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Mathematics

Essays and videos exploring physics, evolution, cosmology and other frontiers in science

Astronomy Biology Biotechnology Chemistry Complexity Computing and artificial intelligence Cosmology Deep time Earth science and climate Ecology and environmental sciences Engineering Evolution Genetics History of science Human evolution Human reproduction Illness and disease Mathematics Medicine Oceans and water Palaeontology Physics Quantum theory Space exploration

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3D colour spectrum graph with X, Y, Z axes and a colourful curved surface on a black background, digital rendering.

videoMathematics

After centuries of trying, we’ve yet to arrive at a perfect way to map colour

20 minutes

3D heat map graph with peaks in red and valleys in blue showing data variation.

videoMusic

A riveting audiovisual dive into what makes sounds harmonious, or not

28 minutes

Illustration of an ancient Greek temple with the golden ratio spiral overlay, featuring bright colours and clear skies.

videoMathematics

Spiral into the ‘golden ratio’ – and separate the myths from the maths

4 minutes

Illustration of two turquoise beams pointing from the Milky Way galaxy toward another galaxy on a black background.

videoHistory of science

How we came to know the size of the Universe – and what mysteries remain

26 minutes

3D digital graphic of geometric shapes—cube, spheres and orbits—in space with a starry background.

videoHistory of science

Ideas ‘of pure genius’ – how astronomers have measured the Universe across history

29 minutes

Black and white photo of man standing in front of a massive industrial tunnel with a Jeumont sign.

essayNeuroscience

Why nothing matters

It took centuries for people to embrace the zero. Now it’s helping neuroscientists understand how the brain perceives absences

Benjy Barnett

Abstract digital art of geometric patterns made with spheres, creating a sense of depth on a black background.

videoComputing and artificial intelligence

Why large language models are mysterious – even to their creators

8 minutes

Photo of a modern bathroom with circular tiled walls and surfaces, two sinks, mirrors and red hand dryers reflected in the mirrors.

essayMathematics

Beyond causality

In order to bridge the yawning gulf between the humanities and the sciences we must turn to an unexpected field: mathematics

Gordon Gillespie

Drawing of Earth and the Moon in orbit with straight lines trailing off each on a white background with grey specks.

videoPhysics

To change the way you see the Moon, view it from the Sun’s perspective

5 minutes

Geometric shapes with triangular patterns in blue, purple, and yellow on a black background. Shapes include squares, triangles, cones, and other polyhedra.

videoFilm and visual culture

Stop-motion origami unfurls in a playful exploration of how senses overlap

3 minutes

Man with glasses speaking, wearing a brown shirt. Background is blurred with a colourful painting visible.

videoMetaphysics

Why mathematical truths exist with or without minds to consider them

8 minutes

Hand holding a paintbrush colouring a vintage map of England with various regions in different colours.

videoMathematics

How a curious question about colouring maps changed mathematics forever

9 minutes

Carl Sagan in a beige blazer and red jumper holding a model against a clear blue sky.

videoHistory of science

How an ancient polymath first calculated Earth’s size, as told by Carl Sagan

7 minutes

A man playing a Yamaha piano with headphones on. Abstract, white ribbon-like lines float above, on a black background.

videoMusic

As a pianist strikes a chord, visualisations of his notes appear in real time

5 minutes

A felted wool fox sculpture with bright yellow eyes stands in front of a blurred background of green trees.

videoLogic and probability

Chew over the prisoner’s dilemma and see if you can find the rational path out

6 minutes

People standing in long, winding queues in a desert camp with numerous tents in the background under a clear blue sky.

essayEthics

Moral mathematics

Subjecting the problems of ethics to the cool quantifications of logic and probability can help us to be better people

Elad Uzan

Cartoon astronaut with clock eyes, wearing a white helmet against a black background.

videoPhysics

An interstellar voyage explores the ‘paradox’ of twins separated by light years

6 minutes

Abstract artwork featuring two interconnected blue shapes, one with concentric circles and the other with a droplet-like form, against a beige background.

essayMathematics

Imaginary numbers are real

These odd values were long dismissed as bookkeeping. Now physicists are proving that they describe the hidden shape of nature

Karmela Padavic-Callaghan

Illustration of a person standing on top of a pyramid made from large bricks, with small plants growing around the structure.

videoMathematics

How a verbal paradox shattered the notion of total certainty in mathematics

5 minutes

Typed title page stating “Intelligent Machinery” by A.M. Turing (1948) on an orange background.

essayComputing and artificial intelligence

AI’s first philosopher

Alan Turing was a pioneer of machine learning, whose work continues to shape the crucial question: can machines think?

Sebastian Sunday Grève

Abstract image featuring a metallic sphere inside a grey circular tunnel, viewed towards a blurred gradient background.

essayPhilosophy of science

What is a law of nature?

Laws of nature are impossible to break, and nearly as difficult to define. Just what kind of necessity do they possess?

Marc Lange

Two scatter plots with points in a circular pattern centred at origin, labelled x and y axes ranging from -1 to 1.

videoLogic and probability

The unresolved probability paradox that goes to the heart of scientific objectivity

8 minutes

Two people walking past The Bank of New York sign, which reads “Founded 1784,” engraved on a stone wall.

essayEconomics

A softer economics

Financial markets are entangled and uncertain. When will economists let go of physics envy to embrace the quantum revolution?

David Orrell

Illustration of a person meditating in a cross-legged position with graphs and documents floating around their head.

videoInformation and communication

The modern world is littered with statistical noise. Here’s how to find the signal

5 minutes