**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!

Created on: 21 September 2023

The UK is aiming for a decarbonised electricity supply by 2035. Generating electricity without the use of fossil fuels is not just an engineering and industrial challenge, it is also a huge mathematical challenge. "We need to force the pace on research and innovation if we are going to achieve the challenging target of decarbonising the electricity supply by the mid 2030s," says Chris Dent, Professor of Industrial Mathematics at the University of Edinburgh.

Created on: 21 September 2023

The UK is aiming for a decarbonised electricity supply by 2035. Generating electricity without the use of fossil fuels is not just an engineering and industrial challenge, it is also a huge mathematical challenge. "We need to force the pace on research and innovation if we are going to achieve the challenging target of decarbonising the electricity supply by the mid 2030s," says Chris Dent, Professor of Industrial Mathematics at the University of Edinburgh.

Created on: 20 September 2023

Non-linear relationships are tricky relationships. To understand why, let's first look at a linear relationship.

Created on: 19 September 2023

This week we co-host a fascinating episode of the Isaac Newton Institute's Living Proof podcas

Created on: 12 September 2023

Did you do anything fun on your summer holidays?

Created on: 8 September 2023

Veganism, vegetarianism, and flexitarianism have been booming. There are three main reasons for people turning away from meat and dairy: concerns about their own health, about the environmental impact of the meat and dairy industries, and about animal cruelty.

Created on: 7 September 2023

Our ability to see inside a person's body, without surgery, has revolutionised modern medicine and saved countless lives. And each life saved is thanks to the mathematics of tomography. This medical imaging technique passes waves through a person's body, mathematically reconstructing an image from the amount these waves are scattered or absorbed by the structures inside. And tomography isn't just important in medicine.

Created on: 7 September 2023

Inverse problems can solve crimes! Image: Klaus with K, CC BY-SA 3.0.

Created on: 7 September 2023

Inverse problems can solve crimes! Image: Klaus with K, CC BY-SA 3.0.

Created on: 30 August 2023

Our ability to see inside a person's body, without surgery, has revolutionised modern medicine and saved countless lives. And each life saved is thanks to the mathematics of tomography. This medical imaging technique passes waves through a person's body, mathematically reconstructing an image from the amount these waves are scattered or absorbed by the structures inside.

Created on: 30 August 2023

Our ability to see inside a person's body, without surgery, has revolutionised modern medicine and saved countless lives. And each life saved is thanks to the mathematics of tomography. This medical imaging technique passes waves through a person's body, mathematically reconstructing an image from the amount these waves are scattered or absorbed by the structures inside.

Created on: 11 August 2023

There's been an exciting breakthrough in the field of topology: a group of mathematicians have disproved the telescope conjecture. It had been famous in the field as the last of a whole series of conjectures, formulated by Douglas Ravenel in 1984, to remain unsolved.

Created on: 11 August 2023

Topology studies shapes without worrying about finer like the values of lengths, angles, or areas. This does make things rather slippery, but maths can help: topology delivers some beautiful examples of how mathematical language can not only make intuition precise, but also expand our intuitive horizon.

Created on: 11 August 2023

As we explained in the first part of this article, mathematicians would ideally like to understand the homotopy groups for all possible combinations of

Created on: 9 August 2023

The concept of homotopy captures the idea that, sometimes, two shapes can be deformed into each other without doing anything drastic, like cutting them up or lifting them out of their surroundings. As an example, look at the yellow and the red curves in the GeoGebra applet below. They form two different types of S-shapes, but it's easy to imagine deforming one into the other. If you don't believe it, use the slider.

Created on: 9 August 2023

The concept of homotopy captures the idea that, sometimes, two shapes can be deformed into each other without doing anything drastic, like cutting them up or lifting them out of their surroundings. As an example, look at the yellow and the red curves in the GeoGebra applet below. They form two different types of S-shapes, but it's easy to imagine deforming one into the other. If you don't believe it, use the slider.

Created on: 23 June 2023

"I think I'll stop here." This is how, on 23rd June 1993, Andrew Wiles ended his series of lectures at the

Created on: 23 June 2023

"I think I'll stop here." This is how, on 23rd June 1993, Andrew Wiles ended his series of lectures at the Isaac Newton Institute (INI), our neighbour here at the Centre for Mathematical Sciences. The applause, so witnesses report, was thunderous. Wiles had just announced a proof that had eluded mathematicians for over 350 years: the proof of Fermat's Last Theorem.

