The Isaac Newton Institute: Creating eureka moments

Image
Logo of the Isaac Newton Institute

One of the most exciting places in the mathematical world is the Isaac Newton Institute for Mathematical Sciences (INI), an international research centre and our neighbour here on the University of Cambridge's maths campus.

The INI attracts leading mathematical scientists from all over the world, and is open to all. We are proud to be collaborating with the INI to bring the cutting edge mathematics that is being done there to the general public. The following content is part of this collaboration.


Article
a wave

The harmonics of a string

When you pluck a guitar string it vibrates at many resonant frequencies at once. What might that look like? Find out with our animation.

Article

Catching waves with the Laplacian

The Laplacian operator turns up all over maths.  Here's a reasonably light-touch introduction and a look at why it forms part of the wave equation.

Collection
Drum

Vibration revelations: Geometric spectral theory

Can you hear the shape of a drum? The question leads to surprisingly rich mathematics that has a huge rage of applications. Find out more with this collection of content.

Referenced articles
Article
Two diagrams

Can you see the sound of a drum?

If you sprinkle sand on a vibrating plate it forms the most beautiful patterns. We explore why that happens, what it has to do with mathematical pioneer Sophie Germain, and how the question opens up a huge range of maths.

Article
Drum

Can you hear the shape of a drum?

The sound of a plucked string depends on how long it is, so you can hear the length of a string. But can you hear the shape of a drum? 

Podcast
The four mathematicians together

Meet a Mathematical Family

Mathematics as a family event? Listen to one family explain how they worked together to prove a new result in group theory.

Podcast
Ramin Zabih in front of blackboard

Ramin Zabih: Welcome to the ArXiv

Around 1,000 articles are published on arXiv every day — from the proof of the Poincaré Conjecture to research from AI companies like DeepSeek and Gemini. In this podcast we go behind the scenes to learn what it takes to run such a huge mathematical institution.

Article
An AI illustration of a mathematical centuar

Enter the centaur

How is AI impacting mathematics today?  Geordie Williamson tells us about recent work resulting from genuine collaboration between human and machine.

Article
coiled pasta

Dive deeper into the loop soup

Fields Medallist Wendelin Werner loves Brownian loop soups. In the second part of this article, we learn more about why they matter so much.

Article
A plate of spagetti hoops

Dive into the loop soup!

Fields Medallist Wendelin Werner loves Brownian loop soups. We explore what they are, why he finds them so "natural", and how they are linked to the physics of elementary particles.