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After losing an eye at the age of 5, the 2024 Abel prize winner Michel Talagrand found comfort in mathematics.

French mathematician Michel Talagrand has won the 2024 Abel prize for his work on probability theory and describing randomness. Shortly after he had heard the news, New Scientist spoke with Talagrand to learn more about his mathematical journey.

Alex Wilkins: What does it mean to win the Abel prize?

Michel Talagrand: I think everybody would agree that the Abel prize is really considered like the equivalent of the Nobel prize in mathematics. So it’s something for me totally unexpected, I never, ever dreamed I would receive this prize. And actually, it’s not such an easy thing to do, because there is this list of people who already received it. And on that list, they are true giants of mathematics. And it’s not such a comfortable feeling to sit with them, let me tell you, because it’s clear that their achievements are on an entirely other scale than I am.

What are your attributes as a mathematician?

I’m not able to learn mathematics easily. I have to work. It takes a very long time and I have a terrible memory. I forget things. So I try to work, despite handicaps, and the way I worked was trying to understand really well the simple things. Really, really well, in complete detail. And that turned out to be a successful approach.

Why does maths appeal to you?

Once you are in mathematics, and you start to understand how it works, it’s completely fascinating and it’s very attractive. There are all kinds of levels, you are an explorer. First, you have to understand what people before you did, and that’s pretty challenging, and then you are on your own to explore, and soon you love it. Of course, it is extremely frustrating at the same time. So you have to have the personality that you will accept to be frustrated.

But my solution is when I’m frustrated with something, I put it aside, when it’s obvious that I’m not going to make any more progress, I put it aside and do something else, and I come back to it at a later date, and I have used that strategy with great efficiency. And the reason why it succeeds is the function of the human brain, things mature when you don’t look at them. There are questions which I’ve literally worked on for a period of 30 years, you know, coming back to them. And actually at the end of the 30 years, I still made progress. That’s what is incredible.

How did you get your start?

Now, that’s a very personal story. First, it helps that my father was a maths teacher, and of course that helped. But really, the determining factor is I was unlucky to have been born with a deficiency in my retinas. And I lost my right eye when I was 5 years old. I had multiple retinal detachments when I was 15. I stayed in the hospital a long time, I missed school for six months. And that was extremely traumatic, I lived in constant terror that there will be a next retinal detachment.

To escape that, I started to study. And my father really immensely helped me, you know, when he knew how hard it was, and when I was in hospital, he came to see me every day and he started talking about some simple mathematics, just to keep my brain functioning. I started studying hard mathematics and physics to really, as I say, to fight the terror and, of course, when you start studying, then you become good at it and once you become good, it’s very appealing.

What is it like to be a professional mathematician?

Nobody tells me what I have to do and I’m completely free to use my time and do what I like. That fitted my personality well, of course, and it’s helped me to devote myself totally to my work.

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to Alex Wilkins*

Matrix multiplication – where two grids of numbers are multiplied together – forms the basis of many computing tasks, and an improved technique discovered by an artificial intelligence could boost computation speeds by up to 20 per cent.

Multiplying numbers is a fundamental task for computers

An artificial intelligence created by the firm DeepMind has discovered a new way to multiply numbers, the first such advance in over 50 years. The find could boost some computation speeds by up to 20 per cent, as a range of software relies on carrying out the task at great scale.

Matrix multiplication – where two grids of numbers are multiplied together – is a fundamental computing task used in virtually all software to some extent, but particularly so in graphics, AI and scientific simulations. Even a small improvement in the efficiency of these algorithms could bring large performance gains, or significant energy savings.

For centuries, it was believed that the most efficient way of multiplying matrices would be proportional to the number of elements being multiplied, meaning that the task becomes proportionally harder for larger and larger matrices.

But the mathematician Volker Strassen proved in 1969 that multiplying a matrix of two rows of two numbers with another of the same size doesn’t necessarily involve eight multiplications and that, with a clever trick, it can be reduced to seven. This approach, called the Strassen algorithm, requires some extra addition, but this is acceptable because additions in a computer take far less time than multiplications.

The algorithm has stood as the most efficient approach on most matrix sizes for more than 50 years, although some slight improvements that aren’t easily adapted to computer code have been found. But DeepMind’s AI has now discovered a faster technique that works perfectly on current hardware. The company’s new AI, AlphaTensor, started with no knowledge of any solutions and was presented with the problem of creating a working algorithm that completed the task with the minimum number of steps.

