Mathematical sociology

The Scientific Method and the question of "Infinite Sets" | Sociology and Pure Maths| N J Wildberger

Let's get some kind of serious discussion going about the differences in methodology and philosophy between the sciences and mathematics, and how these differences manifest themselves in the attitude towards the logical foundations of mathematics. In particular we look at a bulwark notio

From playlist Sociology and Pure Mathematics

The big mathematics divide: between "exact" and "approximate" | Sociology and Pure Maths | NJW

Modern pure mathematics suffers from a major schism that largely goes unacknowledged: that many aspects of the subject are parading as "exact theories" when in fact they are really only "approximate theories". In this sense they can be viewed either as belonging more properly to applied ma

From playlist Sociology and Pure Mathematics

A brief history of geometry I | Sociology and Pure Mathematics | N J Wildberger

An overview of the early history of geometry from Mesolithic times, through to the ancient Greeks, Indian and Islamic mathematicians around 1400 A. D. Along the way we discuss some of the more important theorems in this history, and meet also the Platonic solids. The story of geometry has

From playlist Sociology and Pure Mathematics

A brief history of geometry II: The European epoch | Sociology and Pure Mathematics | N J Wildberger

Let's have a quick overview of some of the developments in the European story of geometry -- at least up to the 19th century. We'll discuss Cartesian geometry, Projective geometry, Descriptive geometry, Algebraic geometry and Differential geometry. This is meant for people from outside m

From playlist Sociology and Pure Mathematics

Towards a Sociology of Pure Mathematics | Sociology and Pure Maths | N J Wildberger

Sociology is a subversive science that delves into the complexities of human relations and interaction. Is it time for a sociology of pure mathematics? What would that involve? What new insights could it bring? This is the first video in a series that will be exploring the sometimes hidde

From playlist Sociology and Pure Mathematics

Quantum Mechanics -- a Primer for Mathematicians

Juerg Frohlich ETH Zurich; Member, School of Mathematics, IAS December 3, 2012 A general algebraic formalism for the mathematical modeling of physical systems is sketched. This formalism is sufficiently general to encompass classical and quantum-mechanical models. It is then explained in w

From playlist Mathematics

What is mathematics?

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From playlist Science Unplugged: Mathematics

Simple groups, Lie groups, and the search for symmetry I | Math History | NJ Wildberger

During the 19th century, group theory shifted from its origins in number theory and the theory of equations to describing symmetry in geometry. In this video we talk about the history of the search for simple groups, the role of symmetry in tesselations, both Euclidean, spherical and hyper

From playlist MathHistory: A course in the History of Mathematics

What is Group Theory?

This video contains the origins of group theory, the formal definition, and theoretical and real-world examples for those beginning in group theory or wanting a refresher :)

From playlist Summer of Math Exposition Youtube Videos

Curt Jaimungal Interview and Theories of Everything | Sociology and Pure Maths | N J Wildberger

In a recent interview that Curt Jaimungal did with me on "Real Numbers aren't Real", we touched upon the idea of reversing roles, that is me interviewing him, and this conversation is the result. Curt has a background in mathematics and physics and has worked as a film maker in Toronto.

From playlist Sociology and Pure Mathematics

Is pure mathematics logically viable? Five Challenges! | Sociology and Pure Maths | N J Wildberger

Some tough talk directed towards the professoriat and students of the subject: is it time to re-evaluate what exactly is going on in Pure Mathematics? This is part of a series on the Sociology of Pure Mathematics, where we try to delve into and unravel some of the mysteries of the profess

From playlist Sociology and Pure Mathematics

History of Science Lecture Series - Steven Shapin

History of Science Lecture Series Topic: "The Social Sciences are Better than the Natural Sciences" Speaker: Steven Shapin Affiliation: Harvard University Date: February 24, 2023 Wolfensohn Hall

From playlist History of Science Series

Emile Borel: Real number enthusiast or skeptic? | Sociology and Pure Mathematics | N J Wildberger

Emile Borel was a prominent French analyst and probabilist, and the founder of modern measure theory. He was also involved in the issue of "real numbers" and just what they actually are, and what it means to do arithmetic with them. This is a first introduction to his thinking, where we d

From playlist Sociology and Pure Mathematics

Greek Pure Mathematics and the "Infinitude of Primes" | Sociology and Pure Maths | N J Wildberger

To understand the sociology of pure mathematics, we need to appreciate the long historical span of the subject, going back at least to ancient Greek times. Euclid's monumental work The Elements set the standard for pure mathematics research and education for more than 2000 years. Mathemati

From playlist Sociology and Pure Mathematics

Pure mathematics relies on a fake arithmetic | Sociology and Pure Mathematics | N J Wildberger

Number systems are at the heart of mathematics --- and have been for at least 4000 years. The Egyptians' had a base 10 system that used fractions, albeit not in the way we do, while the Sumerians remarkably developed a base 60 floating point system. What systems do we teach in schools?

From playlist Sociology and Pure Mathematics

The numerical system of the ancient Greeks | Sociology and Pure Maths | N J Wildberger

We review the ancient Greek approach to arithmetic, both Attic and Ionian systems, discuss Archimedes' extension of it in the Sand Reckoner, and look at gematria, the curious art of linking words and numbers arising from the Greek system. This is one of a series of videos where we look br

From playlist Sociology and Pure Mathematics

A brief history of Geometry III: The 19th century | Sociology and Pure Mathematics | N J Wildberger

The 19th century was a pivotal time in the development of modern geometry, actually a golden age for the subject, which then saw a precipitous decline in the 20th century. Why was that? To find out, let's first overview some of the main developments in geometry during the 1800's, includin

From playlist Sociology and Pure Mathematics

Number theory Full Course [A to Z]

Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure #mathematics devoted primarily to the study of the integers and integer-valued functions. Number theorists study prime numbers as well as the properties of objects made out of integers (for example, ratio

From playlist Number Theory