Domain of Science - 2017-02-01
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. If you would like to buy a poster of this map, they are available here: North America: https://store.dftba.com/products/map-of-mathematics-poster Everywhere else: http://www.redbubble.com/people/dominicwalliman/works/25095968-the-map-of-mathematics French version: https://www.redbubble.com/people/dominicwalliman/works/40572671-the-map-of-mathematics-french-version?asc=u Spanish Version: https://www.redbubble.com/people/dominicwalliman/works/40572693-the-map-of-mathematics-spanish-version?asc=u I have also made a version available for educational use which you can find here: https://www.flickr.com/photos/95869671@N08/32264483720/in/dateposted-public/ 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/Mathematics Earliest human counting: http://mathtimeline.weebly.com/early-human-counting-tools.html First use of zero: https://en.wikipedia.org/wiki/0#History http://www.livescience.com/27853-who-invented-zero.html First use of negative numbers: https://www.quora.com/Who-is-the-inventor-of-negative-numbers Renaissance science: https://en.wikipedia.org/wiki/History_of_science_in_the_Renaissance History of complex numbers: http://rossroessler.tripod.com/ https://en.wikipedia.org/wiki/Mathematics Proof that pi is irrational: https://www.quora.com/How-do-you-prove-that-pi-is-an-irrational-number and https://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational#Laczkovich.27s_proof 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-astro-cats-frontiers-of-space/ Atomic Adventure: http://nobrow.net/shop/professor-astro-cats-atomic-adventure/ Intergalactic Activity Book: http://nobrow.net/shop/professor-astro-cats-intergalactic-activity-book/ Solar System App: http://www.minilabstudios.com/apps/professor-astro-cats-solar-system/ Find me on twitter, instagram, and my website: http://dominicwalliman.com https://twitter.com/DominicWalliman https://www.instagram.com/dominicwalliman https://www.facebook.com/dominicwalliman
“The mathematics we do in school doesn’t quite do the field of mathematics justice.”
So damn true
@young hirsch Lmao no, even in a pure maths mayor you will not encounter most of maths there is because there is just too much.
Yeah, mathematcs is not doing stupid calculations that you can do on a calculator mathematics is the ability to problem sove.Period.
Z
W
@Soyoko U. Indeed. It has been said that the last person who could understand the whole of mathematics was Poincaré. And since then the subject has exploded in so many directions.
Some people think high level maths is just multiplying really big numbers together.
@Richard Rutledge No, not all maths can be boiled down to arithmetic.
@Santiago Rodriguez Newton Not only does it boil down to SIMPLE ADDITION AND SUBTRACTION, but it boils down to SIMPLE ADDITION AND SUBTRACTION of JUST TWO NUMBERS: 1 and 0. If you're too ignorant to figure this out, then you'll never be able to keep up with any advanced conversation.
Sadly, countlessly many people think in that way
Richard Rutledge Again, false, math is based on axioms that DEFINE arithmetic as it is. Computers are based on the Turing Machine and Boolean Algebra, which then allow for arithmetical operations.
That's just high level physics
0:08 what you learn in class
0:10 what’s on the test
what i absorb in class 0:20
HAHA true!
@ScienceDrummer you dumpster
Football Live calm down bro you dedicate your life to socker and it’s ok
Leandro Silva and how can someone who dedicate their life to studying be dumb
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...
@Jesus Christ says the axiomatic human of the west
Maths are cool
But alike other subjects, school makes it suck
Khan Academy is the best!!!!
@Clip It! 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.
@Clip It! True!!
but school doesn’t give me time to learn on my own
School makes everything suck
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
Arkady Zhelezniak
Cayley’s Theorem enters the chat
@Daniel Belkin Category Theory is mentioned in the Foundations section at the end.
The trick is to stay awake 😋
@Daniel Belkin Yeah, this video is very badly made.
@Daniel Belkin Category theory was mentioned.
College: Applied Mathematics
Business: MS Excel
I ♥ spreadsheets
deep
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!
I think Math has a lot of problems and should see a therapist ASAP.
I love the way he pauses for a second after he says " some infinity are bigger than others " 3:02
@iDroid 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.
U deserve a lot more like s
I took it as a joke since math/physics professors tend to say quite frequently
True like thinking about drawing infinite length straight lines from the centre of a circle. They will always diverge a and there are an infinite number of infinities
@iDroid No, that's flat out false.
0:12
Cos = O/A
*Harvard wants to know your location*
@Dingo oh god ive been woshed
Bro I noticed that as well lol
cos = sin
Lol
@Dingo omg how did I not notice that
you mean cambrige?
