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Analysis and Comment (68)

The answer… 56. The answer… 56. Multiplication table by extender_01/Shutterstock

What is 7x8? You’ll need confidence to answer correctly

The British Chancellor George Osborne recently refused to answer a simple times table question posed to him by seven-year-old school boy Samuel Reddings. Osborne was asked the question 7x8, but declined…
How do we make sense of numbers without stats? How do we make sense of numbers without stats? Jeffrey/Flickr

Statistics is more than a numbers game – it underpins all sciences

AUSTRALIA 2025: How will science address the challenges of the future? In collaboration with Australia’s chief scientist Ian Chubb, we’re asking how each science discipline will contribute to Australia…
Maths can help in the hunt for MH370. Maths can help in the hunt for MH370. EPA/Australian Department of Defence

How statistics can help in the mission to find MH370

That the Malaysian government, with the help of the UK’s INMARSAT, was able to dramatically narrow down the search area for flight MH370, made it seem much more likely that the wreckage of the plane might…
Let’s paint a picture of ‘pi’. Let’s paint a picture of ‘pi’. jakedobkin/Flickr (cropped)

We still can’t get enough pi … but why?

The number pi (π = 3.14159265358979323846…), unique among the pantheon of mathematical constants, captures the fascination of the public and professional mathematicians. Three years ago one of the authors…
Once you get a taste, it’s hard to stop playing Candy Crush … but why? Once you get a taste, it’s hard to stop playing Candy Crush … but why? emi iemei/Flickr

Totally addicted to apps: difficulty makes Candy Crush so sweet

It’s been said that in a city, you’re never more than two metres away from a rat. But it seems more likely that you’re never more than two metres from someone playing the puzzle game Candy Crush Saga…
Mathematics is everywhere, from national security and genetics to public transport scheduling. Mathematics is everywhere, from national security and genetics to public transport scheduling. Bonita Club/Flickr (cropped)

Optimising the future with mathematics

AUSTRALIA 2025: How will science address the challenges of the future? In collaboration with Australia’s chief scientist Ian Chubb, we’re asking how each science discipline will contribute to Australia…
A better grounding in mathematics is needed for a career in science. A better grounding in mathematics is needed for a career in science. Shutterstock

A lack of maths just doesn’t add up for a career in science

Our future in science, technology and engineering relies on a foundation and understanding of mathematics. And while it is pleasing to see a growth in interest in our advanced mathematics course at the…
He is on a tour. He is on a tour. artbystevejohnson

How to get ants to solve a chess problem

Take a set of chess pieces and throw them all away except for one knight. Place the knight on any one of the 64 squares of a chess board. Can you make 63 legal moves so that you visit every square on the…
Chalk and talk maths classes are not going to cut it for modern students. Chalk and talk maths classes are not going to cut it for modern students. Maths image from www.shutterstock.com

Who learns in maths classes depends on how maths is taught

Students who are ill-prepared in mathematics are entering university and creating challenges for mathematics departments. There are lots of ideas out there on what to do about this but little evidence…
Look for the patterns… Look for the patterns… Margot Trudell

The 12 days of Pascal’s triangular Christmas

One of the most magical aspects of mathematics is the ability for complex and intricate structures to emerge from the simplest of rules. Few mathematical objects are simpler to create – and few weave such…
The Sydney Opera House, an icon of Australia’s creative and technical achievement. It has won worldwide acclaim for its design and construction. The Sydney Opera House, an icon of Australia’s creative and technical achievement. It has won worldwide acclaim for its design and construction. Linh_rOm

The Golden Mean: a great discovery or natural phenomenon?