Created on: 23 June 2023

To celebrate 30 years since he announced his proof of Fermat's Last Theorem we were lucky enough to visit Andrew Wiles at the University of Oxford. In this video, produced by Dan Aspel and Grace Merton from the Isaac Newton Institute for Mathematical Sciences, Wiles tells us about his experience working on the proof, sharing it with the world, and the exciting mathematics it has led to.

Created on: 23 June 2023

Andrew Wiles, at the University of Oxford in 2023 (Image courtesy of the INI) Fermat's Last Theorem is one of the most beguiling results in mathematics.

Created on: 19 June 2023

There are many reasons why you might want to write for an audience that doesn't consist only of experts in your field.

Created on: 9 June 2023

Waves are all around us. There are sound waves, water waves, electromagnetic waves, and vibration waves to name just a few. When a wave meets an object in its path, it scatters off it in different directions. When many waves meet multiple objects, the scattering pattern soon becomes extremely complex, so complex that the mathematical techniques needed to understand and predict it are still being developed.

Created on: 9 June 2023

Waves come in many different forms and affect many different aspects of our lives. Sound waves allow us to hear; visible electromagnetic waves allow us to see; radio waves allow us to communicate over long distances; microwaves allow our devices to access the internet wirelessly; X-rays and ultrasonic waves allow us to perform internal medical examinations without surgery. Our lives are endlessly shaped by waves.

Created on: 9 June 2023

Waves are all around us. There are sound waves, water waves, electromagnetic waves, and vibration waves to name just a few. Despite the differences between them, all waves have the same underlying mathematical framework. Sine functions describe perfect waves of given frequencies and amplitudes, and more complex waveforms can be built by adding up sine waves of different shapes.

Created on: 23 May 2023

Chocolate and mayonnaise are two of our all time favourite foods, so we were very happy to get the chance to talk to Valerie P

Created on: 9 May 2023

We all know we need to make the best of things – but how exactly do we do that? What we need is an area of maths called optimisation, which usually involves maximising something (say the amount of crops we can grow from a field) or minimising something (say the amount of water you need to grow those crops).

Created on: 9 May 2023

We all know we need to make the best of things – but how exactly do we do that? What we need is an area of maths called optimisation, which usually involves maximising something (say the amount of crops we can grow from a field) or minimising something (say the amount of water you need to grow those crops).

Created on: 9 May 2023

"Oceans are our friends. They suck in carbon, they give out oxygen, they help our planet to breathe," says mathematician Luke Bennetts. "They also soak up 90% of excess heat we create through burning fossil fuels."

Created on: 9 May 2023

"Oceans are our friends. They suck in carbon, they give out oxygen, they help our planet to breathe," says mathematician Luke Bennetts. "They also soak up 90% of excess heat we create through burning fossil fuels."

Created on: 28 March 2023

"What's a statistician's favourite sandwich filling?..."

Created on: 22 March 2023

The Abel Prize 2023 has been awarded to the mathematician Luis A. Caffarelli of the University of Texas at Austin, USA, for his work on what you can think of as the mathematics of change. The Abel Prize is one of the highest accolades in mathematics. Awarded annually by the Norwegian Academy of Science and Letters, it comes with a prize money of 7.5 million Norwegian Kroner (over £575,000). Caffarelli is the 26th mathematician to receive the prize since its establishment in 2002.

Created on: 21 March 2023

Having empathy with your audience – with all your audiences – is the first step for making your content accessible.

Created on: 14 March 2023

Communicating from the mathematical fronti

Created on: 14 March 2023

This Pi Day, March 14th, we say thank you to to all the wonderful mathematicians and scientists who have helped make our podcast, Maths on the move! Our podcast celebrates the researchers themselves, as well as their research, and we hope it conveys the creative and dynamic nature of doing mathematics – bringing mathematics to life.

Created on: 14 March 2023

This Pi Day, March 14th, we say thank you to to all the wonderful mathematicians and scientists who have helped make our podcast, Maths on the move! Our podcast celebrates the researchers themselves, as well as their research, and we hope it conveys the creative and dynamic nature of doing mathematics – bringing mathematics to life.

Created on: 10 March 2023

Mathematics met politics this week, when twenty mathematicians headed to Houses of Parliament for the STEM for BRITAIN awards 2023. In this annual event early career researchers in maths, engineering, the biological and biomedical sciences, chemistry, and physics are invited to submit posters explaining their work. A total of 120 of them are then chosen across all subjects for a poster exhibition in parliament, and a panel of expert judges chooses three medalists for each discipline.

Created on: 7 March 2023

To celebrate this year's International Women's Day on March 8, 2023, we revisit some of the articles and podcasts we have produced with women mathematicians over the last year. We've really enjoyed learning about these women's fascinating work and we hope that you will too!

