Since 2021, the Isaac Newton Institute has enjoyed a fruitful collaboration with Plus magazine. Based, like INI itself, at the University of Cambridge’s Centre for Mathematical Sciences Plus is “a free website produced in the style of a popular science magazine, inviting young adults, students, teachers, and all life-long learners into the world of mathematics”. Their articles cover topics as diverse as art and medicine, cosmology and sport, and routinely provide a level of mathematical insight into major stories that is missed by the mainstream media and popular press. It also acts as a conduit for researchers to communicate their work to new audiences, to mutual benefit.

Plus provides comprehensive coverage of INI’s ongoing research programmes, with the team producing written articles and explainers about the groundbreaking mathematics that occurs here every week, month and year. We hope you find them both accessible and stimulating.

Below you will find a complete list of all articles produced by Plus on behalf of INI. Click the linked titles to read each article on the Plus website… and enjoy!

A short introduction to the work of Mark Braverman

Created on: 5 July 2022

This is an easy introduction to the work of Mark Braverman, you can read more of the mathematical details in this article.

A short introduction to the work of Hugo Duminil-Copin

Created on: 5 July 2022

Hugo Duminil-Copin (Photo Matteo Fieni) This is an easy introduction to the work of Hugo Duminil-Copin, you can read more of the mathematical details in this article.

A short introduction to the work of James Maynard

Created on: 5 July 2022

This is an easy introduction to the work of James Maynard, you can read more of the mathematical details in this article. James Maynard (Photo by Ryan Cowan, used with permission)

A short introduction to the work of June Huh

Created on: 5 July 2022

This is an easy introduction to the work of June Huh, you can read more of the mathematical details in this article. June Huh. Photo: Lance Murphey.

A short introduction to the work of Maryna Viazovska

Created on: 5 July 2022

This is an easy introduction to the work of Maryna Viazovska, you can read more of the mathematical details in this article. Maryna Viazovska. Photo: Matteo Fieni.

The Fields Medals 2022: Maryna Viazovska

Created on: 1 July 2022

You can read a shorter version of this article here.

The Gauss Prize 2022: Elliott Lieb

Created on: 1 July 2022

Elliott Lieb of Princeton University has been awarded the 2022 Gauss Prize at the International Congress of Mathematicians. The Prize is awarded every four years at the Congress to honour scientists whose mathematical research has had an impact outside mathematics. This year the Congress is which is held as a virtual event with only the prize ceremonies and lectures taking place in-person in Helsinki, Finland.

The Chern Medal 2022: Barry Mazur

Created on: 1 July 2022

This year's Chern Medal has been awarded to Barry Mazur, a mathematician of Harvard University. The medal is awarded every four years at the International Congress of Mathematicians "to an individual whose accomplishments warrant the highest level of recognition for outstanding achievements in the field of mathematics". Barry Mazur. Photo: Lance Murphey.

The Fields Medals 2022: June Huh

Created on: 1 July 2022

You can read a shorter version of this article here.

2022 International Congress of Mathematicians

Created on: 1 July 2022

Hello from Helsinki! We are very pleased to be bringing you coverage direct from the 2022 International Congress of Mathematicians (ICM) – one of the highlights of the mathematical calendar. The ICM takes place every four years and it's usually the biggest maths conference of them all, attracting thousands of participants, and also sees the awards of some very prestigious prizes, including the famous Fields Medal.

Kinetic theory: Taming multitudes

Created on: 22 June 2022

On November 30 1889 Henri Poincaré, one of history's greatest mathematicians, found himself in an embarrassing situation. He had won a prestigious prize offered by King Oscar II of Sweden, and he'd just discovered a mistake in the piece of work he had won it for. Poincaré's manuscript was already being printed for presentation to the king and the world. To his credit, he sent word to immediately stop the presses.

The inequalities of COVID-19

Created on: 13 June 2022

At the very start of the COVID-19 pandemic many of us felt we were all pulling together. We stayed home to protect others as much as protect ourselves, helped vulnerable friends and neighbours as best as we could, and waited together with bated breath. It soon became clear, though, that the disease amplified the differences between us. Those from less advantaged backgrounds recorded more infections and died in greater numbers, and differences also emerged between ethnic groups.

Supporting healthcare with AI

Created on: 31 May 2022

Could artificial intelligence support medical doctors in their work? Part of a doctor's task is to process data — blood counts, MIR, CAT or X-ray images, and results from other diagnostic tests, for example. And data processing is something that computers are particularly good at.

Can maths help improve the communities of the future?

