Graph theorists | Linear algebraists | Magic squares | Algebraic geometers

Arthur Cayley

Arthur Cayley FRS (/ˈkeɪli/; 16 August 1821 – 26 January 1895) was a prolific British mathematician who worked mostly on algebra. He helped found the modern British school of pure mathematics. As a child, Cayley enjoyed solving complex maths problems for amusement. He entered Trinity College, Cambridge, where he excelled in Greek, French, German, and Italian, as well as mathematics. He worked as a lawyer for 14 years. He postulated the Cayley–Hamilton theorem—that every square matrix is a root of its own characteristic polynomial, and verified it for matrices of order 2 and 3. He was the first to define the concept of a group in the modern way—as a set with a binary operation satisfying certain laws. Formerly, when mathematicians spoke of "groups", they had meant permutation groups. Cayley tables and Cayley graphs as well as Cayley's theorem are named in honour of Cayley. (Wikipedia).

Arthur Cayley
Video thumbnail

Chester A. Arthur: Turning Tables (1881 - 1885)

Chester Arthur took office upon the assassination of James Garfield. Garfield was liked, but Arthur was not, as people didn't trust his big shot New York stylings. But he surprised them all by doing a lot of good during his time in office, pushing issues of reform. Even still, it wasn't en

From playlist American History

Video thumbnail

Ulysses S. Grant: Civil War Hero (1869 - 1877)

Ulysses S. Grant is best known as the general of the Union Army that brought an end to the Civil War, by getting General Robert E. Lee to surrender. But he also served as a two-term president, and he wasn't a bad one at that. He has been accused of considerable corruption, but he also did

From playlist American History

Video thumbnail

The Cayley Expansion (feat. David Eisenbud) - Objectivity 174

David Eisenbud joins us at The Royal Society to look at the work of one of his all time favourite mathematicians. More links below ↓↓↓ Featuring David Eisenbud speaking with Brady and Keith Moore. Subscribe to Objectivity: http://bit.ly/Objectivity_Sub Check out David on Numberphile: h

From playlist David Eisenbud on Numberphile

Video thumbnail

Astronomy Cast 330 - Arthur C. Clarke

Arthur C. Clarke was one of the greatest science fiction writers of all time. He defined the genre, and revolutionized our ideas about what it will take to become a true space faring civilization. In the first of our two part series on Arthur C. Clarke, we examine the man's life and his bo

From playlist Astronomy Cast

Video thumbnail

Millard Fillmore: Last of the Whigs (1850 - 1853)

There's a reason you've never heard of Millard Fillmore. He wasn't that good of a president. He was so mediocre that he pretty much killed off the Whig Party. But it's still worth learning a bit about him, so let's take a look! Script by Michael Thomas Watch the whole American History pl

From playlist American History

Video thumbnail

Group Multiplication Tables | Cayley Tables (Abstract Algebra)

When learning about groups, it’s helpful to look at group multiplication tables. Sometimes called Cayley Tables, these tell you everything you need to know to analyze and work with small groups. It’s even possible to use these tables to systematically find all groups of small order! Be

From playlist Abstract Algebra

Video thumbnail

Lyndon B. Johnson: A Tragic Figure (1963 – 1969)

Lyndon Johnson ascended to the presidency upon the assassination of John F. Kennedy. He was a large, imposing man, who had been an influential Senate Majority Leader and Vice President. And as President, it is difficult to say whether he is remembered better for his incredible domestic acc

From playlist American History

Video thumbnail

Chapter 7: Group actions, symmetric group and Cayley’s theorem | Essence of Group Theory

Group action can be thought of as a homomorphism to a symmetric group, so apart from orbit-stabiliser theorem, we can also use the isomorphism theorem to analyse any group action. It turns out that this correspondence between group action and homomorphism can be visualised rather easily. T

From playlist Essence of Group Theory

Video thumbnail

The Newton Fractal Explained | Deep Dive Maths

A Newton fractal is obtained by iterating Newton's method to find the roots of a complex function. The iconic picture of this fractal is what I call The Newton Fractal, and is generated from the function f(z)=z^3-1, whose roots are the three cube roots of unity. What is the history of th

From playlist Deep Dive Maths

Video thumbnail

Visual Group Theory, Lecture 1.2: Cayley graphs

Visual Group Theory, Lecture 1.2: Cayley graphs In this lecture, we introduce a visual way to "map out" a group using an object called a Cayley graph. This concept is a useful visualization tool, but it is often omitted entirely from traditional Abstract Algebra classes. Course webpage (