What do the façades of the National Gallery in London’s Trafalgar Square and the Sydney Opera House in Australia have in common? Most people would suggest the two buildings have few similarities – the…
Where do you start building a machine like Deep Thought, the super-intelligent computer who came up with the Answer to The Ultimate Question of Life, the Universe, and Everything? Where do you start building a machine like Deep Thought, the super-intelligent computer who came up with the Answer to The Ultimate Question of Life, the Universe, and Everything? YouTube

To create a super-intelligent machine, start with an equation

Intelligence is a very difficult concept and, until recently, no one has succeeded in giving it a satisfactory formal definition. Most researchers have given up grappling with the notion of intelligence…
Chess can be applied to maths education – you just have to think outside the box. Chess can be applied to maths education – you just have to think outside the box. practicalowl

A good move to master maths? Check out these chess puzzles

In the spirit of the current world championship bout between Norwegian grandmaster Magnus Carlsen and Indian grandmaster Viswanathan Anand, we should seriously consider the role of chess in how young students…
Terry Speed plus maths and stats equals Prime Minister’s Prize for Science 2013. Terry Speed plus maths and stats equals Prime Minister’s Prize for Science 2013. WEHI

Is it possible to add statistics to science? You can count on it

The Prime Minister’s Prizes for Science recognise excellence in science and science teaching. This year, we asked three prizewinners to reflect on their work and factors that influenced their careers…
Forget the calculator: maths is about ideas, not arithmetic. Forget the calculator: maths is about ideas, not arithmetic. celestehopkins

Putting maths on the map with the four colour theorem

Recently, as a community ambassador for ANU Student Equity, I took to a local secondary school to talk maths with a small group of students. The goal? To give them an enjoyable mathematical experience…
We share a birthday? Really? What are the chances? We share a birthday? Really? What are the chances? massdistraction

The birthday problem: what are the odds of sharing b-days?

How many people do you have to put into a room before you are guaranteed that at least two of them share a birthday? We all know and love the blissful feeling of winning an argument. Well, trust me, that’s…
Around 20% of people are maths anxious. To decrease this figure, we need to bust some stereotypes. Around 20% of people are maths anxious. To decrease this figure, we need to bust some stereotypes. Tom Lin :3=

To overcome fear of maths, let’s confront the myths

We all know someone who gets the jitters when they have to make a speech, or breaks out in a cold sweat at the mere thought of being in an enclosed space. That person might even be you. But do you know…
An expanding population means more cars on the road than ever before. So how can maths help ease traffic congestion? An expanding population means more cars on the road than ever before. So how can maths help ease traffic congestion? Mr. T in DC

Stuck in traffic? Maths can get you on your way

Mathematics may not be the first thing your mind turns to when you are caught in a traffic jam. Yet mathematics holds the key to understanding how traffic congestion develops, and how to prevent it. Perhaps…
Going against your intuition could increase your chances of winning a car instead of a goat, according to the Monty Hall problem. Going against your intuition could increase your chances of winning a car instead of a goat, according to the Monty Hall problem. mgbutterfly

The Monty Hall problem: going with your gut will get your goat

The game show host adjusts his bow tie and flashes you an oh-so-wicked smile as he brings your attention to three closed doors. “Behind one of these doors is the prize of your dreams!” he announces excitedly…
We should celebrate recent progress on the understanding of prime numbers. We should celebrate recent progress on the understanding of prime numbers. Pawel Bak

You wait ages for number theory results, then two come at once

In recent weeks, two truly major results have been announced in the realm of (analytic) number theory, namely the mathematics of integers in general and of prime numbers in particular. Number theory, as…
Data and computer code should be made publicly available at an early stage – or else … Data and computer code should be made publicly available at an early stage – or else … esarastudillo

The Reinhart-Rogoff error – or how not to Excel at economics

Last week we learned a famous 2010 academic paper, relied on by political big-hitters to bolster arguments for austerity cuts, contained significant errors; and that those errors came down to misuse of…
Sending secure information? You could do a lot worse than employing the RSA algorithm. Sending secure information? You could do a lot worse than employing the RSA algorithm. Seq

The RSA algorithm (or how to send private love letters)

A couple of days ago on The Conversation, I set myself up with a task: to defend the usefulness of so-called “useless” maths. Today, that defence continues, with a look at the RSA algorithm. I finished…
As all mathematicians know, the rift between useful and useless can change with time. As all mathematicians know, the rift between useful and useless can change with time. Manu gomi

Your number’s up – a case for the usefulness of useless maths

I once made the mistake of asking a mathematician why he devoted his whole life to maths. “Because it’s fun!” he replied wildly, his flabby cheeks beaming with childlike excitement. “Ah, of course,” I…
The predictions of current particle physics have been spectacularly validated. The predictions of current particle physics have been spectacularly validated. Michael J. Linden

A Higgs, the Higgs … is maths at the root of reality?