It found an algorithm for multiplying two matrices of four rows of four numbers using just 47 multiplications, which outperforms Strassen’s 49 multiplications. It also developed improved techniques for multiplying matrices of other sizes, 70 in total.

AlphaTensor discovered thousands of functional algorithms for each size of matrix, including 14,000 for 4×4 matrices alone. But only a small minority were better than the state of the art. The research builds on AlphaZero, DeepMind’s game-playing model, and has been two years in the making.

Hussein Fawzi at DeepMind says the results are mathematically sound, but are far from intuitive for humans. “We don’t really know why the system came up with this, essentially,” he says. “Why is it the best way of multiplying matrices? It’s unclear.”

“Somehow, the neural networks get an intuition of what looks good and what looks bad. I honestly can’t tell you exactly how that works. I think there is some theoretical work to be done there on how exactly deep learning manages to do these kinds of things,” says Fawzi.

DeepMind found that the algorithms could boost computation speed by between 10 and 20 per cent on certain hardware such as an Nvidia V100 graphics processing unit (GPU) and a Google tensor processing unit (TPU) v2, but there is no guarantee that those gains would also be seen on common devices like a smartphone or laptop.

James Knight at the University of Sussex, UK, says that a range of software run on supercomputers and powerful hardware, like AI research and weather simulation, is effectively large-scale matrix multiplication.
“If this type of approach was actually implemented there, then it could be a sort of universal speed-up,” he says. “If Nvidia implemented this in their CUDA library [a tool that allows GPUs to work together], it would knock some percentage off most deep-learning workloads, I’d say.”

Oded Lachish at Birkbeck, University of London, says the new algorithms could boost the efficiency of a wide range of software, because matrix multiplication is such a common problem – and more algorithms are likely to follow.

“I believe we’ll be seeing AI-generated results for other problems of a similar nature, albeit rarely something as central as matrix multiplication. There’s significant motivation for such technology, since fewer operations in an algorithm doesn’t just mean faster results, it also means less energy spent,” he says. If a task can be completed slightly more efficiently, then it can be run on less powerful, less power-intensive hardware, or on the same hardware in less time, using less energy.

But DeepMind’s advances don’t necessarily mean human coders are out of a job. “Should programmers be worried? Maybe in the far future. Automatic optimisation has been done for decades in the microchip design industry and this is just another important tool in the coder’s arsenal,” says Lachish.

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*Credit for article given to Matthew Sparkes*

Mathematicians who have studied the most efficient way to pack spheres in eight-dimensional space and the spacing of prime numbers are among this year’s recipients of the highest award in mathematics, the Fields medal.

Mathematicians who have studied the most efficient way to pack spheres in eight-dimensional space and the spacing of prime numbers are among this year’s recipients of the highest award in mathematics, the Fields medal.

The winners for 2022 are James Maynard at the University of Oxford; Maryna Viazovska at the Swiss Federal Institute of Technology in Lausanne (EPFL); Hugo Duminil-Copin at the University of Geneva, Switzerland; and June Huh at Princeton University in New Jersey.

Kyiv-born Viazovska is only the second female recipient among the 64 mathematicians to have received the award.

“Sphere packing is a very natural geometric problem. You have a big box, and you have an infinite collection of equal balls, and you’re trying to put as many balls into the box as you can,” says Viazovska. Her contribution was to provide an explicit formula to prove the most efficient stacking pattern for spheres in eight dimensions – a problem she says took 13 years to solve.

Maynard’s work involved understanding the gaps between prime numbers, while Duminil-Copin’s contribution was in the theory of phase transitions – such as water turning to ice, or evaporating into steam – in statistical physics.

June Huh, who dropped out of high school aged 16 to become a poet, was recognised for a range of work including the innovative use of geometry in the field of combinatorics, the mathematics of counting and arranging.

The medal, which is considered to be as prestigious as the Nobel prize, is given to two, three or four mathematicians under the age of 40 every four years.

The awards were first given out in 1936 and are named in honour of Canadian mathematician John Charles Fields. This year’s awards were due to be presented at the International Congress of Mathematicians in Saint Petersburg, Russia, but the ceremony was relocated to Helsinki, Finland.