Created on: 3 February 2023

Ants seem to effortlessly cooperate and work together. Just think of how ants travel in well-ordered lanes carrying food back to their nest, all done without any sort of agreement or master plan.

Created on: 1 February 2023

Mathematics in the UK is soon to have a brand new focal point: an Academy for the Mathematical Sciences, which will support the field in all its breadth and represent all people who work in it, from teachers in schools to researchers at university. The website of the Academy has just gone live, taking us one step further toward the Academy's full launch in 2025.

Created on: 20 January 2023

The world of maths is nearing an important date in its calendar: the announcement of the Abel Prize, awarded annually by the Norwegian Academy of Science and Letters.

Created on: 15 December 2022

Weather forecasts are never 100% certain, as you will see when you look at you weather app. Rather than telling you that it's definitely going to rain or not, it'll tell you a percentage chance. For example, at this very moment my app says the chance of rain today is only 10%.

Created on: 2 December 2022

Will climate change leave the region you live in hotter and drier, or wetter and stormier?

Created on: 1 December 2022

A lot of the content we produced over the last year forms part of 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.

Created on: 1 December 2022

We've known for centuries that compass needles point North, but why they do so is still a mystery. It's down to the Earth's magnetic field, of course, but exactly where this field comes from and how it behaves still isn't properly understood. The same goes for the magnetic fields of other planets, the Sun, and other stars further afield.

Created on: 1 December 2022

The Earth has a magnetic field and that's why the needle of a compass always points North. People have been using compasses to find their way around for over 2000 years, but we still don't know where the Earth's magnetic field comes from and how exactly it behaves.

Created on: 30 November 2022

If you've ever marvelled at a rainbow, you have witnessed dispersion in action. Dispersion is where the speed at which a wave moves depends on its frequency, and so wavelength. (You can read a basic introduction to waves and their frequency and wavelengths in Why sine (and cosine) make waves and Give us a wave.)

Created on: 11 November 2022

Yuriy Semenov was forced to leave Ukraine, and his work at the Institute of Hydromechanics at the National Academy of Sciences, due to the Russian invasion of February

Created on: 8 November 2022

Tosin Babasola is a PhD student in mathematics at the University of Bath and the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa). Here he tells us about his work on understanding the impact of climate on cocoa crops, why he chose to work in the area, and why the continuous production of cocoa is in everyone's interest.

Created on: 7 November 2022

Nataliya Vaisfel'd was until recently a mathematician at Odesa I. I. Mechnykov National University.

Created on: 2 November 2022

If you've ever marvelled at a rainbow, you have witnessed dispersion in action. Dispersion is where the speed at which a wave moves depends on its frequency (and so wavelength).

Created on: 2 November 2022

If you've ever marvelled at a rainbow, you have witnessed dispersion in action. Dispersion is where the speed at which a wave moves depends on its frequency (and so wavelength). (You can read a basic introduction to waves and their frequency and wavelengths in Why sine (and cosine) make waves and Give us a wave.)

Created on: 2 November 2022

Think of a wave – what comes to mind? The ocean swell rocking a boat? Ripples on a pond? The loop moving down a whip as it is cracked? Or perhaps your favourite song pumping out of your stereo speaker? Waves happen when a disturbance (of, say, the flat surface of the water by the ripple, the stillness of the air by a sound wave) moves over time.

Created on: 2 November 2022

The coordinate system we commonly use is called the Cartesian system, after the French mathematician René Descartes (1596-1650), who developed it in the 17th century. Legend has it that Descartes, who liked to stay in bed until late, was watching a fly on the ceiling from his bed. He wondered how to best describe the fly's location and decided that one of the corners of the ceiling could be used as a reference point.

Created on: 2 November 2022

Think of a right-angled triangle. Then you’ll probably remember from school that you can use the sine and cosine functions to find out more about the triangle. If is one of the angles that isn’t the right angle then you have

Created on: 1 November 2022

Good question. The Earth is indeed a magnet, although it's very weak. A good fridge magnet is over 200 times stronger. As a very crude approximation, you can imagine the Earth's magnetic field to be that of a bar magnet at the centre of the Earth, which is roughly aligned with the axis the Earth spins around, but tilted by about 11 degrees. The points where the North-South axis of this magnet intersects the Earth's surface are called the geomagnetic poles. Because of the tilt of the magnet's axis, the geomagnetic poles are not in the same places as the geographic poles.

Created on: 13 October 2022

If you're a woman between 50 and 70 in the UK you'll be familiar with the breast cancer screening programme. Women within that age range are invited for a mammogram every three years. If the result looks suspicious they are invited back for further tests. The aim is to spot breast cancers as early as possible as that gives the best prognosis.