So, the Higgs boson … Last week, researchers at the European Organization for Nuclear Research (CERN) finally announced the new particle discovered last summer is indeed a Higgs boson, a particle predicted…
We are all susceptible to being swayed by the whims of social movements. We are all susceptible to being swayed by the whims of social movements. epSos.de

Danger, you’re at serious risk of … no, sorry, it’s all relative

We assess risk every day. But very few of us receive any formal training in the requisite mathematics and statistics, and, partly as a result, poor decisions are made, both by individuals and governmental…
Why do so many people believe in the Mayan apocalypse myth? Why do so many people believe in the Mayan apocalypse myth? Apocalypse image from www.shutterstock.com

Apocalypse myths show our fear of the world as we know it

If you believe the hype, the end of the world has finally come. The Mayan calendar’s “long count” began on 13 August 3114 BCE and will end today on 21 December 2012. Why do people believe the world will…
It’s taken many years of hard work but a new proof of the abc conjecture looks like it could stack up. It’s taken many years of hard work but a new proof of the abc conjecture looks like it could stack up. nettsu

The abc conjecture, as easy as 1, 2, 3 … or not

A couple of months ago, Japanese mathematician Shinichi Mochizuki posted the latest in a series of four papers claiming the proof of a long-standing problem in mathematics – the abc conjecture. The announcement…
What starts as a flap of wings can end – metaphorically – in a hurricane. What starts as a flap of wings can end – metaphorically – in a hurricane. horizontal.integration

Explainer: what is Chaos Theory?

Clouds are not spheres, mountains are not cones … Nature exhibits not simply a higher degree but an altogether different level of complexity. - Benoît Mandelbröt, The Fractal Geometry of Nature Chaos (n…
Thinking about maths problems can produce alarming reactions. Thinking about maths problems can produce alarming reactions. andres.thor

Newly calculated: maths anxiety triggers pain in the brain

So we have a problem for you. Take a moment to steady yourself, maybe sharpen your pencil. Don’t unpack your calculator, and leave your phone to one side. This one will be purely mental – a spot of addition…
Stanford University’s Alvin Roth (pictured) and UCLA’s Lloyd Shapley were given the Nobel prize “for the theory of stable allocations and the practice of market design”. Stanford University’s Alvin Roth (pictured) and UCLA’s Lloyd Shapley were given the Nobel prize “for the theory of stable allocations and the practice of market design”. AAP

Match-making economists earn Nobel prize for economic engineering

The Nobel prize for economics is often awarded for relatively abstract theoretical work. Rather less often, it is awarded for work with clear practical relevance. This year, the committee responsible for…
Mariia Pomazan was stripped of her gold medal following an Australian protest. Mariia Pomazan was stripped of her gold medal following an Australian protest. EPA/Gerry Penny

Discus farce prompts points pow-wow at Paralympics

The final of the women’s discus (F35-36) at the London Paralympic Games on Sunday (AEST) raised a question that doesn’t normally comes up once a sporting contest is over: “So, who won?” Ukrainian F35 thrower…
Physics puts a limit on how far you can throw a javelin. Physics puts a limit on how far you can throw a javelin. Airman Magazine

Yes, there is a limit to athletic ability – physics

In a recent thought-provoking article in The Conversation, Kate Murphy posed the question: “Is there a limit to athletic performance?”. The answer, mathematically speaking, is yes. Kate considered the…
The percentage of maths teachers who struggle with their subject inspires little confidence. The percentage of maths teachers who struggle with their subject inspires little confidence. cmiked