Created on: 27 May 2022

Across the country and around the world, most of us want the same things for our communities. These include good jobs that make people want to stay and attract newcomers, inviting town and city centres that meet local needs and attract outsiders, and effective systems to alleviate poverty and prevent homelessness. Local councils draw on many different experts to help them do this, such as town planners, health professionals and economists. And now it's the turn of mathematicians to see how they can help improve the communities of the future.

Maths in a minute: Utility theory

Created on: 27 May 2022

How much is a £100 worth to you? That might seem like an obvious question, but the value might be different for different people: £100 is worth a lot more to someone in poverty compared to a millionaire. And it might be worth a lot less if there is some risk involved. So how do you value how much something is worth, if the value will be relative depending on who you ask?

Living Proof: Anita Layton – one of Canada’s most powerful women

Created on: 24 May 2022

In this episode of the Living Proof podcast, we meet the irrepressible

Maths in five minutes: Calculus

Created on: 22 April 2022

Curious about calculus? This accessible introduction is for you! It’s a little bit longer than usual for our Maths in a minute series, but we wanted to put all the ideas together in one place so it's an easy reference for those meeting calculus for the first time! One thing that will never change is the fact that the world is constantly changing. And thanks to the tools of calculus, we can mathematically capture change which helps us to understand the world we live in.

Why turbulence is troubling

Created on: 22 April 2022

Turbulence is something we are all familiar with. We've been on bumpy plane rides, admired raging rivers, or watched the water swirl away in our sink while brushing our teeth. But although we all know turbulence, nobody properly understands it. To scientists, mathematicians and engineers it presents a huge challenge — which is why the Isaac Newton Institute for Mathematical Sciences in Cambridge (INI) is currently hosting a major research programme on the topic.

Maths in a minute: Limits

Created on: 22 April 2022

Imagine a cake. Now imagine cutting the cake in half. Then imagine cutting a half into quarters. Then a quarter into eighths, an eighth into sixteenths, and so on, forever. What can we say about the sizes of the pieces of cake as we keep cutting? One thing we can say is that the pieces get smaller and smaller. By keeping cutting you can make the pieces thinner than the width of a human hair, or smaller than the tiniest atom (in theory at least, in practice it's a bit hard to do). In fact, you can make those pieces arbitrarily thin.

Reducing NHS waiting lists in the wake of COVID

Created on: 22 April 2022

In the depth of the pandemic, in February 2021, the Newton Gateway to Mathematics organised a fascinating event. Bringing together mathematicians and clinicians, their Virtual Study Group explored how ever-growing NHS waiting lists could be reduced, using cardiovascular disease as an example.

The calculus of the complex

Created on: 22 April 2022

If you use maths to describe the world around you — say the growth of a plant, the spread of diseases, or physical forces acting on an object — you soon find yourself dealing with differential equations. Differential equations have been an important part of mathematics for centuries. Now there has been a recent surge in fractional differential equations as they can be used to model many complex phenomena, from contamination of groundwater, the electrical dynamics of the heart to the design of new materials.

The calculus of the complex

Created on: 21 April 2022

"Some scientists are mountaineers – they permanently push themselves as high as possible," says Vassili Kolokoltsov. "For me that is dominant, I try to climb high and see as much as possible. Other [scientists] are speleologists – they go deep somewhere, squeezing through the mud, but eventually they find diamonds hidden there."

The STEM for BRITAIN awards

Created on: 9 March 2022

Mathematics is incredibly important to our lives, but it still often hides in the wings. This is why we're extremely pleased that in Monday 20 early career mathematicians got to present their work to politicians in Parliament, via the STEM for BRITAIN competition. This annual event invites researchers in maths, engineering, the biological and biomedical sciences, chemistry, and physics to submit posters explaining their work.

Can game theory help to vaccinate the world?

Created on: 9 March 2022

Back in December, when countries around Europe were ramping up their booster programmes to fight Omicron, the World Health Organisation issued a report. Rather than boosting their own populations, the report said, high-income countries should consider sharing vaccine supplies around the world.

Happy International Women's day 2022!

Created on: 8 March 2022

To celebrate this year's International Women's Day on March 8, 2022, we revisit some of the articles and podcasts we have produced with female mathematicians over the last year. We've really enjoyed learning about these women's fascinating work and we hope that you will too! From logic to cosmology Maths is beautiful in its own right but it also has applications in all of the sciences and beyond. Here's a collection of topics we have explored over the last year with a range of contributors from different fields.

