comprehensively! Thank you! :) A related note: In my point of view, the interesting is that our brain loves creating categories and then, making relations between them, and by this, learn stuff. And this is one of the best methods to create machines that understand and make sense of the stuff. 26 TheTaghound TheTaghound 9 months ago 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. 51 Sreekar G Sreekar G 2 years ago “The mathematics we do in school doesn’t quite do the field of mathematics justice.” So damn true 3.6K pgopa - Priti Natyam pgopa - Priti Natyam 1 year ago Awesome map of mathematics!! I wish I had known this when I was studying pure maths at an introductory level - specifically how it connects and comes together!!! 31 goldCrystalhaze goldCrystalhaze 11 months ago 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. 8 Beulah Venice Bayhon Beulah Venice Bayhon 7 months ago I love it! And I agree with what he said in the end. I became interested in mathematics (although not good at it) because of how amazing that when you solve numbers and equations, you will arrive to an answer that is related to what the universe offers. 12 Jordan Sullivan Jordan Sullivan 1 year ago Yessssss! I so wish that more of the juicy interesting math was taught in primary and secondary school -- so many people mistakenly believe they hate math, but in reality they have only seen a tiny corner of the possibilities! 10 Countably infinite Countably infinite 1 year ago I used to think I was good at math in high school. Then university came and I get destroyed by discrete mathematics cause it’s much more theory than calculus or algebra 194 Ultimate Loser Ultimate Loser 1 year ago 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. 3K Luke T. Luke T. 1 year ago I loved this!!! Really nicely laid out. Brought back lots of memories from university. Great editing too. Props from NL, Canada 16 BehindThePie BehindThePie 2 years ago 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. 2.4K DoS - Domain of Science Marian Mhil Baladjay Marian Mhil Baladjay 1 year ago 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) 40 AJMaths AJMaths 1 year ago @Marian Mhil Baladjay 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. 65 Marian Mhil Baladjay Marian Mhil Baladjay 1 year ago @AJMaths Thank you! I will do my best to learn!!!😊😊😊 12 Marian Mhil Baladjay Marian Mhil Baladjay 1 year ago @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!!! 4 Jordan Jordan 1 year ago Mhil Baladjay everyone started by learning basic math lol 2 Marian Mhil Baladjay Marian Mhil Baladjay 1 year ago @Jordan Ahh hahaha I know😆😅✌ 3 Ahmad AG Ahmad AG 1 year ago @AJMaths the difference is high school they have incredible amounts of memorisation in real math you learn to read the langauge and understand it's core concepts allowing to self teach surprisingly well 10 Jordan Jordan 1 year ago Mhil Baladjay idk why it says I responded to you but I meant to say that to the original connector of this thread 1 Jordan Jordan 1 year ago Ahmad Abdul-Ghaffar if you learn the concepts in high school math, you can derive the things that you’re supposed to memorize, that’s what I did in high school and that’s what you should always do in math 1 x [a] x [a] 7 months ago 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 11 Hemanth Nalluri Hemanth Nalluri 3 months ago (edited) Despite some flaws, this video was very well-written and properly simplifies something that just doesn't make sense to a lot of people. Well done, Dr. Walliman! 2 Joubin Lee Joubin Lee 5 months ago 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! 7 Lianne Byrne - The Productivity Mentor Lianne Byrne - The Productivity Mentor 6 months ago This was brilliant, thank you! I wish I had seen this big picture when I was at school. I am a big picture thinker so maths sometimes scares me, but this makes sense now. Thank you! 10 Louis Andrew Newton Louis Andrew Newton 11 months ago So cool man! Would be an awesome way to visualise courses on maths - maybe as a skill tree! Do you have any versions of this map that are printable in poster form? 10 Roland Heinrich Roland Heinrich 1 year ago Even though I have an Engineering Ph.D. with a minor in Applied Mathematics and had cumulatively 20years of formal mathematics training, I have never seen such a succinct and comprehensive summary of the field. Well done! 3.6K DoS - Domain of Science Mathtronomy Mathtronomy 7 months ago I agree with you, pure mathematics is a kind of art ❤ 8 strangerhythm strangerhythm 1 year ago (edited) This is really good, but there are some fairly major fields of study missing from the structures subcategory: Those are fields of study in Abstract Algebra such as rings, fields, modules, and lattices. The reason this is important is because structures don't always have an isomorphic relationship to number systems, although number systems form, or can be formed into groups, rings, and fields. Matrices/vector spaces are an algebraic structure, usually over the real and/or complex numbers, but a function field or vector space with functions as vectors are a realm of study and application in themselves. But for an 11 minute video, this is an excellent summary! 