## The Isaac Newton Institute: Creating eureka moments

How long does it take for one person to infect another?

*R*number you need to know the time between infections.

How does a smooth flow suddenly become turbulent? The Reynolds number helps understand the transition.

In this year's advent calendar we celebrate our collaboration with the Isaac Newton Institute for Mathematical Sciences.

How does water, or indeed any fluid, move? The Euler equations let us look beneath the surface and mark the beginning of modern fluid dynamics.

Approximating a function with a divergent series.

How a question about rainbows led to an entire field of mathematics.

If you ignore exponentially small terms they can come back to bite you.

Mathematicians from across maths and physics and around the world gathered to celebrate Sir Michael Atiyah.

A quick introduction to an abstract concept that's useful in anything from genetics to cosmology.

How can sporting events, concerts, or festivals be kept safe in the face of rising COVID-19 infections?

This inspiring conference featured speakers from Africa, the US, the Caribbean and the UK. Here are some highlights.

The organisers of a new INI programme explain why we need to know more about the maths behind machine learning and deep neural networks.

Machine learning started with supervised learning and us providing all the training materials, but we are finding ways for algorithms to learn with far fewer resources.

What can last year's experiences tell us about the coming academic year?

A quick look at one of the most important theorems in number theory.

Whether you're lost on a mountainside, or training a neural network, you can rely on the gradient descent algorithm to show you the way!

Explore the maths behind machine learning and deep neural networks with this collection of short introductions and in-depth articles.

Machine learning makes many daily activities possible, but how does it work?

When trying to build an artificial intelligence, it makes sense to mimic the human brain. Artificial neurons do just that.

There are a million things in maths named after Leonard Euler. Here's a beautiful formula involving complex numbers.

How to take the square root of a complex number — and discover a beautiful new surface in the process.

The mathematical equations governing fluid flow may have no known solutions, but maths still has the answers!

How do you calculate your risk of catching an airborne disease?

As the Delta variant is worrying the UK, researchers from the JUNIPER consortium have published all they know about it.

Next month sees the 60th birthday of a famous algorithm called Quicksort. Its inventor Tony Hoare told us that it all started with bubbles.

Quicksort is a famous algorithm which celebrates its 60th birthday this year. We explore its clever workings.

Next month sees the 60th birthday of a famous algorithm called Quicksort. We explore its origin, its workings, and some other work of its inventor Tony Hoare.

Curves can be crazy, but asymptotes are nice and straight.

Can the virus that causes COVID-19 mutate into a vaccine-resistant strain? And if yes, what would this mean for our vaccination strategy?

In this podcast we ask two experts to explain the models that predict how the Earth's climate will behave in the future.

Using artificial intelligence to improve traffic, protecting the environment and human health.

Where have the COVID-19 vaccines got us so far and where we are likely to be when the rollout is complete?

Mathematicians meet clinicians to challenge the NHS backlog on cardiovascular disease — find out more in this podcast!

What's the safest way to reopen schools? And can testing make things better?

Explore the mathematical study of symmetry with this collection of content, which includes short introductions, in-depth articles, a podcast, and some magic!

In this podcast mathematician Cheryl Praeger and magician Will Houstoun reveal the maths and magic behind shuffling cards.

What is group theory and why is it such an exciting area of maths? Two experts explain.

Groups occur all over mathematics, so it makes sense to find a common language to talk about them all.

When things go round and round, a cyclic group may be just what you need!

A journey into the maths of card shuffling gives us a great insight into how mathematicians work.

Want to shuffle like a professional magician? Find out how to shuffle perfectly, imperfectly, and the magic behind it.