Articles on Mathematics

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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…
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. 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. 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. 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. 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. 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. 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…
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…
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. 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? 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. 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…

Maths ability may be inborn

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

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