Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline.Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A proof consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of the theory under consideration.Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science and the social sciences. Although mathematics is extensively used for modeling phenomena, the fundamental truths of mathematics are independent from any scientific experimentation. Some areas of mathematics, such as statistics and game theory, are developed in close correlation with their applications and are often grouped under applied mathematics. Other areas are developed independently from any application (and are therefore called pure mathematics), but often later find practical applications. The problem of integer factorization, for example, which goes back to Euclid in 300 BC, had no practical application before its use in the RSA cryptosystem, now widely used for the security of computer networks.Historically, the concept of a proof and its associated mathematical rigour first appeared in Greek mathematics, most notably in Euclid's Elements. Since its beginning, mathematics was essentially divided into geometry and arithmetic (the manipulation of natural numbers and fractions), until the 16th and 17th centuries, when algebra and infinitesimal calculus were introduced as new areas. Since then, the interaction between mathematical innovations and scientific discoveries has led to a rapid lockstep increase in the development of both. At the end of the 19th century, the foundational crisis of mathematics led to the systematization of the axiomatic method, which heralded a dramatic increase in the number of mathematical areas and their fields of application. The contemporary Mathematics Subject Classification lists more than 60 first-level areas of mathematics.
Source: Mathematics (wikipedia.org)
Related links
Collatz Conjecture in Color - Numberphile
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This video features Alex Bellos. More info and links in full description.
Extra footage with Alex and coloring: https://youtu.be/w8nc8wbgXPU
Or real-time video of the coloring: https://youtu.be/wH141HLD57o
Our previous Collatz Conjectur
UNCRACKABLE? The Collatz Conjecture - Numberphile
Catch David on the Numberphile podcast: https://youtu.be/9y1BGvnTyQA
Professor David Eisenbud on the infamous Collatz Conjecture, a simple problem that mathematicians may not be "ready" to crack.
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Extra footage from this interview: https://youtu
The unexpected maths problem at work during the women's World Cup
There was something strange about the recent Women's World Cup in Australia. If you were paying close attention, you might have spotted it. Many of the international teams had players who were born on the same day of the year – they shared birthdays. What was going on?
Benford's law
Benford's law, also known as the Newcomb–Benford law, the law of anomalous numbers, or the first-digit law, is an observation that in many real-life sets of numerical data, the leading digit is likely to be small.
Roger Penrose explains Godel's incompleteness theorem in 3 minutes
good explanation
from his interview with joe rogan
https://www.youtube.com/watch?v=GEw0ePZUMHA
Elliptical Pool Table - Numberphile
A game to play on the elliptical table: http://youtu.be/3WHBlPvK3Ek
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And more extra footage: http://youtu.be/pulp55gTKGE
Alex Bellos' Loop Table website: http://www.loop-the-game.com
Alex discusses the topic in his book Alex Through the Looking
The numbers that are too big to imagine
What's the biggest number you can think of? When I was a child, it's the kind of question we'd ask each other in the school playground.
Explaining the SECRET of Penrose Patterns
The first 200 people to https://brilliant.org/minutephysics get 20% off an annual premium subscription to Brilliant. Thanks to Brilliant for their support.
This video is about a better way to understand Penrose tilings (the famous tilings invented by Roger Penrose that never repeat themselves but s
Why Is 1/137 One of the Greatest Unsolved Problems In Physics?
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The Reciprocals of Primes - Numberphile
Matt Parker explores the work of William Shanks - and boots up the ShanksBot.
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Matt Parker's 2022 Pi Day Video: https://youtu.be/dtiLxLrzjOQ
Discussing William Shanks on Objectivity: https://youtu.be/7yTXMeiVBCc
Prime Number playlist: https://b
Why π^π^π^π could be an integer (for all we know!).
Check out the Jane Street programs if you're considering a mathematics/finance/programming job:
https://www.janestreet.com/join-jane-street/our-programs/
Here is Tim Gowers's reply to the original tweet:
https://twitter.com/wtgowers/status/1346212151581700096
Start your Schanuel's Conjecture journ
Euler's Formula - Numberphile
Tom Crawford shows us some cool things about Euler's Formula... Check https://brilliant.org/numberphile for Brilliant and get 20% off their premium service (episode sponsor)
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Tom Crawford's website, with links to his work and other outreach: htt
Twin Proofs for Twin Primes - Numberphile
With Ben Sparks... Check https://brilliant.org/numberphile for Brilliant and get 20% off their premium service (episode sponsor)
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Twin primes with James Maynard: https://youtu.be/QKHKD8bRAro
Ben Sparks on the Numberphile Podcast: https://youtu.