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*Credit for article given to Matthew Sparkes*

P is not NP? That is the question

One of the biggest open problems in mathematics may be solved within the next decade, according to a poll of computer scientists. A solution to the so-called P versus NP problem is worth $1 million and could have a profound effect on computing, and perhaps even the entire world.

The problem is a question about how long algorithms take to run and whether some hard mathematical problems are actually easy to solve.

P and NP both represent groups of mathematical problems, but it isn’t known if these groups are actually identical.

P, which stands for polynomial time, consists of problems that can be solved by an algorithm in a relatively short time. NP, which stands for nondeterministic polynomial time, comprises the problems that are easy to check if you have the right answer given a potential candidate, although actually finding an answer in the first place might be difficult.

NP problems include a number of important real-world tasks, such as the travelling salesman problem, which involves finding a route between a list of cities that is shorter than a certain limit. Given such a route, you can easily check if it fits the limit, but finding one might be more difficult.

Equal or not

The P versus NP problem asks whether these two collections of problems are actually the same. If they are, and P = NP, the implications are potentially world-changing, because it could become much easier to solve these tasks. If they aren’t, and P doesn’t equal NP, or P ≠ NP, a proof would still answer fundamental questions about the nature of computation.

The problem was first stated in 1971 and has since become one of the most important open questions in mathematics – anyone who can find the answer either way will receive $1 million from the Clay Mathematics Institute in Cambridge, Massachusetts.

William Gasarch, a computer scientist at the University of Maryland in College Park, conducts polls of his fellow researchers to gauge the current state of the problem. His first poll, in 2002, found that just 61 per cent of respondents thought P ≠ NP. In 2012, that rose to 83 per cent, and now in 2019 it has slightly increased to 88 per cent. Support for P = NP has also risen, however, from 9 per cent in 2002 to 12 per cent in 2019, because the 2002 poll had a large number of “don’t knows”.

Confidence that we might soon have an answer is also rising. In 2002, just 5 per cent thought the problem would be resolved in the next decade, falling to 1 per cent in 2012, but now the figure sits at 22 per cent. “This is very surprising since there has not been any progress on it,” says Gasarch. “If anything, I think that as the problem remains open longer, it seems harder.” More broadly, 66 per cent believe it will be solved before the end of the century.

There was little agreement on the kind of mathematics that would ultimately be used to solve the problem, although a number of respondents suggested that artificial intelligence, not humans, could play a significant role.

“I can see this happening to some extent, but the new idea needed will, I think, come from a human,” says Gasarch. “I hope so, not for any reason of philosophy, but just because if a computer did it we might know that (say) P ≠ NP, but not really know why.”

Neil Immerman at the University of Massachusetts Amherst thinks that this kind of polling is interesting, but ultimately can’t tell us much about the P versus NP problem.

“As this poll demonstrates, there is no consensus on how this problem will be eventually solved,” he says. “For that reason, it is hard to measure the progress we have made since 1971 when the question was first stated.”

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to Jacob Aron*

Grab a few balls and get calculating pi

Pi Day, which occurs every 14 March – or 3/14, in the US date format – celebrates the world’s favourite mathematical constant. This year, why not try an experiment to calculate its value? All you will need is a cardboard tube and a series of balls, each 100 times lighter than the next. You have those lying around the house, right?

This experiment was first formulated by mathematician Gregory Galperin in 2001. It works because of a mathematical trick involving the masses of a pair of balls and the law of conservation of energy.

First, take the tube and place one end up against a wall. Place two balls of equal mass in the tube. Let’s say that the ball closer to the wall is red, and the other is blue.

Next, bounce the blue ball off the red ball. If you have rolled the blue ball hard enough, there should be three collisions: the blue ball hits the red one, the red ball hits the wall, and the red ball bounces back to hit the blue ball once more. Not-so-coincidentally, three is also the first digit of pi.

To calculate pi a little bit more precisely, replace the red ball with one that is 100 times less massive than the blue ball – a ping pong ball might work, so we will call this the white ball.

When you perform the experiment again, you will find that the blue ball hits the white ball, the white ball hits the wall and then the white ball continues to bounce back and forth between the blue ball and the wall as it slows down. If you count the bounces, you’ll find that there are 31 collisions. That gives you the first two digits of pi: 3.1.

