MathHistory1a

MathHistory1a: Pythagoras' theorem

Pythagoras' theorem is both the oldest and the most important non-trivial theorem in mathematics.

This is the first part of the first lecture of a course on the History of Mathematics, by N J Wildberger, the discoverer of Rational Trigonometry. We will follow John Stillwell's text Mathematics and its History (Springer, 3rd ed). Generally the emphasis will be on mathematical ideas and results, but largely without proofs, with a main eye on the historical flow of ideas. A few historical tidbits will be thrown in too...

In this first lecture (with two parts) we first give a very rough outline of world history from a mathematical point of view, position the work of the ancient Greeks as following from Egyptian and Babylonian influences, and introduce the most important theorem in all of mathematics: Pythagoras' theorem.

Two interesting related issues are the irrationality of the 'square root of two' (the Greeks saw this as a segment, or perhaps more precisely as the proportion or ratio between two segments, not as a number), and Pythagorean triples, which go back to the Babylonians. These are closely related to the important rational parametrization of a circle, essentially discovered by Euclid and Diophantus. This is a valuable and under-appreciated insight which high school students ought to explicitly see.

In fact young people learning mathematics should really see more of the history of the subject! The Greeks thought of mathematics differently than we do today, and all students can benefit from a closer appreciation of the difficulties which they saw, but which we today largely ignore.

This series has now been extended a few times--with more than 35 videos on the History of Mathematics.

My research papers can be found at my Research Gate page, at I also have a blog at where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at Of course if you want to support all these bold initiatives, become a Patron of this Channel at .

MathHistory32: Astronomy and trigonometry in India

This is a brief overview of some aspects of ancient Indian contributions to astronomy and related trigonometry.

Math And The Rise Of Civilization. Ep.01 - The Beginning of Numbers

Math And The Rise Of Civilization. Season 1.
Episode 1. The Beginning of Numbers.

1. General Overview and the Development of Numbers

(October 1, 2012) Keith Devlin gives an overview of the history of mathematics. He discusses how it has evolved over time and explores many of its practical applications in the world.

Originally presented in the Stanford Continuing Studies Program.

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Mathematics | BBC Science Documentary |

BBC Science Documentary | Cosmic time the true nature of time Science Channel bbc documentary 2015, bbc documentary history, bbc documentary .



BBC Documentary The Math Mystery Mathematics in Nature and Universe Science Documentary.

Astrophysicist Mario Livio, along with a colorful cast of mathematicians, physicists, and engineers, follow math from Pythagoras to Einstein and beyond, .

Please ☞ See more: documentary 2015 national geographic Full Episodes: .

History of Maths

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Algebra - Pythagorean Theorem

Sure, technically it's a Geometry topic, but why not learn about it in Algebra? Don't be lured into a false sense of security, there may be problems on this video that you may not be able to do! Check out my tie. YAY MATH!
Visit yaymath.org
Videos copyright (c) Yay Math

50 Centuries in 50 minutes (A Brief History of Mathematics)

John Dersch (9/19/12)

How did we get the mathematics that is studied today? Who was responsible for major advances in the mathematics that we now take for granted? When and where did this work take place? Such questions will be addressed by tracing the development of mathematics from 3000 B.C. to the dawn of the 21st century. There will be time for questions and suggestions for further study will be made.

The Birth Of Calculus (1986)

A documentary on Leibniz and the calculus.

3. The Birth of Algebra

(October 15, 2012) Professor Keith Devlin looks at how algebra, one of the most foundational concepts in math, was discovered.

Originally presented in the Stanford Continuing Studies Program.

Stanford University:


Stanford Continuing Studies Program:


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Algebraic Topology - Fernando Rodriguez Villegas - Lecture 01

AlgTop0: Introduction to Algebraic Topology

This is the Introductory lecture to a beginner's course in Algebraic Topology given by N J Wildberger of the School of Mathematics and Statistics at UNSW in 2010.

This first lecture introduces some of the topics of the course and three problems.

His YouTube site Insights into Mathematics at under user: njwildberger also contains series on MathFoundations, History of Mathematics, LinearAlgebra, Rational Trigonometry and even one called Elementary Mathematics (K-6) Explained.

What Mathematicians Actually Do

John Franks presents What Mathematicians Actually Do, his inaugural lecture as the Henry S. Noyes Professor in Mathematics at Weinberg College of Arts and Sciences, Northwestern University. January 27, 2010.

Tadashi Tokieda || Toys in Applied Mathematics || Radcliffe Institute

Tadashi Tokieda RI '14 invents, collects, and studies toys—simple objects from daily life that can be found or made in minutes, yet which, if played with imaginatively, exhibit behaviors so surprising that they intrigue scientists for weeks. In this video, he explores toys and their relevance to applied mathematics.

MathHistory5a: Number theory and algebra in Asia

After the later Alexandrian mathematicians Ptolemy and Diophantus, Greek mathematics went into decline and the focus shifted eastward. This lecture discusses some aspects of Chinese, Indian and Arab mathematics, in particular the interest in number theory: Pell's equation, the Chinese remainder theorem, and algebra. Most crucial was the introduction of the Hindu-Arabic number system that we use today.

We also discuss the influence of probably the most important problem of the mathematical sciences from a historical point of view: understanding the motion of the night sky, in particular the planets. This motivated work in trigonometry, particularly spherical trigonometry, of both Indian and Arab mathematicians.

Prominent mathematicians whose work we discuss include Sun Zi, Aryabhata, Brahmagupta, Bhaskara I and II, al-Khwarizmi, al-Biruni and Omar Khayyam.

If you are interested in supporting my YouTube Channel: here is the link to my Patreon page:
You can sign up to be a Patron, and give a donation per view, up to a specified monthly maximum.

Introduction to Pythagoras' Theorem

Jump In, the Water is Lovely!

(January 26, 2012) Professor Margot Gerritsen shares her experience being a math instructor, swim coach, and cheerleader simultaneously. She shares her thoughts on how to help new graduate students overcome common anxieties and thrive.

The Center for Teaching and Learning's longest-running lecture series, Award-Winning Teachers on Teaching invites faculty winners of Stanford's major teaching awards to deliver a lecture on a teaching topic of their choice.
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Center for Teaching and Learning:


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An extra little bit for the Happy Ending Problem

This is just an extra snippet - the main video is at:
Featuring Ron Graham

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Numberphile is supported by the Mathematical Sciences Research Institute (MSRI):

Videos by Brady Haran

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Welcome to Algebraic Calculus One!

In 2018, we are going to re-landscape the Garden of Calculus. Things will be moved around, put in better positions, decent walkways will be installed, new exhibits will be introduced, and there will be lots of fun Activities in the shape of Problems and Questions.

It's all happening on the Open Learning platform with the Wild Egg mathematics course Algebraic Calculus One. Which aims to bring calculus into a pure mathematics setting---where clear definitions, explicit examples and concrete computations ground the subject. And where we avoid high blown fantasies involving real numbers, infinite sets, and computer programs that run to infinity, and then yield outputs.

In this video you get a heads up about the course. Make sure you are part of the mathematical event of the decade!

Non-Euclidean Geometry [Topics in the History of Mathematics]

Another Open University oldie. This one's a bit more hxc (and considerably older - the 1970s public were apparently considered far smarter than we are today!), but it's mostly easy enough to grasp if you put your mind to it.

Non-Euclidean Geometry is relevant for the Riemann curvature of space-time in General Relativity and all that. It's also interesting to watch logic (or a bearded professor) decimate what was once considered to be a fundamental truth of mathematics and reality, if you're into that sort of thing. (maybe that's a bit over-dramatic).

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