Goldbach Conjecture - Numberphile
Professor David Eisenbud on the famed Goldbach Conjecture.
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Catch David on the Numberphile podcast: https://youtu.be/9y1BGvnTyQA
Extra footage from this interview: https://youtu.be/7D-YKPMWULA
Prime Playlist: http://bit.ly/primevids
Prime Num
Big Factorials - Numberphile
Large factorials and the use of Stirling's Approximation. Featuring Professor Ken McLaughlin.
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Professor McLaughlin is based at Colorado State University: https://www.math.colostate.edu/~kenmcl/
We filmed this during his time at the Mathematica
Is The Metric System Actually Better?
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All the Numbers - Numberphile
Matt Parker talks about numbers - as he often does. His book "Humble Pi" is at: http://bit.ly/Humble_Pi
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The book on Amazon: https://amzn.to/2NKposg
Numberphile podcast is on your podcast player.
Or the website is: https://www.numberphile.com/p
What is a Number? - Numberphile
Featuring Asaf Karagila.
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Asaf is a UKRI Future Leaders Fellow. Asaf's blog - http://karagila.org
Asaf's Twitter - https://twitter.com/AsafKaragila
Numberphile podcast featuring Asaf - https://youtu.be/b6GLCTh5ARI
All the Numbers with Matt Pa
The Most Wanted Prime Number - Numberphile
Featuring Neil Sloane.
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Neil Sloane is the founder of The OEIS: https://oeis.org
More videos
Witness Numbers (and the truthful 1,662,803) - Numberphile
Featuring Matt Parker - more Parker links below.
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MATT PARKER STUFF
Stand-Ups Maths on YouTube: https://www.youtube.com/user/standupmaths
Matt's
What is the factorial of -½?
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Here is all the integration you ever wanted over on my second channel: https://youtube.com/mattparker2
Thanks to Ben Sparks for helping with all of the plots for this video. Ben's companion video on their chann
Infinitely Many Touching Circles - Numberphile
Featuring Matt Henderson.
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Matt Henderson: https://twitter.com/matthen2
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The Doomsday Algorithm - Numberphile
Featuring James Grime.
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James Grime: https://www.singingbanana.com
John Conway: http
Protecting Privacy with MATH (Collab with the Census)
This video was made in collaboration with the US Census Bureau and fact-checked by Census Bureau scientists. Any opinions and errors are my own. For more information, visit https://census.gov/about/policies/privacy/statistical_safeguards.html or search "differential privacy" at http://census.gov.
The Simplest Math Problem No One Can Solve
The Collatz Conjecture is the simplest math problem no one can solve — it is easy enough for almost anyone to understand but notoriously difficult to solve. This video is sponsored by Brilliant. The first 200 people to sign up via https://brilliant.org/veritasium get 20% off a yearly subscription.
The Volume of a Sphere - Numberphile
Johnny Ball discusses Archimedes and the volume of a sphere.
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Johnny Ball: https://johnnyball.co.uk
More Numberphile videos with Johnny
Mandelbrot set
The Mandelbrot set (/ˈmændəlbroʊt, -brɒt/)[1][2] is the set of complex numbers c{\displaystyle c} for which the function fc(z)=z2+c{\displaystyle f_{c}(z)=z^{2}+c} does not diverge to infinity when iterated from z=0{\displaystyle z=0}, i.e.
Parabolas and Archimedes - Numberphile
This video features Johnny Ball.
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Johnny Ball: https://johnnyball.co.uk
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Jo
How they found the World's Biggest Prime Number - Numberphile
Featuring Matt Parker...