Galperin calculated that if you continue the same way, you will keep getting more digits of pi. If you replace the white ball with another one that is 10,000 times less massive than the blue ball, you will find that there are 314 collisions, and so on. If you have enough balls, you can count as many digits of pi as you like.

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*Credit for article given to Leah Crane*

The problem’s been solved … but the sweet treats were declined. Back to the Cutting Board

In 1904, French mathematician Henri Poincaré asked a key question about three-dimensional spaces (“manifolds”).

Imagine a piece of rope, so that firstly a knot is tied in the rope and then the ends are glued together. This is what mathematicians call a knot. A link is a collection of knots that are tangled together.

It has been observed that DNA, which is coiled up within cells, occurs in closed knotted form.

Complex molecules such as polymers are tangled in knotted forms. There are deep connections between knot theory and ideas in mathematical physics. The outsides of a knot or link in space give important examples of three-dimensional spaces.

Torus. Fropuff

Back to Poincaré and his conjecture. He asked if the 3-sphere (which can be formed by either adding a point at infinity to ordinary three-dimensional Euclidean space or by gluing two solid three-dimensional balls together along their boundary 2-spheres) was the only three-dimensional space in which every loop can be continuously shrunk to a point.

Poincaré had introduced important ideas in the structure and classification of surfaces and their higher dimensional analogues (“manifolds”), arising from his work on dynamical systems.

Donuts to go, please

A good way to visualise Poincaré’s conjecture is to examine the boundary of a ball (a two-dimensional sphere) and the boundary of a donut (called a torus). Any loop of string on a 2-sphere can be shrunk to a point while keeping it on the sphere, whereas if a loop goes around the hole in the donut, it cannot be shrunk without leaving the surface of the donut.

Many attempts were made on the Poincaré conjecture, until in 2003 a wonderful solution was announced by a young Russian mathematician, Grigori “Grisha” Perelman.

This is a brief account of the ideas used by Perelman, which built on work of two other outstanding mathematicians, Bill Thurston and Richard Hamilton.

3D spaces

Thurston made enormous strides in our understanding of three-dimensional spaces in the late 1970s. In particular, he realised that essentially all the work that had been done since Poincaré fitted into a single theme.

He observed that known three-dimensional spaces could be divided into pieces in a natural way, so that each piece had a uniform geometry, similar to the flat plane and the round sphere. (To see this geometry on a torus, one must embed it into four-dimensional space!).

Thurston made a bold “geometrisation conjecture” that this should be true for all three-dimensional spaces. He had many brilliant students who further developed his theories, not least by producing powerful computer programs that could test any given space to try to find its geometric structure.

Thurston made spectacular progress on the geometrisation conjecture, which includes the Poincaré conjecture as a special case. The geometrisation conjecture predicts that any three-dimensional space in which every loop shrinks to a point should have a round metric – it would be a 3-sphere and Poincaré’s conjecture would follow.

In 1982, Richard Hamilton published a beautiful paper introducing a new technique in geometric analysis which he called Ricci flow. Hamilton had been looking for analogues of a flow of functions, so that the energy of the function decreases until it reaches a minimum. This type of flow is closely related to the way heat spreads in a material.

Hamilton reasoned that there should be a similar flow for the geometric shape of a space, rather than a function between spaces. He used the Ricci tensor, a key feature of Einstein’s field equations for general relativity, as the driving force for his flow.

He showed that, for three-dimensional spaces where the Ricci curvature is positive, the flow gradually changes the shape until the metric satisfies Thurston’s geometrisation conjecture.

Hamilton attracted many outstanding young mathematicians to work in this area. Ricci flow and other similar flows have become a huge area of research with applications in areas such as moving interfaces, fluid mechanics and computer graphics.

Ricci flow. CBN

He outlined a marvellous program to use Ricci flow to attack Thurston’s geometrisation conjecture. The idea was to keep evolving the shape of a space under Ricci flow.

Hamilton and his collaborators found the space might form a singularity, where a narrow neck became thinner and thinner until the space splits into two smaller spaces.

Hamilton worked hard to try to fully understand this phenomenon and to allow the pieces to keep evolving under Ricci flow until the geometric structure predicted by Thurston could be found.