3 The Chremmas The Chremmas 8 months ago Really cool! Its never too late to learn. Well done guys. 3 mizzmusicthief mizzmusicthief 1 year ago super glad i stumbled onto this videol. i got my degree in pure math, and hadn't even heard about all he things you put on this map so i really appreciate this video. keep up the great work! 4 Dario Persechino Dario Persechino 1 month ago This is wonderful, just the conceptual mapping I was looking for! Thank you :D SpectralBacon SpectralBacon 1 year ago 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. 1.7K MrTubularBalls MrTubularBalls 11 months ago "Mathematics is just something made up by humans" is a very strange way to interpret Goedel's incompleteness theorem. What it states is that sufficiently powerful formalisms, like predicate logic, can reason about themselves. This allows the expression of paradoxes. Solution: don't use such over-powered systems!.Defining systems with the "right"amount of power for a given task is now a major part of logic research. Something comparable happened with Russell's paradox, which led to the development of type theory. 9 Matthew A Matthew A 9 months ago Very comprehensive thanks for this and all of your other videos. My curious mind, which has an insatiable desire to learn more about math, science, philosophy and so on, thanks you. Really brilliant work. 2 Devon Plaza Devon Plaza 1 year ago A three dimensional model showing relational links would be awesome too! I know that would be hard but it would be LOVED!!! 2 Tariq Habib Tariq Habib 8 months ago Love it. Super brilliant, awesome visualization. Thanks so much for this work. Brandon Tea Brandon Tea 1 year ago GREAT video, honestly this inspire me to create similar content as well, been wanting to do that but, time management issues. Anyway, could you take a look at Chinese metaphysics? I didn't know the question to the usefulness of incomplete mathematics is a mysterious... In Chinese metaphysics, we're well aware that everything we conceptualise is directly or indirectly derived from nature, it only make sense if it could explain nature very well. 2 Colin Java Colin Java 2 years ago Some people think high level maths is just multiplying really big numbers together. 5.7K Mikhail Franco Mikhail Franco 7 months ago (edited) Glad to see Origins and Foundations in different parts of the map. So often these are conflated, and we are presented with historical development as if it were a search for foundations, which is not always true, and even when it is true, it is not always useful. Drakonus Drakonus 1 year ago The more I learn about things, the less I understand. 4.8K Barin Barin 9 months ago Thank YOU so much for your incredible contents. I'm always fascinated by the information you share in this channel! Keep it up 3 Lucas Mazzino Lucas Mazzino 1 year ago Simplemente BRILLANTE !!! Muchas gracias por crear este tipo de contenidos. Onebeets Onebeets 11 months ago 6th graders: i understand enough to be an adult! university graduates: proceeds to show this graph* 207 rmalara rmalara 6 months ago (edited) Great stuff.. thanks for making It so easy. I was wondering where would it fit the Fourier and Laplace transforms. They do really intrigue me. Thanks Travis Travis 10 months ago Outstanding examples, your a wonderful science communicator. People like you really help shift focus back to interest which a wonderfully slippery slope. Cheers and thank you. 1 izaiaz12 izaiaz12 3 years ago I wanna learn all of this. 3.9K Engineering with Dr. Kelsey Joy Engineering with Dr. Kelsey Joy 12 days ago Love this big picture view of mathematics with all the explanations and connections you present! Very cool video! Inspirational! 1 Marshall Weber Marshall Weber 8 months ago A wonderful overview of the field of math! I wonder if modeling deserves to be a category of its own on the applied side of things. 4 Pear Tree Education Inc. Pear Tree Education Inc. 13 days ago This is a great video, and I love your illustration! I can't wait to show it to our teachers! I should say that math in school is improving. At our own school, the focus is on applied math, even at a kindergarten level. There's no point 'learning' something if you can't use it! And, if you don't use it, you'll never really understand it or remember it! We teach through themes, so that allows us to use math in context (in the context of science-related and social studies-related topics) and enables us to think 'why would we use these math skills?'