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See part one at: https://youtu.be/tlpYjrbujG0
Part three on Numberphile2: https://youtu.be/jNXAMBvYe-Y
Matt's interview with Curtis Cooper: https://youtu.be/q5ozBnrd5Zc
The previous record: https://youtu.be/QSEKzFGpCQs
Matt Parker: Stand-up Maths Routine (about barcodes)
Matt Parker performs a stand-up maths routine about barcodes at the Hammersmith Apollo, as part of the 2011 Uncaged Monkeys national tour. http://standupmaths.com/
Stand-up comedy routine about Spreadsheets
Matt Parker’s comedy routine about spreadsheets. From the Festival of the Spoken Nerd DVD: Full Frontal Nerdity
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What was the first (known) maths mistake?
Thanks to Waterstones for choosing Humble Pi as a 'top 100' paperback of the year.
https://www.waterstones.com/book/humble-pi/matt-parker/9780141989143
Signed copies are available at Maths Gear. It's cheaper at Waterstones, but not signed. You choose!
https://mathsgear.co.uk/collections/books/produ
Tribonacci Numbers (and the Rauzy Fractal) - Numberphile
Edmund Harriss introduces a very cool tiling and talks about Tribonacci Numbers.
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Numberphile Podcast: https://www.numberphile.com/podcast
Or on YouTube: http://bit.ly/Numberphile_Pod_Playlist
More Edmund on Numberphile: http://bit.ly/Ed_Harris
Don't Know (the Van Eck Sequence) - Numberphile
Neil Sloane on the Van Eck Sequence... Check out Brilliant (get 20% off their premium service): https://brilliant.org/numberphile (sponsor)
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Van Eck sequence on OEIS: https://oeis.org/A181391
How many chess games are possible?
Dr James Grime talking about the Shannon Number and other chess stuff.
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NUMBERPHILE
Website: http://www.numberphile.com/
Numberp
The Discovery That Transformed Pi
For thousands of years, mathematicians were calculating Pi the obvious but numerically inefficient way. Then Newton came along and changed the game. This video is sponsored by Brilliant. The first 314 people to sign up via https://brilliant.org/veritasium get 20% off a yearly subscription.
Happy P
357686312646216567629137 - Numberphile
Truncatable Primes with Dr James Grime... Check out Brilliant (and get 20% off their premium service): https://brilliant.org/numberphile (sponsor)
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Zeno's Paradox - Numberphile
Dr James Grime is back and talking about tortoises.
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In many ways this video follows on from http://www.youtube.com/watch?v=bFNjA9LOPsg and then http://www.youtube.com/watch?v=CMP9a2J4Bqw
James Grime's website is: http://singingbanana.com
NUMB
Is zero an even number?
Superstorm Sandy had many consequences, some easier to foresee than others. Millions experienced floods and power cuts, the New York marathon was cancelled, and pictures of sharks in the city appeared on the internet. Another outcome was to draw attention to the unique position of the number zero.
Fibonacci Mystery - Numberphile
Brady's view on people who write: "FIRST" - http://youtu.be/CmRh9tFYC68
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Dr James Grime on the Pisano Period - a seemingly strange property of the Fibonacci Sequence.
Available Brown papers: http://periodicvideos.blogspot.co.uk/2013/09/brown.ht
The Golden Ratio (why it is so irrational) - Numberphile
Catch a more in-depth interview with Ben Sparks on our Numberphile Podcast: https://youtu.be/-tGni9ObJWk
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Golden seeds limited edition T-Shirt: https://teespring
The Feigenbaum Constant (4.669) - Numberphile
Binge on learning at The Great Courses Plus: http://ow.ly/Z5yR307LfxY
The Feigenbaum Constant and Logistic Map - featuring Ben Sparks.
Catch a more in-depth interview with Ben on our Numberphile Podcast: https://youtu.be/-tGni9ObJWk
Ben Sparks: https://twitter.com/SparksMaths
Random numbers: htt
Euclid's Big Problem - Numberphile
Trisecting angles and calculating cube roots was a big problem for Euclid and his cohorts. Discussed by Zsuzsanna Dancso at MSRI.
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TRISECT WITH ORIGAMI: http://youtu.be/SL2lYcggGpc
CIRCLE THE SQUARE: http://youtu.be/CMP9a2J4Bqw
Support us on Pat
The Riemann Hypothesis, Explained
The Riemann hypothesis is the most notorious unsolved problem in all of mathematics. Ever since it was first proposed by Bernhard Riemann in 1859, the conjecture has maintained the status of the "Holy Grail" of mathematics. In fact, the person who solves it will win a $1 million prize from the Clay
A proof that e is irrational - Numberphile
Professor Ed Copeland shows a proof by Joseph "Voldemort" Fourier that e is irrational.