Perelman

This is when Perelman burst on to the scene. He had produced some brilliant results at a very young age and was a researcher at the famous Steklov Institute in St Petersburg. Perelman got a Miller fellowship to visit UC Berkeley for three years in the early 1990s.

I met him there around 1992. He then “disappeared” from the mathematical scene for nearly ten years and re-emerged to announce that he had completed Hamilton’s Ricci flow program, in a series of papers he posted on the electronic repository called ArXiv.

His papers created enormous excitement and within several months a number of groups had started to work through Perelman’s strategy.

Eventually everyone was convinced that Perelman had indeed succeeded and both the geometrisation and Poincaré conjecture had been solved.

Perelman was awarded both a Fields medal (the mathematical equivalent of a Nobel prize) and also offered a million dollars for solving one of the Millenium prizes from the Clay Institute.

He turned down both these awards, preferring to live a quiet life in St Petersburg. Mathematicians are still finding new ways to use the solution to the geometrisation conjecture, which is one of the outstanding mathematical results of this era.

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to Hyam Rubinstein*

Machines are getting better at maths – artificial intelligence has learned to solve university-level calculus problems in seconds.

François Charton and Guillaume Lample at Facebook AI Research trained an AI on tens of millions of calculus problems randomly generated by a computer. The problems were mathematical expressions that involved integration, a common technique in calculus for finding the area under a curve.

To find solutions, the AI used natural language processing (NLP), a computational tool commonly used to analyse language. This works because the mathematics in each problem can be thought of as a sentence, with variables, normally denoted x, playing the role of nouns and operations, such as finding the square root, playing the role of verbs. The AI then “translates” the problem into a solution.

When the pair tested the AI on 500 calculus problems, it found a solution with an accuracy of 98 per cent. A comparable standard program for solving maths problems had only an accuracy of 85 per cent on the same problems.

The team also gave the AI differential equations to solve, which are other equations that require integration to solve as well as other techniques. For these equations, the AI wasn’t quite as good, solving them correctly 81 per cent for one type of differential equation and 40 per cent on a harder type.

Despite this, it could still correctly answer questions that confounded other maths programs.

Doing calculus on a computer isn’t especially useful in practice, but with further training AI might one day be able to tackle maths problems that are too hard for humans to crack, says Charton.

The efficiency of the AI could save humans time in other mathematical tasks, for example, when proving theorems, says Nikos Aletras at the University of Sheffield, UK.

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to Gege Li*

Money should be no object when it comes to the numbers game. krissyho

Mathematics has many grand challenge problems, but none that can potentially be settled by pouring in more money – unlike the case of the Large Hadron Collider, the Square Kilometre Array or other such projects.

Maths is a different beast. But, of course, you’re offering me unlimited, free dosh, so I should really think of something.

Grand Challenges in Mathematics

In his famous 1900 speech The Problems of Mathematics David Hilbert listed 23 problems that set the stage for 20th century mathematics.

It was a speech full of optimism for mathematics in the coming century and Hilbert felt open (or unsolved) problems were a sign of vitality:

“The great importance of definite problems for the progress of mathematical science in general … is undeniable … [for] as long as a branch of knowledge supplies a surplus of such problems, it maintains its vitality … every mathematician certainly shares … the conviction that every mathematical problem is necessarily capable of strict resolution … we hear within ourselves the constant cry: There is the problem, seek the solution. You can find it through pure thought …”

Hilbert’s problems included the continuum hypothesis, the “well-ordering” of the reals, Goldbach’s conjecture, the transcendence of powers of algebraic numbers, the Riemann hypothesis, the extension of Dirichlet’s principle and many more.

Many were solved in subsequent decades, and each time it was a major event for mathematics.

The Riemann hypothesis (which deals with the distribution of prime numbers) remains on a list of seven “third millennium” problems.

For the solution of each millennium problem, the Clay Mathematics Institute offers – in the spirit of the times – a one million dollar prize.

This prize has already been awarded and refused by Perelman for resolving the Poincaré conjecture. The solution also merited Science’s Breakthrough of the Year, the first time mathematics had been so honoured.

Certainly, given unlimited moolah, learned groups could be gathered to attack each problem and assisted in various material ways. But targeted research in mathematics has even less history of success than in the other sciences … which is saying something.