I'm more amazed at the fact that you didn't try to pitch me a brilliant subscription at the end
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 YouTube and YouTube 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.
@Marctary Darius Don't get him started. He goes on forever.
CrimsonNite Plot twist : No one cares about you not caring, you're just being rude.
@CrimsonNite dude chill
Some youtuber give any content and ask to subscribe and some give great content and dont ask to subscribe because they know we will subscribe because of the content
The section "Foundations" has activated my insomnia.
I think that I might show this video to my classes at the beginning of the school year to show them how math is interconnected!
Do a quick Boolean algebra equation of 2B or not 2B and show them how computers intersect with Shakespeare! lol (Then show them the answer is 'unity' (1)!!!)
Virginity acquired
@[ Quax ] Changing from Math to Science: Virginity is not acquired. It is the natural initial condition at birth; and then lost later in life--except maybe in your case...
@Richard Rutledge LOL
The virgin group
my friends: "i dont have to be good at maths, i dont need it where i'm going"
me, after watching this: "BRUH"
I would like a T-shirt with all the map ;)
I wanna learn all of this.
@Don Vreeland I am in sir.
Lol same here
@Shriniwas Yadav bruh no not at all
@Robbie Rotten lol
Get to work ASAP and do not expect to actually know all of the mentioned subjects (which are pretty badly arranged).
“A Rubik’s Cube is an example of a permutation group”
Cayley: “Yes”
Every mathematics fan will buy this map!
I second that
Honestly, needs a lot more detail if I'm going to buy it; I want to be able to see specific branches of each genre of mathematical study. Bonus points if they encapsulate the whole thing without a border, since we will never find the end to mathematics - there will always be a new research field to explore.
You must remember the mathematics of the YouTube algorithm recommending this video more than 2 years later
my maths videos help your maths works.
I am so amazed by math always. I am weak in math but i love it so much how it tries to explains everything.
Lol same
Xd same
2:55 whaaaaat? i think my brain just fell out of my skull. Thanks 😵 (ps., this is marvellously fascinating: great job 👍)
Philosophy: I am the mother of science and logic.
Mathematics: what?!
1:53 is the trippiest thing I've ever seen
I love Maths so much , my dream is becoming a villant mathematician 😍
The holy trinity of math:
• Graph
• Equation
• Data set
Math is prediction.
"life without Maths is hard"
"Without maths life is more hard"
no one:
Indian high school mathematics:
I have covered all of it
Indians have so much potential in maths but since pure mathematics is not introduced in Higher Indian Education we can't bring out that potential. India is still a developing country so more emphasis is paid on applied maths, engineering and medical fields
@Ameya Chandra In Pure mathematics... trigonometry , algebra , differentiation , matrices , graphs are included in the indian high school syllabus..but I do agree with the point that Indians always lose in IMO but the only reason that it happens is bcuz people prepare for JEE which has a completely different syllabus than IMO .. people get colleges based on ur jee mains and advanced rank so people don't care about IMO
I am an Indian and this comment is pure bullshit.You can't cover all of it until you do a Phd in Mathematics.In the Msc course you have to choose some special topics like topolgy or something else.
@meow guyIt's probably the "no one" thing that he doesn't like.
@Amirul Azhar Omar an illiterate pakistani spotted 😂😂😂
But seriously get your facts cleared mate.. In India more than 98% population have access to toilets as of 2019 reports..
"How does one begin to describe the surd as a function rather than a relation?"
No, game theory is about a guy who talks about fnaf for a few years and then decided to make emotinal videos. Trust me, I have a PhD on this
He is know talking about yt bs
sigh
@Eric Daniel laws of governing dynamics
Dir Hell he actually uses a lot of math and science in his videos, but he’s also an emotional nerd, so yeah, pretty much.
@dbltrplx A NP-Completeness problem in computer science , were NP means that the POLYNOMIAL "algebraically , OR ALGORITHMICALLY "CANNOT BE dETERMINED", or is UNKNOWN Compared to a Parrell Programming Machine , were the computer HARDWARE or PROGRAM can "SOLVE" the entire problem space in terms of polynomial. time complexity for a Given time , because the ALGORITHM Seems to Run in PARRELL VS. "A LOGICAL or A LOGARITHMIC FUNCTION" , In CLASSICAL VON NUEMAN ARCHITECTURE
Rather than use a 'EXPOTENTIAL OR QUADRIATIC FUNCTION' in . ZEROTH ORDER TIME AND SPACE DOMAIN. in terms of time AND SPACE , because the problem space "DATA" is growing as fast than the computers Speed to solve the problem in N time , OR ANOTHER WAY OF SAYING IT because the Problem SPACE is REACHING a ' LIMIT as Fast as than the computation Complexity is GROWING. This Boils down to the Combining the "FUNCTION AL DOMAIN" Algebraically the computer is "functioning" in, time , meaning domain as in Program " DATA STRUCTURE" space and "ZEROTH ORDER FUNCTIONAL PROCESS Are the SAME"LIMITING CONCEPTS of the Functions and INVERSE functions are QUADRATICALY induced , THIS reduces the POLYNOMIAL to a FINTE LEVEL thereby Also reduces Computation Complexity and increasing the 'APPARENT 'speed of COMPUTATION TO solve the problem .
