Beautiful, Useful and Fun

ThatsMaths is the blog for a series of articles on mathematics to be published in the Irish Times, starting on 19 July 2012. Among the goals of the articles are to:

  • Demystify Mathematics
  • Show the breathtaking power of the subject
  • Discuss a range of technological applications
  • Enlighten readers about exciting developments
  • Explain recent advances and developments
  • Describe some major unsolved problems
  • Inspire interest in the subject?

Beautiful, Useful & Fun: That’s Maths

Type a word into Google: a million links come back in a flash. Tap a destination into your SatNav: distances, times and highlights of the route appear. Get cash from an ATM, safe from prying eyes. Choose a tune from among thousands squeezed onto a tiny chip. How are these miracles of modern technology possible? What is the common basis underpinning them?

The answer is mathematics. Maths now reaches into every corner of our lives. Our technological world would be impossible without it. Electronic devices like smart phones and iPods, that we use daily, depend on the application of maths. Likewise, computers, communications and the internet. International trade and the financial markets depend critically on secure communications, using encryption methods that spring directly from number theory, once thought to be an area of pure mathematics without “useful” applications.

We are living longer and healthier lives, partly due to the application of maths to medical imaging, automatic diagnosis and modelling the cardiovascular system. The pharmaceuticals that cure us and control disease are made possible through applied mathematics. Agricultural production is more efficient thanks to maths, forensic medicine and crime detection depend on it. Control and operation of air transport would be impossible without maths. Sporting records are broken by studying and modelling performance and designing equipment mathematically. Maths is everywhere.

Galileo is credited with quantifying the study of the physical world, and his philosophy is encapsulated in an oft-quoted aphorism “The Book of Nature is written in the language of mathematics”. This development flourished with Newton, who unified terrestrial and celestial mechanics in a grand theory of universal gravitation, showing that the behaviour of a projectile like a cannon ball and the trajectory of the moon are governed by the same dynamics.

Mechanics and astronomy were the first areas to be “mathematicised” but over the past century the influence of quantitative methods has spread to many other areas. Statistical analysis now pervades the social sciences. Computers enable us to simulate complex systems and predict their behaviour. Modern weather forecasting is an enormous arithmetical calculation, underpinned by mathematical and physical principles. With the recent untangling of the human genome, mathematical biology is a hot topic.

The mathematics that we learnt at school was developed centuries ago, so it is easy to get the idea that maths is static, frozen in the seventeenth century or fossilised since ancient Greece. In fact, the vast bulk of mathematics has emerged in the past hundred years, and the subject continues to blossom. It is a vibrant and dynamic field of study. The future health of our technological society depends on this continuing development.

When scientific funding is under stress, as at present, cuts are difficult to avoid. There is great pressure on investigators to focus on applications that deliver results on a short time-scale. But experience has shown repeatedly that scientific endeavours impelled by pure curiosity, so-called blue-skies research, frequently yield unanticipated practical benefits. The synergy between pure and applied mathematics is testament to this, and it is important to encourage and support research across the entire gamut of the subject.

While a deep understanding of advanced mathematics requires intensive study over a long period, we can appreciate some of the beauty of maths without detailed technical knowledge, just as we can enjoy music without being performers or composers. It is a goal of this series of articles to aid in this appreciation. Over the coming weeks, I hope to convince you that mathematics is beautiful, useful and fun.

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