Doron Zeilberger famously said that the Riemann hypothesis is the only piece of mathematics whose proof (i.e. certainty of knowledge) merits $10 billion being spent.

As John McCarthy wrote in Science in 1997:

“In 1965 the Russian mathematician Alexander Konrod said ‘Chess is the Drosophila [a type of fruit fly] of artificial intelligence.

“But computer chess has developed as genetics might have if the geneticists had concentrated their efforts, starting in 1910, on breeding racing Drosophila. We would have some science, but mainly we would have very fast fruit flies.”

Unfortunately, the so-called “curse of exponentiality” – whereby the more difficult a problem becomes, the challenge of solving it increases exponentially – pervades all computing, and especially mathematics.

As a result, many problems – such as Ramsey’s Theorem – will likely be impossible to solve by computer brute force, regardless of advances in technology.

Money for nothing

But, of course, I must get to the point. You’re offering me a blank cheque, so what would I do? A holiday in Greece for two? No, not this time. Here’s my manifesto:

Google has transformed mathematical life (as it has with all aspects of life) but is not very good at answering mathematical questions – even if one knows precisely the question to ask and it involves no symbols.

In February, IBM’s Watson computer walloped the best human Jeopardy players in one of the most impressive displays of natural language competence by a machine.

I would pour money into developing an enhanced Watson for mathematics and would acquire the whole corpus of maths for its database.

Maths ages very well and I am certain we would discover a treasure trove. Since it’s hard to tell where maths ends and physics, computer science and other subjects begin, I would be catholic in my acquisitions.

Since I am as rich as Croesus and can buy my way out of trouble, I will not suffer the same court challenges Google Books has faced.

I should also pay to develop a comprehensive computation and publishing system with features that allow one to manipulate mathematics while reading it and which ensures published mathematics is rich and multi-textured, allowing for reading at a variety of levels.

Since I am still in a spending mood, I would endow a mathematical research institute with great collaboration tools for roughly each ten million people on Earth.

Such institutes have greatly enhanced research in the countries that can afford and chose to fund them.

Content with my work, I would then rest.

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to Jonathan Borwein (Jon)*

Reduce wastage and enjoy deeply satisfying neat folds by applying a little geometry to your gift-wrapping, says Katie Steckles.

Wrapping gifts in paper involves converting a 2D shape into a 3D one, which presents plenty of geometrical challenges. Mathematics can help with this, in particular by making sure that you are using just the right amount of paper, with no wastage.

When you are dealing with a box-shaped gift, you might already wrap the paper around it to make a rectangular tube, then fold in the ends. With a little measuring, though, you can figure out precisely how much paper you will need to wrap a gift using this method, keeping the ends nice and neat.

For example, if your gift is a box with a square cross-section, you will need to measure the length of the long side, L, and the thickness, T, which is the length of one side of the square. Then, you will need a piece of paper measuring 4 × T (to wrap around the four sides with a small overlap) by L + T. Once wrapped around the shape, a bit of paper half the height of the square will stick out at each end, and if you push the four sides in carefully, you can create diagonal folds to make four points that meet neatly in the middle. The square ends of the gift make this possible (and deeply satisfying).

Similarly, if you are wrapping a cylindrical gift with diameter D (such as a candle), mathematics tells us you need your paper to be just more than π × D wide, and L + D long. This means the ends can be folded in – possibly less neatly – to also meet exactly in the middle (sticky bows are your friend here).

How about if your gift is an equilateral triangular prism? Here, the length of one side of the triangle gives the thickness T, and your paper should be a little over 3 × T wide and L + (2 × T) long. The extra length is needed because it is harder to fold the excess end bits to make the points meet in the middle. Instead, you can fold the paper to cover the end triangle exactly, by pushing it in from one side at a time and creating a three-layered triangle of paper that sits exactly over the end.

It is also possible to wrap large, flat, square-ish gifts using a diagonal method. If the diagonal of the top surface of your box is D, and the height is H, you can wrap it using a square piece of paper that measures a little over D + (√2 × H) along each side.

Place your gift in the centre of the paper, oriented diagonally, and bring the four corners to meet in the middle of your gift, securing it with one piece of tape or a sticky bow. This will cover all the faces exactly, and look pretty smart too.