. In doing so, we quickly realised that in the real world, you use math in the same way as you've illustrated on your diagram: for statistical analysis, for physics calculations, for finance, for biological calculations, etc. A number is never just a number in our classes. It's a number with a value or measurement of something, e.g. $, kg, km/h, etc. As these skills can be used in many contexts, it allows us to continually practice these skills in these different contexts, yet with increasingly more challenging examples as the students become more familiar with them. It also challenges the students' schema (i.e. mental blueprint of how math works) and reinforces their prior learning (through re-learning). Another factor with applying math is that you realise that multiple math skills are often required to solve certain real-life problems, which makes learning much more time efficient. Alternatively, you realise that it makes no sense to teach certain math concepts separate from interrelated ones, e.g. teaching fractions separately from percentages, decimals and ratio (and then ironically expecting students to see they are related at a later grade level!). The challenge for us is to find applications that can be simplified for an elementary to high school level, since the moment you put math into context, it becomes much more challenging. In spite of this, because the math has a purpose, the students enjoy it. The students are intrinsically motivated to do more challenging versions of the same skills that other schools are teaching. With this in mind, our provincial exams (for BC) are now dedicated to applied math. The math skills are more much basic (more like grade 8-9 math), but in context. Ironically, there are students in other schools doing AP Math who struggle with these applied math exams, but can do calculus. Thomas Makryniotis Thomas Makryniotis 1 year ago It's fun how, after all these years in school and university, I can officially say that I've got a taste of almost all math areas described here... 13 Chin Fung So Chin Fung So 2 days ago This is a really great video!!! I wish all high school students get to see this to get the context of what they are learning! Hemansh Pandya Hemansh Pandya 1 year ago My Mathematics teacher used to say "Without mathematics the world would be zero, and that also belongs to Mathematics". 177 Vincent Self Vincent Self 8 months ago This is one of my favorite videos on the internet right now, I've watched twice. Thank you! Naim Mahmud Rahad Naim Mahmud Rahad 3 months ago so precise and informative....dude...! you're doing a great job...! keep it up <3 Logan Gantner Logan Gantner 4 months ago I can honestly say that I have spent an extended amount of time studying almost every subject on this map. And I feel like a moron in every one of these categories! Every single branch of math eventually gets excessively complicated; you never actually reach the knowledge boundaries in any of these topics unless you devote your life to it. 1 임im 임im 6 months ago Im so grateful to watch this video and I felt like maybe its a sign cuz bro I'm really stress with math right now! And this video helped me to give math a second chance. Thank you so much 3 Ot Ratsaphong Ot Ratsaphong 1 year ago Great overview and history of mathematics 👍 I touch on statistical analysis and machine learning for stock market analysis. Also love the artistic aspects of maths. 1 DrexFactor Poi DrexFactor Poi 5 years ago What are the odds you'd be willing to print up posters of your map? I'd surely buy one :) 1.7K paul motter paul motter 5 months ago I’ve been thinking recently about making a mathematics flow chart. Generally it would be used to visualize how to solve many (definitely not all) types of problems. The only reasons I haven’t started is my very limited knowledge of the big picture and being lazy. For reference I’m a calc1 student. I would probably limit the chart to only deal with pure mathematics. 3 rishikkesh suresh rishikkesh suresh 1 year ago MATH ---- YES EXAM ---- NO 2.1K Malkidrs Malkidrs 6 months ago 10:24 exactly this... like after i learnt how some type of math work and understand it, i just subconsciously feel that it can be used everywhere in the universe for something, like it has an absolute purpose, then i can feel some sort of dopamine rush after preceding to do a few more questions on that certain math 'pattern', which gives me confidence and more faith in my maths. 