From playlist Visual Group Theory

Video thumbnail

Regular permutation groups and Cayley graphs

Cheryl Praeger (University of Western Australia). Plenary Lecture from the 1st PRIMA Congress, 2009. Plenary Lecture 11. Abstract: Regular permutation groups are the 'smallest' transitive groups of permutations, and have been studied for more than a century. They occur, in particular, as

From playlist PRIMA2009

Video thumbnail

TEDxCaltech - Stephen Hawking, John Preskill, Rives, Kip Thorne - Finding Things Out

Stephen Hawking is a theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity. He is known for his contributions to the fields of cosmology and quantum gravity, especially in the context of black holes. He has also achieved su

From playlist TEDxCaltech - 1/14/11

Video thumbnail

Sir Charles G. Darwin - This I Believe (1950s) - Radio broadcast

Charles Galton Darwin, the grandson of Sir Charles Darwin, was an English physicist. Director of the National Physical Laboratory (NPL) during the Second World War.

From playlist Voices of History

Video thumbnail

Can you Find your Soulmate Using Maths? | Earth Lab

Can maths work out how to increase your chance of finding "the one" when dating? Surprisingly, there's a mathematical formula to help in the quest for love. Best of Earth Lab: http://bit.ly/EarthLabOriginals Best of BBC Earth: http://bit.ly/TheBestOfBBCEarthVideos The Doctors Are In The

From playlist How To Find Love Online

Video thumbnail

Robert Bosch - Figurative Subgraphs - G4G13 Apr 2018

Given a graph (a collection of dots and line segments connecting certain pairs of dots) and a target image, we form subgraphs that look like the image.

From playlist G4G13 Videos

Video thumbnail

John Tyler: His Accidency (1841 - 1845)

John Tyler was the first person to ever be president without being elected president. That's because he took over for William Henry Harrison when he died a month into his term, as it was decided that the vice president should become the president in such a circumstance. He turned his back

From playlist American History

Video thumbnail

Am I Smarter than my Students' Homework? Professor vs. Computer Quiz Bowl [Expo]

This is a single lecture from a course. If you you like the material and want more context (e.g., the lectures that came before), check out the whole course: https://boydgraber.org/teaching/CMSC_470/ (Including homeworks and reading.)

From playlist Human-Computer QA

Video thumbnail

De Gaulle - Force of Character

Portraits of Power - DeGaulle - Force of Character Narrated by Henry Fonda Charles André Joseph Marie de Gaulle was a French general and statesman who led the Free French Forces during World War II. He later founded the French Fifth Republic in 1958 and served as its first president from

From playlist Portraits of Power - Those who shaped the Twentieth Century

Video thumbnail

Does the Universe have Higher Dimensions? Part 1

Signup for your FREE trial to The Great Courses Plus here: http://ow.ly/6ymM30rvhBa What do physicists mean when they talk about higher dimensional spaces, or space-times? How could we possibly not have noticed if space was not three-dimensional? In this first part, we will talk about th

From playlist Physics

Video thumbnail

Arthur Schopenhauer - Bryan Magee & Frederick Copleston (1987)

Frederick Copleston and Bryan Magee discuss the work of the 19th century German philosopher Arthur Schopenhauer in this 1987 program. Schopenhauer is perhaps most famous for his extreme pessimism. Seeing the world as something horrific and bleak, he urged that we turn against it. As a foll

From playlist Bryan Magee Interviews - The Great Philosophers (1987)

Related pages

Tetrahedroid | Cayley–Purser algorithm | Quippian | Characteristic polynomial | Elliptic function | Linear algebra | James Joseph Sylvester | Binary function | Group (mathematics) | Cayley–Bacharach theorem | Cubic surface | Quaternion | Cayley–Klein metric | Permutation group | Cayley's ruled cubic surface | Cayleyan | Determinant | Hyperbolic geometry | Hyperdeterminant | William Rowan Hamilton | Algebra | Cayley's formula | Cayley–Hamilton theorem | Cayley's nodal cubic surface | Alexander Macfarlane | Actuary | Grassmann–Cayley algebra | Mathematics | Octonion | Square matrix | Algebraic geometry | Cayley's theorem | Cayley's mousetrap | Group theory | Chow variety | Cayley graph | Chasles–Cayley–Brill formula | Ruled surface | Cayley–Menger determinant | Isaac Newton | Cayley–Dickson construction | Cayley's Ω process | Pure mathematics | Cayley's sextic | Cayley transform | Cayley table