population numbers

The first part of Welch Labs' series on imaginary numbers, presenting them as the natural extension of the number line into two dimensions. It covers the history and the math with strong visuals.

Matt Parker talks Numberphile through the different kinds of numbers: algebraic, transcendental, computable, normal, and beyond. It shows how few numbers we can actually name or describe.

A Kurzgesagt explainer on why the human population exploded and why growth is slowing, drawing on Our World in Data. It argues that birth rates fall as countries develop, easing overpopulation fears.

Veritasium tells the history of how imaginary numbers arose from the quest for a general solution to the cubic equation, including the duels and secrecy among Renaissance mathematicians. It argues math had to give up the requirement that it mirror reality.

Hans Rosling uses population statistics to explain why the world population will level off rather than grow without limit. He shows that falling child mortality and rising prosperity lead to smaller families.

A Numberphile interview with Donald Knuth about how he came to write the first book on surreal numbers after a lunch with John Conway. He tells the story casually in about 14 minutes.

Sabine Hossenfelder asks whether complex numbers are just a convenient tool or necessary in physics. She discusses a recent paper arguing that quantum mechanics cannot be done with real numbers alone.

Hans Rosling uses data and animated statistics to show how world population is changing, why birth rates fall as child survival and wealth rise, and why population is expected to peak around 11 billion. It also tackles common misconceptions about Africa and family planning.

Hans Rosling's TED@Cannes talk uses boxes and animated data graphics to show how world population will grow to about 9 billion. He argues that raising living standards for the poorest is what reduces population growth.

Numberphile's James Grime discusses highly composite numbers, nicknamed anti-primes, which have more factors than any smaller number, using 5040 as the central example. It touches on Plato and Ramanujan.

Roy Beck's short gumball presentation using World Bank and Census data to argue that letting people immigrate to the US cannot solve world poverty because the numbers are so large. It is made by NumbersUSA, an immigration-restriction advocacy group.

Physicist Al Bartlett's well-known lecture on the arithmetic of exponential growth, applied to population, energy consumption and resource depletion. He argues that steady percentage growth cannot be sustained on a finite planet and that most public discussion ignores this.

A recording of physicist Albert Bartlett's well-known lecture on the arithmetic of exponential growth, applied to population and energy use. He argues that steady percentage growth in a finite world cannot continue and sneaks up suddenly.

The first lecture of Francis Su's Harvey Mudd real analysis course, covering the construction of the rational numbers. It begins a full lecture series that follows a standard analysis text.

Physicist Albert Bartlett's full-length lecture on how steady exponential growth in population and energy use collides with finite resources. It uses examples like bacteria in a bottle and covers peak oil.

The first video in a series on extremely large numbers, introducing the topic with examples. Later parts go deep into the fast-growing hierarchy.

Tom Scott explains for Computerphile how floating point numbers work, why moving the binary point is fast, and why it handles money badly.

Part 1 of a lecture by physicist Albert Bartlett on the exponential function and its consequences for population growth, resource use and energy. It argues that steady growth rates quickly lead to enormous quantities.

Hans Rosling's TEDxSummit talk asks whether some religions have higher birth rates and how that affects population growth. He charts data across time and religions and reaches a surprising conclusion about fertility.

Owen Maitzen's animated hour-long introduction to Hackenbush, a simple combinatorial game, and how its strategy leads to surreal numbers and the roots of the number system.

CityNerd's Ray Delahanty tallies the personal costs of driving and then the externalities that car dependency imposes on everyone else, with numbers for each. It is an urbanist case that driving is heavily subsidized and costs society far more than drivers pay.

Episode 4 of James Burke's Connections series, tracing how commercialism, climate change and the Black Death shaped the move to the Renaissance. It follows threads through waterpower, the printing press, the Jacquard loom and the Hollerith punch card toward modern computing.

3Blue1Brown builds visual intuition for quaternions, showing how to think about this four-dimensional number system using stereographic projection and rotations in 3D space. It is part one of a two-part series with an interactive companion site.

Numberphile talks with mathematician Ron Graham about the magnitude of Graham's number, building up from arrow notation to show how impossibly large it is. It is part of a series of videos on this number.

Freya Holmer's Dutch Game Day 2023 talk asking why vectors can't be multiplied, building from complex numbers to a single axiom and arriving at geometric algebra, quaternions and multivectors.

3Blue1Brown explores infinite sums from convergent to divergent, with an introduction to the 2-adic metric, themed on the cycle between discovering and inventing mathematics.

3Blue1Brown explains why plotting primes in polar coordinates produces spiral patterns, using modular arithmetic, Dirichlet's theorem and rational approximations of pi.

Vsauce's Michael Stevens takes viewers past infinity using transfinite numbers, ordinals and cardinals, with input from mathematician Hugh Woodin. It is a fast-paced, mind-bending tour of different sizes of infinity.

A Veritasium video on the logistic map, showing how a simple population equation leads to chaos and bifurcation. It connects the idea to convection, neuron firing and the Mandelbrot set, with interactive animations.

A PBS Infinite Series episode explaining the mathematics of quantum computers, including how qubits store complex numbers and how quantum computation differs from classical computation. Hosted by Kelsey Houston-Edwards.

Numberphile's James Grime introduces quaternions, a type of number beyond the complex numbers, building up from real and complex numbers and explaining why they are useful.

3Blue1Brown shows how pi emerges from prime numbers via complex numbers and sums of squares, culminating in a formula for approximating pi.

Numberphile's Tony Padilla and Matt Parker discuss Graham's number, once the largest number used in a mathematical proof, and how enormous it is.

David MacKay, scientific advisor to the UK energy department, gives a Harvard talk on sustainable energy at macro and micro scale, drawn from his book Sustainable Energy Without the Hot Air. It stresses the land area renewables require.

Tom Scott makes the difference between a million and a billion dollars tangible by using distance on a road trip instead of volume. The drive makes the scale of a billion intuitively felt.

Vsauce explores math through card tricks and big numbers, including an animation of how enormous 52 factorial, the number of deck orderings, really is.

A Kurzgesagt animation on South Korea's record-low fertility rate and rapidly aging population. It explains why a demographic collapse looks hard to reverse and projects the population shrinking sharply by 2060.

Mike Wallace interviews Aldous Huxley in 1958 about the warnings in Brave New World, including mass persuasion, overpopulation and voluntary totalitarianism.

Steven Pinker's TED talk presents data on homicide, war, poverty and pollution to argue that the world has improved over the past decades. He frames progress as problem-solving, not inevitability.

A Kurzgesagt animation on longtermism, arguing that because the future could hold trillions of people, our actions' effect on future generations may be what matters most.