On the mathematical frontline: Ed Hill

Created on: 3 March 2022

Ed Hill

Hiding in plane sight

Created on: 14 February 2022

Imagine you are flying a plane on a secret mission. How can you minimise your chance of being captured by an adversary on the ground using radar? That's one of the question discussed by mathematicians, experts from industry, and the Defence Science and Technology Laboratory (Dstl) at a recent event organised by the Newton Gateway for Mathematics.

Why the generation time of COVID-19 is important

Created on: 21 December 2021

Living through a pandemic we all know by now how important the reproduction ratio, R, is to understanding the progress of a disease. But what do you need to know to calculate it? How long does it take until one infection generates another?

Understanding the generation time for COVID-19

Created on: 21 December 2021

How long does it take a person infected with a virus to infect someone else? How long does it take one infection to generate another? Answering this question requires knowledge from all the levels on which a virus operates: inside our bodies, how it spreads from one person to another and how the disease behaves across the whole population. This makes the generation time of a virus both a fascinating and challenging area of research.

Maths in a minute: QALYs

Created on: 9 December 2021

Public health can present us with stark choices. How much are we, as a society, prepared to pay for life-saving treatments for horrible diseases? How much economic loss are we prepared to accept to save a life from COVID-19 through measures such as lockdowns? Is a treatment worth the extra cost?

Pandemics and psychology

Created on: 9 December 2021

See here for all our coverage of the COVID-19 pandemic. It's often assumed that in an emergency people will panic until the emergency services appear, from which point onwards they will calm down and do as they are told. "But we have overwhelming evidence to suggest that people become inter-dependent and cooperative. Panic does exist, but it is rare."

Maths in a Minute: Turbulence and the Reynolds number

Created on: 7 December 2021

If you've ever observed a mountain stream you know that it can change its behaviour quite dramatically over time. At some times of the year it'll flow along smoothly and calmly, but at others it'll turn into a raging, turbulent mass of water. What makes a fluid flow turn turbulent?

Turbulence: Where do we stand?

Created on: 7 December 2021

Turbulence is dramatic, beautiful and potentially dangerous. It happens in liquids as well as gases — think of breaking waves and raging rivers, or air streaming around a car or plane. By its very nature, turbulence is incredibly hard to describe. At the same time, a proper understanding of turbulence would have applications ranging widely across the mathematical, physical and engineering sciences.

The Plus advent calendar 2021

Created on: 29 November 2021

This year we are proud to have started our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI). The INI is an international research centre that attracts leading mathematical scientists from all over the world, and our neighbour here on the University of Cambridge's maths campus.

Maths in a Minute: Fluid dynamics and the Euler equations

Created on: 22 November 2021

The motion of water, air, or indeed any fluid, is weird when you think about it. It moves as a continuous mass, and can move with great force, yet it is made up of tiny individually moving molecules. We know from personal experience that external forces, like gravity, or the push of an oar, can make water move, as can changing the pressure when we open a tap. And movement passes through a body of water, such as ripples moving across a pond.

Maths in a minute: Asymptotic expansions

Created on: 5 November 2021

If you're familiar with some calculus, then you might know that certain types of functions can be approximated using convergent series. (If that's news to you, then you might first want to read this short article and familiarise yourself with the idea.)

The power of small things: Resurgent asymptotics

Created on: 5 November 2021

Over the last year and a half we have all become used to the term exponential growth. Mathematically, the nature of this kind of growth is captured by the expression

The power of small things

Created on: 5 November 2021

Life is the art of approximation. If we took into account all the details of every aspect of the things we experience, we'd never get anywhere. We need to be careful about which things to ignore, though, because if those details contain a proverbial devil, they can come back to bite us.

Stokes's phenomenon: An asymptotic adventure

Created on: 5 November 2021

Life is the art of approximation. If we took into account all the details of every aspect of the things we experience, we'd never get anywhere. We need to be careful about which things to ignore, though, because if those details contain a proverbial devil, they can come back to bite us.

The unity of mathematics: a meeting in honour of Sir Michael Atiyah

Created on: 28 October 2021

Richard Feynman: "If all mathematics disappeared overnight, physics would be set back by about a week." Michael Atiyah: "That was the week that God created the Universe"

Black Heroes of Mathematics 2021

Created on: 21 October 2021

In his welcome to the 2021 Black Heroes of Mathematics (BHoM) conference, Nira Chamberlain said the aim was to showcase amazing black mathematicians, with speakers from Africa, the US, the Caribbean and the UK. Chamberlain is President of the Institute of Mathematics and its Applications (IMA) and was one of the organisers and the chair of the conference. "The IMA believes mathematics should have no boundaries.