Created on: 13 October 2022

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. Many aspects of our lives today are possible thanks to machine learning – where a machine is trained to do a specific, yet complex, job.

Created on: 11 October 2022

Today is Ada Lovelace Day, held on the second Tuesday in October every year, to celebrate the achievements of women in science, technology, engineering and mathematics. The day is in honour of Ada Lovelace, a female mathematician and pioneer in computing who was born over 200 years ago. (You can read more about her in our article, Ada Lovelace - visions of today.)

Created on: 19 August 2022

The 2022 International Congress of Mathematicians (ICM) was due to take place in July in St Petersburg, Russia. However, with Russia's invasion of Ukraine, the ICM couldn't take place as planned. Despite this challenge the international mathematics community has come together to create an ICM in 2022 like no other.

Created on: 9 August 2022

While the COVID-19 pandemic separated us physically, it also caused parts of our communities to pull together to meet the challenge. One group of people who have done this particularly well are mathematicians — those who already worked in the field of epidemiology when the pandemic started, and those whose expertise in building mathematical models could be repurposed to modelling the spread of the virus.

Created on: 26 July 2022

June Huh has won one of this year's Fields Medals at the International Congress of Mathematicians. The Fields Medal is one of the most prestigious prizes in mathematics.

Created on: 18 July 2022

This year the Isaac Newton Institute for Mathematical Sciences (INI) in Cambridge celebrates its 30th birthday. The INI gives mathematicians from around the world a place to come together to focus on their chosen area of maths for extended periods of time. All types of mathematics are covered and the focus is on interaction and collaboration.

Created on: 18 July 2022

Hugo Duminil-Copin has won a 2022 Fields Medal for his work transforming the mathematical theory of phase transitions in statistical physics.

Created on: 11 July 2022

James Maynard has won a 2022 Fields Medal for "spectacular contributions to number theory".

Created on: 5 July 2022

See here for all our coverage of the ICM 2022 and the prizes awarded there.

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.

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.

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)

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.

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.

Created on: 2 July 2022

You can read a shorter version of this article here.Hugo Duminil-Copin (Photo Matteo Fieni)

Created on: 2 July 2022

You can read a shorter version of this article here. Mark Braverman of Princeton University has been awarded the 2022 Abacus Medal at the International Congress of Mathematicians. The Abacus Medal is awarded for "outstanding contributions in Mathematical Aspects of Information Science". The Medal used to be called the Rolf Nevanlinna prize, and is awarded every four years at the International Congress of Mathematicians.

Created on: 1 July 2022

You can read a shorter version of this article here.

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.

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.

Created on: 1 July 2022

You can read a shorter version of this article here.

Created on: 1 July 2022

You can read a shorter version of this article here.

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.

Created on: 23 June 2022

How likely are you to win the lottery? In the UK lottery you have to choose 6 numbers out of 49, and for a chance at the jackpot you need all of your 6 numbers to come up in the main draw. So the question is really how many possible combinations of 6 numbers can be drawn out of 49?

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.

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.

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.

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.

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?

Created on: 24 May 2022

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

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.

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.

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.

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.

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.

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."

Created on: 23 March 2022

Things don't need to be perfectly round to count as balls. Footballs, golf balls, and tennis balls have seams and dimples, and even the Earth isn't perfectly round because it has mountain ranges and is slightly flattened at the poles. Yet, we still think of all of these things as spherical.

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 on 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.

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.

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.

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.

Created on: 12 January 2022

When you put your hand in the fire you'll get burnt, and when you put it in the snow your fingers will get cold. Temperature is something our bodies can easily sense, and it's a very important phenomenon in the physical world. But what exactly is temperature? Why is ice cold? Statistical mechanics can explain.

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?

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.

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?

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."

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?

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.

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.

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.

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.)

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

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.

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.

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"

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.

Created on: 21 October 2021

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

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.

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.

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.

Created on: 25 August 2021

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

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.

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.

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!

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.

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.

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

Created on: 6 July 2021

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

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:

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.

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.

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

Created on: 4 June 2021

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

Created on: 4 June 2021

There aren't many computer algorithms famous enough to get their very own birthday party, but Quicksort is one of them. Invented by the computer scientist Tony Hoare and published in July 1961, the algorithm's task is to put lists of things into the correct order: numbers in numerical order, words into alphabetical order, or dates into chronological oder. It does this so successfully, it is still hailed as one of the best sorting algorithms and implemented in many programming languages and libraries.

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.

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.

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.

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.

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.

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?

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!

Created on: 8 March 2021

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

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."

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.

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.

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.

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.

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!

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.