School maths is failing children – a US and Australian perspective

Those that can’t do, teach – or so goes the famous saying. But what of those who want to do teaching. What of those who do maths teaching? Can we be sure the job they are doing is the best one for our…
The US is expected to dine out on its successes at London 2012. The US is expected to dine out on its successes at London 2012. US Army

And the winner is …? Predicting gold medals at the Olympics

A small number of countries competing at the Olympic Games will win a large proportion of the medals available. There are 80 countries competing in London who have yet to win a single medal in the Olympics…
Roll up for the mathematical mystery tour. Roll up for the mathematical mystery tour. Lucy (嘉莉)

A Hard Day’s Night by numbers: The Beatles decoded

“TWANG! It’s been a …” There is perhaps no song as quintessentially Beatle-ish as A Hard Day’s Night - it just bubbles with unbridled enthusiasm and joy. And in my mind, there’s no other opening chord…
Bogus certainty in the reporting of numbers can have dire consequences. Bogus certainty in the reporting of numbers can have dire consequences. rbbaird

Bad numbers make for killer headlines – and dodgy news

Last week, The Guardian informed us the Eurozone Crisis will Cost World’s Poorest Countries US$238bn. Really? Not US$237 billion or US$239 billion? Perhaps it was just a wonky headline, and the article…
According to some, computer intelligence is on course to match human intelligence by 2045. According to some, computer intelligence is on course to match human intelligence by 2045. Sybren A. Stüvel

Person or computer: could you pass the Turing Test?

As mentioned already on this site and others, this year marks the 100th anniversary of the birth of famed British mathematician Alan Turing. The outline of his remarkable life and sad ending has by now…
Finland has much to offer Australia and other nations when it comes to mathematics education. Finland has much to offer Australia and other nations when it comes to mathematics education. StreetFly JZ

Yes, there’s a numeracy crisis – so what’s the solution?

There’s been plenty of commentary recently on the “numeracy crisis” threatening the economies of many developed nations, including Australia. A 2009 report by the National Academies in the US was not the…
Uncertainty exists – but that’s no excuse for a lack of action. Uncertainty exists – but that’s no excuse for a lack of action. @Doug88888

Hot and bothered: the uncertain mathematics of global warming

These are painful times for those hoping to see an international consensus and substantive action on global warming. In the US, Republican presidential front-runner Mitt Romney said in June 2011: “The…
There’s far more to the popular maths puzzle than putting numbers in a box. There’s far more to the popular maths puzzle than putting numbers in a box. zlovall

Good at Sudoku? Here’s some you’ll never complete

Last month, a team led by Gary McGuire from University College Dublin in Ireland made an announcement: they had proven you can’t have a solvable Sudoku puzzle with less than 17 numbers already filled in…
We can’t tame the oceans, but modelling can help us better understand them. We can’t tame the oceans, but modelling can help us better understand them. Badruddeen

Super models – using maths to mitigate natural disasters

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…
Our present achievements will look like child’s play in a few years. Our present achievements will look like child’s play in a few years. Rinoninha

Make mine a double: Moore’s Law and the future of mathematics

What do iPhones, Twitter, Netflix, cleaner cities, safer cars, state-of-the-art environmental management and modern medical diagnostics have in common? They are all made possible by Moore’s Law. Moore’s…
The humble pigeon mightn’t look smart, but it’s no bird-brain. The humble pigeon mightn’t look smart, but it’s no bird-brain. Seamoor

Are pigeons as smart as primates? You can count on it

We humans have long been interested in defining the abilities that set us apart from other species. Along with capabilities such as language, the ability to recognise and manipulate numbers (“numerical…
Momentum is gathering behind calls to pardon the father of computer science. Momentum is gathering behind calls to pardon the father of computer science. BinaryApe

Calls for a posthumous pardon … but who was Alan Turing?