Keeping people safe at large events

Created on: 21 October 2021

"If the government implements its plan B, then what impact will that have on event venues?"

Maths in a Minute: Category theory

Created on: 21 October 2021

At this year's Black Heroes of Mathematics conference, Maurine Atieno Songa, a PhD student at the University of KwaZulu-Natal, South Africa, gave a brilliant introduction to category theory.

Opening the black box

Created on: 15 October 2021

Many aspects of our lives today are possible thanks to machine learning – where a machine is trained to do a specific, yet complex, job. We no longer think twice about speaking to our digital devices, clicking on recommended products from online stores, or using language translation apps and websites.

Maths in a minute: Semi-supervised machine learning

Created on: 8 October 2021

One of the most significant recent developments in artificial intelligence is machine learning. The idea is to look at intelligence, not as something that is taught to a machine (in the sense of a traditional computer program), but something that a machine learns by itself, so that it learns how to do complex tasks directly from experience (or data) of doing them.

Maths in a minute: The prime number theorem

Created on: 25 August 2021

The prime numbers are those integers that can only be divided by themselves and 1. The first seven are

COVID-19 and universities: What do we know?

Created on: 25 August 2021

"This year we will have students going into the third year of their degree who have not had a single complete year of normal face-to-face education," says epidemiologist Mike Tildesley from the University of Warwick. It's a stark illustration of just how much the pandemic has disrupted student life, depriving students of what should have been one of the most formative, and fun, periods of their lives.

Learning the mathematics of the deep

Created on: 10 August 2021

Many aspects of our lives today are possible thanks to machine learning – where a machine is trained to do a specific, yet complex, job. We no longer think twice about speaking to our digital devices, clicking on recommended products from online stores, or using language translation apps and websites.

Maths in a minute: Gradient descent algorithms

Created on: 10 August 2021

You are out on a mountain and the mist has descended. You can't see the path, let alone where it leads, so how on Earth do you find your way down to the safety of the village at the bottom of the mountain? Never fear! Maths has come to your rescue! You can use a gradient descent algorithm – a mathematical technique for finding the minimum of smooth (i.e. differentiable) functions!

Maths in a minute: Machine learning and neural networks

Created on: 10 August 2021

We're not anywhere close to the scifi concept of strong artificial intelligence, where a machine can learn any task and react to almost any situation, indistinguishably from a human. But we are surrounded by examples of weak artificial intelligence – such as the speech recognition in our phones – where a machine is trained to do a specific, yet complex, job.

Maths in a minute: Artificial neurons

Created on: 8 July 2021

When trying to build an artificial intelligence, it seems a good idea to try and mimic the human brain. The basic building blocks of our brains are neurons: these are nerve cells that can communicate with other nerve cells via connections called synapses.

Complex square roots

Created on: 6 July 2021

This article about complex numbers is a little advanced. See here for a basic introduction to complex numbers. Every positive real number has two square roots, one being the negative of the other. It's easy to tell them apart by specifying whether you're looking at the positive or the negative square root. This means you can unambiguously define the square root function

Euler's formula

Created on: 6 July 2021

This article about complex numbers is a little advanced. See here for a basic introduction to complex numbers.

Maths in a minute: The Wells-Riley model

Created on: 11 June 2021

What is the risk of catching an airborne disease? There are many mathematical models that describe the behaviour of gases and contaminants within them. An interesting example is the Wells-Riley equation, which estimates the expected number of people who become infected by sharing a room with people who have an airborne disease:

Maths in a Minute: Computational fluid dynamics

Created on: 11 June 2021

Suppose you want to design the fastest car, engineer a replacement heart valve or simulate the flow of air in a building to limit the risk of infectious disease. All of these rely on fluid dynamics, which can lead to some pretty tricky mathematics.

The Delta variant: What do we know?

Created on: 11 June 2021

The UK is yet again bracing itself for a government announcement regarding COVID-19 restrictions. The worry this time surrounds the Delta variant, first detected in India and classed a variant of concern by the UK government on May 6, 2021.

A breath of fresh air

Created on: 11 June 2021

There would be a scandal if thousands of people were dying from a disease caught from the water that comes out of the tap. Or if commonly used building materials were causing widespread disease. Could the COVID-19 pandemic change our expectations about catching diseases from the air indoors? Lidia Morawska

Happy birthday Quicksort!

Created on: 4 June 2021

Tony Hoare, the inventor of Quicksort, in 2011. Photo: Rama, CC BY-SA 2.0 FR

Happy birthday Quicksort!

