This was first broadcast on East Coast FM on 19-11-2016

The Mars Curiosity Rover, pictured here, navigated its way to the surface of Mars in August 2012 thanks to equations invented by an Irishman in 1843 (Credit: NASA)

This episode covers the story of a Dubliner born in 1805, who became one of the greatest mathematicians the world has ever seen.

Hamilton invented mathematical equations, called quaternions, in 1843 which are still used today to navigate and land spacecraft (eg the Moon in 1969 and Mars in 2012) and as software ‘under the hood’ which depicts the relative movement of figures in 3D space in the top selling computer games.

GPS in cars, is largely based on Hamilton’s mathematics, and radio waves were predicted by James Clarke Maxwell before they were invented based on Hamilton’s totally unconventional, brilliant new mathematics.

Hamilton was objects rotate in 3D space, dared to imagine it. Came up with quaternions, totally unconventional and knocked traditional mathematics on its head. Thinking about this problem for years.

Mathematicians thought he was crazy, didn’t accept it, but then came to be called the ‘liberator of algebra’ – new way of thinking of mathematics.

Hamilton connected to fact we can hear audio on the radio, James Clark Maxwell predicted oscillating waves of energy traveling at speed of light – radio waves were detected, used by maxwell to predict these waves exist before they were found.

Hamilton was a brilliant, popular scientist. He was moody; a romantic, with a dark side, who survived an early crisis in his life to go on achieve great things.

When many of us think of maths, we might instinctively suppress a yawn as we recall boring theorems, dull algebra and uninspiring teachers.

Yet without question, maths is exciting, challenging and responsible for some of humanity’s greatest achievements.

The landing of two men on the Moon in 1969 would not have been possible without maths, nor would we be able to appreciate the great harmonic symphonies of Mozart or Beethoven.

Without maths, in fact, there would be a lot less beauty in the world, and in this episode we explore the majesty, beauty and even poetry of maths.

The seven minutes of Martian terror

In August 2012 the most complicated robotic landing of a craft in the history of space exploration took place on the surface of Mars.

It was an amazing feat of engineering. The Mars Science Laboratory (MSL), weighing about two tonnes, landed safely with all its high-tech equipment.

The spacecraft decelerated in the Martian atmosphere from 13,000 miles per hour to zero miles per hour on the surface, using all manner of engineering tricks.

Throughout the complex landing and navigation sequence a type of mathematical equation, devised in 1843 by an Irishman in Dublin, proved crucial to its success.

That man was William Rowan Hamilton, a brilliant mathematician from Trinity College Dublin, and the equations in question are called quaternions.

We talk to the chief NASA engineer responsible for landing the MSL on Mars about the importance of quaternions to the success of the mission.

Miguel San Martin describes the terror he felt when his team had to wait seven minutes for a signal from Mars to confirm the craft was safe or destroyed.

It was a moment of high tension involving eight years of preparation and an investment of $2.5 billion – and quaternions were at the heart of the drama.

View video depiction of seven minutes of terror below:

Moon landings: The Dublin link

Regan Hutchins describes the often troubled life and work of one of Ireland’s greatest mathematicians, William Rowan Hamilton.

WR Hamilton, a Dubliner born on Dominick Street, lived in the 19^{th} century, but his mathematics continues to have enormous impact on the world today.

For example, his work is considered crucial to the navigation and landing of spacecraft, and is also used to design the latest high-tech video games.

His most important piece of work stemmed from an insight he had while walking along the banks of the Royal Canal one bright morning in 1843.

Regan Hutchins visited the spot at Broom Bridge in Cabra with Dr. Fiacre O’Cairbre, senior lecturer in maths at NUI Maynooth, where Hamilton had a flash of inspiration about quaternions.

Regan also paid a visit to Hamilton’s home in Dunsink Observatory with Professor Iggy McGovern from Trinity College Dublin, to find out more about Hamilton’s life.

Pythagoras and musical harmony

The reason we hear music as “nice” or “not nice” depends on mathematical ratios, Dr. Bob Lawlor, NUI Maynooth, told our reporter Lorcan Clancy.

Pythagoras, the famous mathematician of the ancient world, invented the theorem we learned in school, but he also developed the original musical scale.

It is thought Pythagoras gained insight into how mathematical ratios explain pitch and harmony by listening to blacksmiths striking anvils.

He built a monochord – an early single-stringed instrument – and found that pitch was inversely proportional to the length of the monochord string.

This work by Pythagoras explains why we can recognise a discordant sound in the midst of a beautiful, harmonic piece of music.

We humans, it seems, prefer symmetry, even when it comes to music.

Maths can forecast volcanic eruptions

You might be surprised to learn that scientists are still unable to predict the precise time, date and location of a volcanic eruption.

However, scientists like Professor Chris Bean (University College Dublin), a mathematician by training, are getting far better at forecasting the chances of an eruption.

We visited the UCD campus to talk to Chris about maths and its importance in his volcano work.

Maths is used to forecast the weather. It’s not possible to predict that it will rain on Grafton Street at 2pm tomorrow, but we can say there is a “strong chance of showers”. The same applies to how scientists predict volcanic eruptions.

Chris Bean was inspired to apply his mathematical skills to the study of volcanoes after watching the Mount Saint Helens eruption in 1980 on TV.

Sensors are placed on the volcano to measure things like how the ground is shaking, the nature of gas leakages, and the surrounding water chemistry.

Mathematics are used to analyse the resulting data, which then allows scientists to make reliable forecasts.

Each volcano is different, but the scientific strategy is the same: monitor the patterns leading up to a known eruption to try and predict the next one.

Why do we use certain numbers?

Fiacre O’Cairbre tells Lorcan Clancy why certain numbers like 12 are important to us.

The use of 12 as a so-called base number – a basic multiplication unit underpinning a system of numbers – has its origins in the ancient world.

The fact that there are seven days in a week can be traced back to the Babylonians who believed there were seven planets, including the Sun. The Babylonians dedicated one day each to a planet, which is how we came to have seven days in a week.

Meanwhile, the reason that 60 is important, says Fiacre O’Cairbre, is because it is the smallest number divisible by 1, 2, 3, 4, 5 and 6.

The Babylonians saw that 60 was a good base number for doing divisional calculations in real world, such as dividing up inheritances or bags of grain.

Today, base 10 is the key to the metric system. However, number systems go in and out of fashion and today’s system could change again in the future.

The majesty of maths in ancient Ireland

There is plenty of evidence that the people of the ancient world, the builders and architects at least, had a very good knowledge of mathematics.

The builders of Stonehenge, for example, clearly had an understanding of squares and circles, but in Ireland we something just as fascinating.

The Céide Fields near Belderrig, north Mayo, were discovered by Patrick Caulfield in 1934 when he found stone walls buried beneath the bog.

Researchers, including Patrick’s son Seamus Caulfield, have since unearthed a huge, buried landscape 5,500 years old.

Our reporter Lorcan Clancy visited the Céide Fields Visitor Centre and spoke to site manager Greta Byrne about why the site is so special.

Lorcan also spoke to Seamus Caulfield, who began work on the Céide Fields in 1970, and who gave up his job as a teacher to become an archaeologist.

Seamus describes how the buried Fields, which cover thousands of acres of north Co. Mayo, were systematically divided up thousands of years ago.