You may have read the British Government is being petitioned to grant a posthumous pardon to one of the world’s greatest mathematicians and most successful codebreakers, Alan Turing. You may also have…
There’s a contradiction between classical and quantum theories. There’s a contradiction between classical and quantum theories. TonZ

Millennium Prize: the Yang-Mills Existence and Mass Gap problem

MILLENNIUM PRIZE SERIES: The Millennium Prize Problems are seven mathematics problems laid out by the Clay Mathematics Institute in 2000. They’re not easy— a correct solution to any one results in a US$1,000,000…
Our best efforts to gauge threats may be counter-productive. Our best efforts to gauge threats may be counter-productive. bre pettiss

Danger of death: are we programmed to miscalculate risk?

Assessing risk is something everyone must do every day. Yet few are very good at it, and there are significant consequences of the public’s collective inability to accurately assess risk. As a first and…
What will be the next number in this sequence? What will be the next number in this sequence? crisinplymouth

Millennium Prize: the Riemann Hypothesis

MILLENNIUM PRIZE SERIES: The Millennium Prize Problems are seven mathematics problems laid out by the Clay Mathematics Institute in 2000. They’re not easy—a correct solution to any one results in a US$1,000,000…
If this doesn’t bake your hippy noodle, nothing will. If this doesn’t bake your hippy noodle, nothing will. stuartpilbrow

Millennium Prize: the Birch and Swinnerton-Dyer Conjecture

MILLENNIUM PRIZE SERIES: The Millennium Prize Problems are seven mathematics problems laid out by the Clay Mathematics Institute in 2000. They’re not easy – a correct solution to any one results in a US$1,000,000…
The problem’s been solved … but the sweet treats were declined. The problem’s been solved … but the sweet treats were declined. Back to the Cutting Board

Millennium Prize: the Poincaré Conjecture

MILLENNIUM PRIZE SERIES: The Millennium Prize Problems are seven mathematics problems laid out by the Clay Mathematics Institute in 2000. They’re not easy – a correct solution to any one results in a US$1,000,000…
Deciding whether a statement is true is a computational head-scratcher. Deciding whether a statement is true is a computational head-scratcher. rofi

Millennium Prize: P vs NP

MILLENNIUM PRIZE SERIES: The Millennium Prize Problems are seven mathematics problems laid out by the Clay Mathematics Institute in 2000. They’re not easy – a correct solution to any one results in a US$1,000,000…
The Hodge Conjecture has stimulated the development of revolutionary tools and techniques. The Hodge Conjecture has stimulated the development of revolutionary tools and techniques. sensesmaybenumbed

Millennium Prize: the Hodge Conjecture

MILLENNIUM PRIZE SERIES: The Millennium Prize Problems are seven mathematics problems laid out by the Clay Mathematics Institute in 2000. They’re not easy – a correct solution to any one results in a US$1,000,000…
How fluids move has fascinated researchers since the birth of science. How fluids move has fascinated researchers since the birth of science. tonyhall

Millennium Prize: the Navier–Stokes existence and uniqueness problem

MILLENNIUM PRIZE SERIES: The Millennium Prize Problems are seven mathematics problems laid out by the Clay Mathematics Institute in 2000. They’re not easy – a correct solution to any one results in a US$1,000,000…
If you want to optimise scramjets you’re going to need the rule of the jungle. If you want to optimise scramjets you’re going to need the rule of the jungle. EPA/NSAS

Explainer: evolutionary algorithms

My intention with this article is to give an intuitive and non-technical introduction to the field of evolutionary algorithms, particularly with regards to optimisation. If I get you interested, I think…
We know the universe is vast, but how do we measure the distances between things? We know the universe is vast, but how do we measure the distances between things? Dave Scrimshaw.