Check out episode sponsor http://KiwiCo.com/Numberphile for 50% off your first month of any subscription. The crates are great!
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Ed Copeland is a physics pro
The Dollar Game - Numberphile
Featuring Holly Krieger... Check out Brilliant (and get 20% off their premium service): https://brilliant.org/numberphile (sponsor)
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With Dr Holly Krieger from Murray Edwards College, University of Cambridge.
Check out the monster dollar game s
Loop (graph theory)
In graph theory, a loop (also called a self-loop or a buckle) is an edge that connects a vertex to itself. A simple graph contains no loops. In a graph with one vertex, all edges must be loops. Such a graph is called a bouquet.
The simple maths error that can lead to bankruptcy
As we head into 2021, Worklife is running our best, most insightful and most essential stories from 2020. Read our full list of the year’s top stories here. Fifteen years ago, the people of Italy experienced a strange kind of mass hysteria known as “53 fever”.
ANU QRNG – Quantum random numbers
This website offers true random numbers to anyone on the internet. The random numbers are generated in real-time in our lab by measuring the quantum fluctuations of the vacuum. The vacuum is described very differently in the quantum physics and classical physics.
Noli turbare circulos meos!
According to Valerius Maximus, the phrase was uttered by the ancient Greek mathematician and astronomer Archimedes. When the Romans conquered the city of Syracuse after the siege of 214–212 BC, the Roman general Marcus Claudius Marcellus gave the order to retrieve Archimedes.
Inca Knot Numbers - Numberphile
Alex Bellos discusses how the Incans used knots in string (Quipu) to record numbers.
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Check out the Language Lover's Puzzle Book) on Amazon: htt
How modern mathematics emerged from a lost Islamic library
The House of Wisdom sounds a bit like make believe: no trace remains of this ancient library, destroyed in the 13th Century, so we cannot be sure exactly where it was located or what it looked like.
Euler's identity
Euler's identity is named after the Swiss mathematician Leonhard Euler. It is considered to be an exemplar of mathematical beauty as it shows a profound connection between the most fundamental numbers in mathematics.
Path-based strong component algorithm
In graph theory, the strongly connected components of a directed graph may be found using an algorithm that uses depth-first search in combination with two stacks, one to keep track of the vertices in the current component and the second to keep track of the current search path.
Strongly connected component
In the mathematical theory of directed graphs, a graph is said to be strongly connected if every vertex is reachable from every other vertex. The strongly connected components of an arbitrary directed graph form a partition into subgraphs that are themselves strongly connected.
Directed graph
In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges often called arcs.
Cycle (graph theory)
In graph theory, a cycle in a graph is a non-empty trail in which only the first and last vertices are equal. A directed cycle in a directed graph is a non-empty directed trail in which only the first and last vertices are equal.
Graph theory
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called links or lines).
Tarjan's strongly connected components algorithm
Tarjan's strongly connected components algorithm is an algorithm in graph theory for finding the strongly connected components (SCCs) of a directed graph.
The violent attack that turned a man into a maths genius
This article was inspired by an episode of The Outlook Podcast, where you can hear more about Jason Padgett's experience in his own words. Jason Padgett sees maths everywhere.
From The MIT Press Reader
One of the key findings over the past decades is that our number faculty is deeply rooted in our biological ancestry, and not based on our ability to use language. Considering the multitude of situations in which we humans use numerical information, life without numbers is inconceivable.
The maths problem that could bring the world to a halt
It’s not easy to accurately predict what humans want and when they will want it. We’re demanding creatures, expecting the world to deliver speedy solutions to our increasingly complex and diverse modern-day problems.
The myth of being 'bad' at maths
Are you a parent who dreads having to help with maths homework? In a restaurant, do you hate having to calculate the tip on a bill? Does understanding your mortgage interest payments seem like an unsurmountable task? If so, you’re definitely not alone.
Solving the Three Body Problem
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mathematics