2 Frank Damelio Frank Damelio 10 months ago This makes math look like so much fun! Nice job. houghtor houghtor 6 months ago Love this and your summation of what you love about the insights maths gives you James Brodski James Brodski 2 months ago Amazing video! So beautiful to watch. Thank you so much for it. 1 Jesas Maria Jesas Maria 5 months ago Great video! I'm trying to get more into maths, especially game theory right now. Tudiflex Tudiflex 2 years ago Maths are cool But alike other subjects, school makes it suck 1.8K Classroom Teacher Classroom Teacher 6 months ago That's a very comprehensive discussion! Good job! Aaron Kalahar Aaron Kalahar 4 months ago Thank you for this. So well made!!! Sundar B. Sundar B. 6 months ago You have done not just justice but given such a glimpse in to the entire Mathematics that I have never ever known before. Great job indeed. oumaima oueghleni oumaima oueghleni 1 year ago After this video, I am officially in love with mathematics . Thank you for making it ❤ 1 Shana Shinigami Shana Shinigami 7 months ago Such an interesting video, thank you for all that effort, great visualisation and beautiful storyline throughout it all 1 tAroi tAroi 2 years ago 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 :) 315 Keith Sedoripa Keith Sedoripa 1 year ago Back in highschool I always asked myself how are these mathematical equations and logic can be useful. I never knew the concept. I just do the math and didn't know the purpose. It was only then when I got to college I realize the meaning. I actually started to like it now that I can see the bigger picture. 1 SlashZooka SlashZooka 1 year ago (edited) First of all, thanks for this interesting video! 9:34 I know there are people who say mathematics was alredy "there" and everything is based on it. But if you think of it, we've just watched our enviorment and we literally try to break down everything to mathematical descriptions when we put something in context with math. This only works because the world we life in has constants (which as said in the definition never change). Systems can't change irrational, there is not a real "random" even the chaos-theory doesn't describe it. It's basically just a series of chain reactions. Everything has a system somehow that we can try to describe. The whole world couldn't exist without these rules, without some constants. So, ofcourse the systems are there, but the mathematical description is (imo obviously) created by humans. But this is a wonderful fact, because it allows us to understand more and more of the world we life in. Basically you can say, there is no "impossible" sometimes it's just hard and complex to achieve. In History people said, the humans will never be able to fly. But now we have airplanes. Solutions are often not straight forward, maybe we can't realize the things directly like we have them in our imagination, but I'm sure we'll always find alternatives some day to achieve atleast a similar effect. I'm sorry if I did any mistakes in writing. 1 Hajerah Umar Hajerah Umar 10 months ago WOW. As someone who had math anxiety before, it surprises me how much I'm finding it to be intellectually stimulating. I just came after watching the video 'Math has a fatal flaw' which just made my mind explode. Thank you for this video, I now have some other documentaries to watch, and things to learn. 4 seok0511kim seok0511kim 1 year ago thanks a lot! it’s very helpful to get the big picture of math :) Elvis Sibilia Elvis Sibilia 1 year ago Nice video. Philochrony is the theory that describes the nature of time and demonstrates its existence. Philochrony establishes an analogy between zero and time thus arising the linear zero. 1 Homer Calcalavecchia Homer Calcalavecchia 3 years ago I'm more amazed at the fact that you didn't try to pitch me a brilliant subscription at the end 4K Grid Matrix Grid Matrix 1 year ago Thank you so much for the mapping/visualization of the mathematical world. I have the next problem, at least for me. How/where do I go to learn let say calculus, fourier, intergration and derivations? I really want to learn these things, but I find it hard finding good visualization or knowing what to start with. Is there anyone that have anything good from here? Lillianna Duff Lillianna Duff 3 years ago As a math major this really helped me get a glimpse of what I actually know and have built over so many years 76 peter kogl peter kogl 1 year ago Excellent, enjoyed it! Thank you! Nature Lover 💚 Nature Lover 💚 1 year ago Do you know I'm from India and I took Biology (means I can't study maths )but after watching this amazing video I thought I must took Maths... ❤️🤩 2 Alex Young Alex Young 6 months ago I could listen to him all day long and learn something new every time. I wish I have him as my teacher lol. Venus Venus 11 months ago Thank you! This has helped so much. James Steven James Steven 5 months ago Having the right teacher to explain math can make you enjoy learning it. In my school, I never found one so here I am on youtube. 😔 1 Kratagya Agarwal Kratagya Agarwal 2 years ago 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 723 편경훈 편경훈 1 year ago 하나의 지도에 수학 영역의 전체를 한 눈에 볼 수 있는 좋은 영상인 것 같습니다. 