How far away is everybody? Climbing the cosmic distance ladder

Let’s talk numbers for a moment. The moon is approximately 384,000 kilometres away, and the sun is approximately 150 million kilometres away. The mean distance between Earth and the sun is known as the…
Australia ranks poorly for the number of graduates emerging with a science degree. Australia ranks poorly for the number of graduates emerging with a science degree. epSos.de

Science, maths and the future of Australia

Australia faces many big challenges – in the economy, health, energy, water, climate change, infrastructure, sustainable agriculture and the preservation of our precious biodiversity. To meet these, we…
Are we getting closer to solving one of life’s greatest mysteries? Are we getting closer to solving one of life’s greatest mysteries? jcoterhals

Where is everybody? Doing the maths on extraterrestrial life

During a lunch in the summer of 1950, physicists Enrico Fermi, Edward Teller and Herbert York were chatting about a recent New Yorker cartoon depicting aliens abducting trash cans in flying saucers. Suddenly…
A universe composed differently could still support complex life. A universe composed differently could still support complex life. Susan NYC

Peer Review: The Fallacy of Fine-Tuning

Welcome to Peer Review, a series in which we ask leading academics to review books written by people working in the same field. Here Geraint Lewis, Professor of Astrophysics at the University of Sydney…
The cut-and-choose technique has been preventing tantrums since antiquity. The cut-and-choose technique has been preventing tantrums since antiquity. free form by prudence

Cutting cake (and eating it too) – the sticky maths of fair division

I work on the mathematics of sharing resources, which has led me to consider emotions such as envy, behaviour such as risk-taking and the best way to cut a cake. Like, I suspect, many women, my wife enjoys…
Do we take the sophistication of numbers one to ten for granted? Do we take the sophistication of numbers one to ten for granted? duncan

Magic numbers: the beauty of decimal notation

While adding up your grocery bill in the supermarket, you’re probably not thinking how important or sophisticated our number system is. But the discovery of the present system, by unknown mathematicians…
Improved modelling will help predict future climatic events, like changing summer rainfall. Improved modelling will help predict future climatic events, like changing summer rainfall. AAP

Getting projections right: predicting future climate

Region by region projections of how climate is likely to change over the coming decades help to make the prospect of global warming more tangible and relevant. Picturing the climate we are likely to have…
Alan Turing, through pure mathematics, laid the foundations for the modern computer. Alan Turing, through pure mathematics, laid the foundations for the modern computer. Leo Reynolds

Explainer: the point of pure mathematics

What is pure mathematics? What do pure mathematicians do? Why is pure mathematics important? These are questions I’m often confronted with when people discover I do pure mathematics. I always manage to…
More maths teachers means better outcomes for students. More maths teachers means better outcomes for students. Flickr

Mathematics: Why we need more qualified teachers

There is a crisis in the education system, and it’s affecting the life chances of many young Australians. The number of secondary teaching graduates with adequate qualifications to teach mathematics is…
Knowing what’s hard and easy is, in itself, quite hard. Knowing what’s hard and easy is, in itself, quite hard. JuniorMonkey

Timetables – hard to read, even harder to build

When you look at a train or university timetable you don’t think about how the timetable was made – you’re thinking about your trip or where your next class is. In that moment, you couldn’t care less about…
When you know the numbers, things get a whole lot easier. When you know the numbers, things get a whole lot easier. Roberto Bouza

Want to win at gambling? Use your head

GAMBLING IN AUSTRALIA – Some say “punting is a mug’s game”. But is this always true, or can an astute gambler make long-term profits? Certainly not from casino games. Casinos make profits by paying less…
Is it a plane? No, it’s Smoothed Particle Hydrodynamics. Is it a plane? No, it’s Smoothed Particle Hydrodynamics. William West/AFP

Superman returns – but who’s looking after his water?

Watching films such as Superman Returns or The Day after Tomorrow, you would have seen dramatic sequences of surging water and crumbling buildings. While doing so, mathematics was probably the last thing…
Pi pie Pi pie

Are Pi’s days numbered?

Some people have argued that Pi’s days are numbered and that other tools, such as tau, could do its job more efficiently. As someone who has studied Pi throughout his entire working life, my response to…

Research and News (4)

Research Briefs (10)

Hand gestures help kids learn maths

Using hand gestures may help children learn mathematics better, according to a recent study. Researchers, led by Miriam A…

Maths maps out gang territories

An American mathematical model that has been used for more than 80 years to determine the hunting range of animals in the…

Maths ability may be inborn

Maths ability in preschool children is strongly linked to an inborn and primitive “number sense,” according to new research…