6:16 says all that is in the left side.... (Sad physicist cries heard)
mire al cielo y dije:
desearia que alguien separace todas las secciones de un tema en un diagrama.
youtube: me recomienda un video tuyo*
It’s kinda scary isn’t it how all or most of the high paying jobs either require a knowledge of mathematics or fundamentally rely on mathematics...
Literally every job requires maths.....
@Daniel de Burgh
Except being a filthy priest, those guys are the only ones that, really, don't need math, more than the economic revenue they have after sessions
@鳳凰院凶真 Who hurt you?
Not really, most highly payed managers or CEOs know jack shit about college level mathematics
and some people says maths is useless lmao
Math is a part of nature 🤷♂️
Nature is math
ah yes, a list of things that lower my GPA
@NiceWhenEarned RudeMostlyElse lol. If you "can't" understand a basic human concept then you're simply below intelligent or mentally retarded. So it's not him, it's his genetics, according to you.
Ha, math raised mine. English/writing lowered it. I just didn't do as well with a subjective subject like that where you're trying to feel out what the instructor is asking for. I would have done more math study if I had the choice at the time.
NiceWhenEarned RudeMostlyElse the school systems ruins everyone's GPA by making something inherently creative and logical into something that you just have to accept and memorize
@NiceWhenEarned RudeMostlyElse r/whooosh
(It's overused I'm sorry but seriously it's just a joke, no need to be so rude)
@Darticus the Great How do I make it creative again then?
You’ve successfully sparked so much interest in me! This is amazing
Wait till you start learning calculus and logarithms !
01:23 I'm so proud I recognised Leibniz
How come I’ve only done calculus the last 5 years in school?
" Hello internet, welcome to 7:19!"
Being a computer science student, I've touched so many of these areas , yet I've not really learnt anything...
me looking at this video the night before an optimization exam
This made me want to study math in school even more!
then you start studying and question 1 already messes you up.💔😪
This is one of the most beautiful videos Ive had the fortune to come across, thanks very much, I might buy it and print it on my wall to keep the inspiration every morning
Nobel prize for the best editing and the best explanation of 2019
My teacher : ~Explaining...
Me : I can't take this anymore :C
Youtube : Recommend this
Me : It's that simple? :D...
Shreya the work of a teacher is to teach something. If a student doesn’t learn it means the teacher has failed
Simple or organized?
Topaz Nico this has got to be one of the most insightful comments I have ever read on this platform.
Take a set theory class then reconsider
i think thats closely related to the dunning-kruger effect
mathematicians are a pain in the ass, for they just create more problems than they solve
most of those are not even problems
I was positively surprised how accurate this video was! Great job!
Although I would like to point out that the fact the decimal expansion of pi goes on forever, is not a special property of pi. This is in fact true for a lot of fractions.
The key difference between a rational number and an irrational number is that the decimal expansion of a rational number will after a finite amount of indices be periodic. In particular, the period of the expansion of 1/p with p a prime number which is not 2 or 5, is equal to the order of 10 in Z/pZ.
If a number is not periodic after some point, then it's not rational. This does not imply that every combination of numbers appear in the sequence. Liouville's number is an easy example of a transcendental number that only has 1's and 0's in it's expansion.
I don't know whether he popular belief that you can find your phone number in pi is actually true. However if this were the case, this is not because pi goes on forever. In fact, the fact that pi is irrational or even transcendental is not enough to show this.
"Some infinities are bigger than others"
Mathematics=infinity you would need a thousand lives to study maths
this is the video that I was looking for all my life
KingsleyIII - 2017-02-05
Mapthematics.
Matron - 2019-10-13
5,4 thousands :(
Orpheus - 2019-11-29
Only clicked on this video to leave that comment. Damn you!
Ace Bell - 2019-11-30
WHEESE
Lobster - 2020-01-10
Thank you.
Dani Gorodetsky - 2020-03-08
Mapthematics => map the matics => Map The Matix