Created on: 4 June 2021

Next month sees the 60th birthday of Quicksort, a sorting algorithm that even at its advanced age is still hailed as one of the best. In the previous article Quicksort's inventor, Tony Hoare, told us how his famous brain child was preceded by something called bubble sort. We now go on to explore Quicksort itself. It's not as simple as bubble sort, but the idea is beautifully elegant.

Happy birthday Quicksort: Starting with bubbles

Created on: 4 June 2021

When you are buying online you usually get the option to see the items you searched for ordered by price, average customer rating, or perhaps date. If you have ever tried to put a bunch of things (e.g. books on your shelf) in order, you'll know it takes time. This is why the world owes a huge debt of gratitude to computer scientist Tony Hoare for inventing Quicksort — a famous sorting algorithm which celebrates its 60th birthday this year.

Maths in a minute: Asymptotes

Created on: 20 May 2021

Some curves get simple in the limit. As an example, look at the red curve below. As you move out to the right along the -axis, the curve gets closer and closer to the horizontal blue line.

Will the virus escape the vaccines?

Created on: 11 May 2021

Over the last few months SARS-CoV-2, the virus causing COVID-19, has racked up a number of mutations. Some variants, like the one first identified in Kent, are more transmissible and harmful than the original wild type. Others, like the one first identified in Brazil, appear to be more resistant to the vaccines that are being rolled out.

How to predict our changing climate

Created on: 4 May 2021

Emily Shuckburg

Seeing traffic through new eyes

Created on: 22 April 2021

Roads are arteries of modern life, but traffic comes with problems. It's bad for the environment and for our climate, and it can also be bad for our health. Road accidents cause deaths and injuries, pollution causes lung and respiratory diseases, as well as cancers, and the noise and stress of traffic can impact people's mental health.

Vaccination: Where do we stand and where are we going?

Created on: 1 April 2021

The roll-out of COVID-19 vaccines in the UK is going well, so it seems there are grounds for optimism. But what can we really say about where the vaccines have got us so far and where we are likely to be when the rollout is complete?

All about Plus on the Living Proof podcast

Created on: 19 March 2021

We are very proud to have been invited to Living Proof, the podcast of the iconic Isaac Newton Institute in Cambridge!

Reducing NHS waiting lists in times of COVID

Created on: 8 March 2021

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

Testing testing in schools

Created on: 4 March 2021

What's the safest way of opening schools? Researchers from the JUNIPER Consortium have been exploring this question and have come up with some very interesting results. "We weren't investigating whether we should reopen schools," says Louise Dyson, Associate Professor in Epidemiology at the University of Warwick and a member of the JUNIPER consortium. "Instead we were asking, are there things we can do with testing to make things better."

Welcome to the world of symmetry

Created on: 2 March 2021

When mathematicians study symmetry they use the theory of groups. The field underpins much of modern mathematics and is also hugely relevant to other areas — from physics to computer science. And although it's over two hundred years old, group theory is still a vibrant and dynamic area in which exciting things are happening right now.

New perspectives in symmetry

Created on: 2 March 2021

Group theory is essentially the study of symmetry. It underpins much of modern mathematics and is also hugely relevant to other areas — from physics to computer science. And although the field is over two hundred years old, it's still a vibrant and dynamic area in which exciting things are happening right now.

The maths and magic of shuffling

Created on: 2 March 2021

Will Houstoun and Cheryl Praeger

Maths in a minute: Cyclic groups

Created on: 1 February 2021

This article is about understanding abstracts objects called groups. If you don't know what they are, then you might want to read this brief explanation. Some things go round and round. An example are the hours of a clock. If you start at 12 and add one hour you get to 1, add another hour and you get to 2, and so on, until after twelve additions you're back to where you started.

Maths in a minute: Representing groups

Created on: 1 February 2021

This article is about understanding abstracts objects called groups. If you don't know what they are, then you might want to read this brief explanation.

The magic of shuffling

Created on: 29 January 2021

How do you shuffle a pack of cards? Our shuffling is very unimpressive, we've even been known to resort to jumbling them around in a big pile on the table. But good news – here is how you shuffle like a professional!

The mathematics of shuffling

Created on: 29 January 2021

In the Plus article, The magic of shuffling, we found out what a magician can do with a card shuffle. But what might a mathematician do when shuffling cards? To find out we asked Cheryl Praeger, from the University of Western Australia. It was Praeger who first intrigued us in card shuffling with her fascinating talk at the Isaac Newton Institute last year.

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