또 하나의 영역에서 다른 영역으로 전개해 나갈 때 역사적인 흐름에 따라서 사건을 설명해주셔서 이해가 훨씬 쉬웠던 것 같습니다. 30 Neshie Neshie 1 month ago I'm getting ready to apply for graduate programs in mathematics and it's kind of gotten to the point where learning new branches of mathematics doesn't really feel like their own subject anymore, but rather an amalgamation of everything else I've learned in math plus one or two additional details. It's pretty weird tbh 1 Damocles Damocles 1 day ago I’m a Junior in Aerospace, pretty cool to know that I’ve mastered probably 50% of the subjects in the video. John Hatcher John Hatcher 1 year ago Great video... however I have a different take on the implication of Godel's theorem: This video suggests that the theorem implies that mathematics is a made up human construct. I'd say that the theorem suggests quite the opposite... that there does not exist a "made up by humans" formal system that completely captures/describes all of mathematics. Godel's theorem is more about the limitations of formal systems. 2 omkar kamble omkar kamble 2 months ago Thanks for this. Really usefull and the way you explained ❤️💯😍 Brendan Brendan 4 years ago (edited) This was really interesting, thanks! I only recently started to enjoy and appreciate math after years of struggling with it. The right mindset is everything. 86 Stepan Stulov Stepan Stulov 1 year ago Would be epic to see a similar map for software development. Like island of embedded software and continent of web. I know, not this channel's focus but nevertheless. 1 Gilberto Torres Gilberto Torres 1 year ago Props to you for summing it up so well Blue Angel Blue Angel 1 year ago Thank you so much! This was excellent. Rashid Iqbal Academy Rashid Iqbal Academy 4 months ago very informative. awesome work 👍 Aj Pancho Aj Pancho 6 months ago I learned a lot about this wonderful video about mathematics and I appreciated it thank you Nicholas Lipanovich Nicholas Lipanovich 4 years ago You should do many more of these. I'm envisioning map of computer science, map of statistics, map of electrical engineering, etc. 189 Sreya Ghosh Sreya Ghosh 1 year ago It's amazing! Thank you so much! KingsleyIII KingsleyIII 5 years ago Mapthematics. 14K DoS - Domain of Science Abdul Gani Punjabi Abdul Gani Punjabi 5 months ago Thank you soo much for this clarity 💯 Nimbo Stratus Nimbo Stratus 1 year ago 4:33 fractals aren't always the same as you zoom in, it's just the mathematics of rough shapes that are never smooth no matter how far you "zoom in" James Barclay James Barclay 6 months ago Learning complex numbers, then years later learning how they’re applied to AC circuits? And how that leads to transfer functions and Bode plots and Fourier transforms, and then further to Z transforms and DSP? That was an incredible coupling of pure and applied mathematics for me. Isabella Diem phuong Isabella Diem phuong 3 months ago Your video are amazing and you inspired me to learn more things:) TheNob TheNob 6 months ago This is by far the most awesome summary I've ever encountered nikolas doubourhydes nikolas doubourhydes 5 years ago keep up the great job, you should do one for chemistry some day 622 DoS - Domain of Science Hedi Muhamad Hedi Muhamad 1 day ago This is the main thing that anyone who is just starting to learn mathematics should know, without it the student will be frustrated and hate mathematics, because of its foggy world. Thanks man. <3 Willy H. R. Willy H. R. 6 months ago My math verbal mapping in one simple sentence would be: "Exploring math entities by expressing or linking patterns from various perspectives." If this simple sentence is well inculcated with appropriate practices, everyone can learn math easily. My 30 years math teaching experience across the world. Joz Joz Joz Joz 5 months ago It's really superb to know about the maths how it works from our very beginning...tq so much for your videos..it's very clear for my children to understand about the maths as a story...so happy 😊... Eli Jai Eli Jai 6 months ago Computer science made me love maths again. Once something clicks, it feels like your eyes have being open to nature itself! Twisted Twisted 10 months ago What a truly awesome video . . . Great job man. Michael Colon-Arce Michael Colon-Arce 1 year ago I love the way in which you describe the connections and applications of math it has really broadened my horizons , i wish we had more math teachers like you in our schools. 11 Panda's Data Diaries Panda's Data Diaries 3 weeks ago Thanks for the great overview! SHEJIN ALEX VARGHESE SHEJIN ALEX VARGHESE 3 months ago Hey Man, This was a very interesting video. Great work. Brother if I were to start learning math at the age of 25. Considering I have been extra-ordinarily poor at Math throughout my life so far, where should I begin according to you?