One of the beautiful things about maths is that every concept is part of a bigger picture — a picture that grows over time, transcends traditional boundaries, and often informs a range of real-world applications. The collections below aim to present some of these mathematical jigsaws by bringing together content exploring specific topics from different perspectives and at varying levels of depth.

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The 2010 Plus advent calendar

It's not long until Christmas! To help you pass the time (or ease your nerves if you're stressed), we bring you the Plus advent calendar with a mathsy goody from the Plus archive lurking behind each door. Find out what's behind today's door...

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Teacher package: Mathematics in sport

This teacher package brings together all our articles that have to do with sport, from cricket to football and from the sport itself to sporting architecture and infrastructure.

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Do you know what's good for you: the next microscope

"Mathematics is biology's next microscope, only better." That's what the scientist Joel E Cohen once said of the power of mathematics to revolutionise biology and the biomedical sciences. And he was right. Maths enables scientists to understand complex organisms and diseases, it's crucial in developing sophisticated medical technology and materials, and we can even use it to model our psyche and intelligence. In this sense maths has become a genuine research instrument for biomedical sciences. The insight it gives them are on a par with the revolutionising power of the microscope.

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Latest news from the ICM 2010

Journey to the frontiers of maths with Plus as we cover the International Congress of Mathematics in Hyderabad, India
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Do you know what's good for you - what's the best medicine?

How do you judge the risks and benefits of new medical treatments, or of lifestyle choices? With a finite health care budget, how do you decide which treatments should be made freely available on the NHS? Historically, decisions like these have been made on the basis of doctors' individual experiences with how these treatments perform, but over recent decades the approach to answering these questions has become increasingly rational.
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Do you know what's good for you? — The maths of infectious diseases

Infectious diseases hardly ever disappear from the headlines — swine flu is only the last in a long list containing SARS, bird flu, HIV, and childhood diseases like mumps, measles and rubella. If it's not the disease itself that hits the news, then it's the vaccines with their potential side effects. It can be hard to tell the difference between scare mongering and responsible reporting, because media coverage rarely provides a look behind the scenes. So how do scientists reach the conclusions they do?
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Do you know what's good for you - unravelling genetic secrets

One of the greatest advances in the biomedical sciences has been the unravelling of our genetic code. This new understanding sheds light on what makes organisms function and how they are related to each other, helps to combat diseases, and to convict criminals. But it also poses great mathematical challenges: the genetic revolution is an information explosion which can only be tamed using mathematical methods.
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Teacher package: Trigonometry

This teacher package brings together our material on trigonometry, from problems about simple triangles to the wavy behaviour of trig functions.
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Teacher package: Maths and art

Maths is all about patterns and rhythms, so it's no surprise that there's plenty of maths in art. Whether it's the visual or the performing arts, maths can be a tool, an inspiration, or simply something that's naturally contained within the structures and patterns.

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Seven things everyone wants to know about the Universe

The year 2009 was International Year of Astronomy, and to celebrate, we asked you what you'd most like to know about your Universe in a series of online polls. You came up with seven questions, which we put to world-leading astronomers and cosmologists. Find their answers in seven articles, as well as some podcasts.
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Teacher package: Proofs

The notion of proof lies at the very heart of maths: it's when it comes to proving things that mathematicians let lose their genius and creativity, and in the process often discover unexpected surprises or deep philosophical issues. But proofs can also be daunting. So to help you and your students along, we've brought together a range of Plus articles on proofs.