For maximum mathematical satisfaction, what you want is to get the pattern on the paper to line up exactly. This is easier for a soft gift, where you can squash it to line up the pattern, but will only work with a box if the distance around it is exactly a multiple of the width of the repeat on the pattern. Otherwise, follow my example (above) and get your own custom wrapping paper printed!

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to Katie Steckles*

We can’t tame the oceans, but modelling can help us better understand them.

Last year will go on record as one of significant natural disasters both in Australia and overseas. Indeed, the flooding of the Brisbane River in January is still making news as the Queensland floods inquiry investigates whether water released from Wivenhoe Dam was responsible. Water modelling is being used to answer the question: could modelling have avoided the problem in the first place?

This natural disaster – as well as the Japanese tsunami in March and the flooding in Bangkok in October – involved the movement of fluids: water, mud or both. And all had a human cost – displaced persons, the spread of disease, disrupted transport, disrupted businesses, broken infrastructure and damaged or destroyed homes. With the planet now housing 7 billion people, the potential for adverse humanitarian effects from natural disasters is greater than ever.

Here in CSIRO’s division of Mathematical and Information Sciences, we’ve been working with various government agencies (in Australia and China) to model the flow of flood waters and the debris they carry. Governments are starting to realise just how powerful computational modelling is for understanding and analysing natural disasters and how to plan for them.

This power is based on two things – the power of computers and the power of the algorithms (computer processing steps) that run on the computers.

In recent years, the huge increase in computer power and speed coupled with advances in algorithm development has allowed mathematical modellers like us to make large strides in our research.

These advances have enabled us to model millions, even billions of water particles, allowing us to more accurately predict the effects of natural and man-made fluid flows, such as tsunamis, dam breaks, floods, mudslides, coastal inundation and storm surges.

So how does it work?

Well, fluids such as sea water can be represented as billions of particles moving around, filling spaces, flowing downwards, interacting with objects and in turn being interacted upon. Or they can be visualised as a mesh of the fluids’ shape.

Let’s consider a tsunami such as the one that struck the Japanese coast in March of last year. When a tsunami first emerges as a result of an earthquake, shallow water modelling techniques give us the most accurate view of the wave’s formation and early movement.

Mesh modelling of water being poured into a glass.

Once the wave is closer to the coast however, techniques known collectively as smoothed particle hydrodynamics (SPH) are better at predicting how the wave interacts with local geography. We’ve created models of a hypothetical tsunami off the northern Californian coastline to test this.

A dam break can also be modelled using SPH. The modelling shows how fast the water moves at certain times and in certain places, where water “overtops” hills and how quickly it reaches towns or infrastructure such as power stations.

This can help town planners to build mitigating structures and emergency services to co-ordinate an efficient response. Our models have been validated using historical data from a real dam that broke in California in 1928 – the St. Francis Dam.

Having established that our modelling techniques work better than others, we can apply them to a range of what-if situations.

In collaboration with the Satellite Surveying and Mapping Application Centre in China we tested scenarios such as the hypothetical collapse of the massive Geheyan Dam in China.

We combined our modelling techniques with digital terrain models to get a realistic picture of how such a disaster would unfold and, therefore, what actions could mitigate it.

Our experience in developing and using these techniques over several decades allows us to combine them in unique ways for each situation.

We’ve modelled fluids not just for natural disaster planning but also movie special effects, hot metal production, water sports and even something as everyday as insurance.

Insurance companies have been looking to us for help to understand how natural disasters unfold. They cop a lot of media flak after disasters for not covering people affected. People living in low-lying areas have traditionally had difficulty accessing flood insurance and find themselves unprotected in flood situations.

Insurers are starting to realise that the modelling of geophysical flows can provide a basis for predicting localised risk of damage due to flooding and make flood coverage a viable business proposition. One Australian insurance company has been working with us to quantify risk of inundation in particular areas.

Using data from the 1974 Brisbane floods, the floods of last year and fluid modelling data, an insurance company can reliably assess residents’ exposure to particular risks and thereby determine suitable premiums.

With evidence-based tools such as fluid modelling in their arsenal, decision-makers are better prepared for the future. That may be a future of more frequent natural disasters, a future with a more-densely-populated planet, or, more likely, a combination of both.

For more such insights, log into www.international-maths-challenge.com.

*Credit for article given to Mahesh Prakash*