Plato’s Cave: Thinking about Climate Change

In The Republic, Plato explores the predicament of the Cave: a passive citizen body, a conniving and self-interested set of sophistic opinion-formers and demagogic political leaders, a systematically misleading and damaging order of political structures and common beliefs and appetites. Does this have lessons for tackling climate change? In clinging to our current way of […]

A Mathematician’s View of Proof

The idea of proof is fundamental to mathematics. We could argue that science consists of testable theories, and therefore that it is about what can be disproved, not what can be proved. In law, the test is “beyond reasonable doubt”. Famous conjectures in mathematics have been tested by computers for trillions of numbers – but […]

First light: Revealing the Early Universe

The final lecture in the series returned to the theme of how insight is derived from observations, considering the cosmic microwave background. This oldest light in the Universe, emitted just 400,000 years after the Big Bang, contains the seeds of the structures we see around us, and tells us about conditions at the Universe’s beginning. […]

How to Prove 1=0, And Other Maths Illusions

In this lecture Professor Hart showed some mathematical illusions: “proofs” that 1 = 0, that fractions don’t exist, and more. There are curious and important implications behind what’s going on. These “proofs” reveal some very common logical slips that can go unnoticed when we are trying to prove more plausible statements. And the stakes are […]

Is it Aliens? The Most Unusual Star In The Galaxy

Boyajian’s star, a faint and unprepossessing presence in the constellation of Cygnus, attracted astronomers’ attention when it began to flicker alarmingly. The lecture discussed explanations for its behaviour, from disintegrating comets to alien megastructures, and considered how modern astronomy hunts for the truly unusual objects in the Universe. For this task, the involvement of large […]

Climate Tipping Points in Oceans, Ice, Forests

Professor Myles Allen Frank Jackson Foundation Professor of the Environment (2022-) Professor Myles Allen took his first degree in Physics and Philosophy, followed by a doctorate in Atmospheric, Oceanic and Planetary Physics, both at the University of Oxford. He has worked at Oxford for most of his career, with early stints at MIT and the […]

The Mathematics of Coincidence

We regularly hear of amazing coincidences – people winning the lottery twice, or getting a phone call from a long-lost friend just when you were thinking about them. Is this telepathy? Is there a greater power at work when someone survives seven lightning strikes? There can be terrible consequences from the misunderstanding of coincidence. https://www.gresham.ac.uk/sites/default/files/transcript/2024-03-05-1800_Hart-T.pdf […]

The Colour Spectrum of Scales and Modes

A musical scale – a hierarchical collection of pitches spread over multiple octaves – is a fundamental building block in the creation of melodies and harmonies in a wide range of musical practices. But where do these scales come from? Are they invented or discovered? This lecture looked at the history, theory and artistry of […]

Pulsars, Microwave Ovens and the Radio Sky

There have been two major revolutions in how we look at the sky – the shift beyond the optical to other wavelengths, particularly the radio, and the increasing attention paid to how objects change over time. The talk started with the discovery of pulsars by Jocelyn Bell Burnell, explored how a microwave oven bamboozled astronomers, […]

Mathematical Puzzles and Paradoxes

Many puzzles have a long history, such as water pouring puzzles, where you need to measure (for example) one pint of water equipped only with an eight-pint and a five-pint jug. The mathematics behind the solution has many useful applications. Meanwhile, paradoxes such as: “some men shave themselves; those that do not shave themselves are […]