When Frederick the Great was crowned King of Prussia in 1740 he immediately revived the Berlin Academy of Sciences and invited scholars from throughout Europe to Berlin. The most luminous of these was Leonhard Euler, who arrived at the academy in 1741. Euler was an outstanding genius, brilliant in both mathematics and physics. Yet, a … Continue reading Euler and the Fountains of Sanssouci
Category: Irish Times
Articles in Irish Times
It’s as Easy as Pi
Every circle has the property that the distance around it is just over three times the distance across. This has been known since the earliest times [see TM120 or search for “thatsmaths” at irishtimes.com]. The constant ratio of the circumference to the diameter, denoted by the Greek letter pi, is familiar to every school-child. You … Continue reading It’s as Easy as Pi
Quadrivium: The Noble Fourfold Way
According to Plato, a core of mathematical knowledge – later known as the Quadrivium – was essential for an understanding of the Universe. The curriculum was outlined in Plato's Republic. The name Quadrivium means four ways, but this term was not used until the time of Boethius in the 6th century AD [see TM119 or search … Continue reading Quadrivium: The Noble Fourfold Way
Robert Murphy, a “Brilliant Meteor”
“A brilliant meteor that flared intensely but all too briefly”; this was how Des MacHale described the Cork-born mathematician Robert Murphy in his biography of George Boole, first professor of mathematics in Cork. Murphy was a strong influence on Boole, who quoted liberally from his publications [see TM118 or search for “thatsmaths” at irishtimes.com]. Robert Murphy was … Continue reading Robert Murphy, a “Brilliant Meteor”
Fractal Complexity of Finnegans Wake
Tomorrow we celebrate Bloomsday, the day of action in Ulysses. Most of us regard Joyce's singular book as a masterpiece, even if we have not read it. In contrast, Finnegans Wake is considered by some as a work of exceptional genius, by others as impenetrable bafflegab [See TM117 or search for “thatsmaths” at irishtimes.com]. Sentence Length … Continue reading Fractal Complexity of Finnegans Wake
Beautiful Patterns in Maths and Music
The numerous connections between mathematics and music have long intrigued practitioners of both. For centuries scholars and musicians have used maths to analyze music and also to create it. Many of the great composers had a deep understanding of the mathematical principles underlying music. Johann Sebastian Bach was the grand master of structural innovation and … Continue reading Beautiful Patterns in Maths and Music
Yves Meyer wins 2017 Abel Prize
On 23 May King Harald V of Norway will present the Abel Prize to French mathematician Yves Meyer. Each year, the prize is awarded to a laureate for “outstanding work in the field of mathematics”. Comparable to a Nobel Prize, the award is named after the exceptional Norwegian, Niels Henrik Abel who, in a short … Continue reading Yves Meyer wins 2017 Abel Prize
When Roughly Right is Good Enough
How high is Liberty Hall? How fast does human hair grow? How many A4 sheets of paper would cover Ireland? How many people in the world are talking on their mobile phones right now? These questions seem impossible to answer but, using basic knowledge and simple logic, we can make a good guess at the … Continue reading When Roughly Right is Good Enough
The Water is Rising Fast
Seventy percent of the Earth is covered by water and three quarters of the world's great cities are on the coast. Ever-rising sea levels pose a real threat to more than a billion people living beside the sea. As the climate warms, this is becoming a greater threat every year [TM113 or search for “thatsmaths” … Continue reading The Water is Rising Fast
The Improbability Principle
Extremely improbable events are commonplace. “It's an unusual day if nothing unusual happens”. This aphorism encapsulates a characteristic pattern of events called the Improbability Principle. Popularised by statistician Sir David Hand, emeritus professor at Imperial College London, it codifies the paradoxical idea that extremely improbable events happen frequently. [TM112 or search for “thatsmaths” at irishtimes.com]. We … Continue reading The Improbability Principle
A Life-saving Whirligig
Modern science is big: the gravitational wave detector (LIGO) cost over a billion dollars, and the large hadron collider (LHC) in Geneva took decades to build and cost almost five billion euros. It may seem that scientific advances require enormous financial investment. So, it is refreshing to read in Nature Biomedical Engineering (Vol 1, Article … Continue reading A Life-saving Whirligig
Enigmas of Infinity
Children sometimes amuse themselves searching for the biggest number. After trying millions, billions and trillions, they realize that there is no end to the game: however big a number may be, we can always add 1 to produce a bigger number: the set of counting numbers is infinite. The concept of infinity has intrigued philosophers … Continue reading Enigmas of Infinity
The Spire of Light
Towering over O'Connell Street in Dublin, the Spire of Light, at 120 metres, is about three times the height of its predecessor [TM109 or search for “thatsmaths” at irishtimes.com]. The Spire was erected in 2003, filling the void left by the destruction in 1966 of Nelson's Pillar. The needle-like structure is a slender cone of stainless … Continue reading The Spire of Light
Voronoi Diagrams: Simple but Powerful
We frequently need to find the nearest hospital, surgery or supermarket. A map divided into cells, each cell covering the region closest to a particular centre, can assist us in our quest. Such a map is called a Voronoi diagram, named for Georgy Voronoi, a mathematician born in Ukraine in 1868. He is remembered today … Continue reading Voronoi Diagrams: Simple but Powerful
The Library of Babel and the Information Explosion
The world has been transformed by the Internet. Google, founded just 20 years ago, is a major force in online information. The company name is a misspelt version of "googol", the number one followed by one hundred zeros. This name echoes the vast quantities of information available through the search engines of the company … Continue reading The Library of Babel and the Information Explosion
The Citizens’ Assembly: Why do 10 Counties have no Members?
Recently, the Irish Government established the Citizens' Assembly, a body of 99 citizens that will consider a number of constitutional issues. The Assembly meets on Saturday to continue its deliberations on the Eighth Amendment to the Constitution, which concerns the ban on abortion. It will report to the Oireachtas (Parliament) on this issue in June … Continue reading The Citizens’ Assembly: Why do 10 Counties have no Members?
The Edward Worth Library: a Treasure Trove of Maths
Infinite Riches in a Little Room. Christopher Marlowe. The Edward Worth Library may be unknown to many readers. Housed in Dr Steevens' Hospital, Dublin, now an administrative centre for the Health Service Executive, the library was collected by hospital Trustee Edward Worth, and bequeathed to the hospital after his death in 1733. The original book … Continue reading The Edward Worth Library: a Treasure Trove of Maths
The Shaky Foundations of Mathematics
The claim is often made that mathematical results are immutable. Once proven, they remain forever valid. But things are not so simple. There are problems at the very core of mathematics that cast a shadow of uncertainty. We can never be absolutely sure that the foundations of our subject are rock-solid [TM104 or search for … Continue reading The Shaky Foundations of Mathematics
Marvellous Merchiston’s Logarithms
Log tables, invaluable in science, industry and commerce for 350 years, have been consigned to the scrap heap. But logarithms remain at the core of science, as a wide range of physical phenomena follow logarithmic laws [TM103 or search for “thatsmaths” at irishtimes.com]. The method of logarithms was first devised by John Napier, 8th Laird … Continue reading Marvellous Merchiston’s Logarithms
A New Window on the World
The motto of the Pythagoreans was “All is Number” and Pythagoras may have been the first person to imagine that the workings of the world might be understood in mathematical terms. This idea has now brought us to the point where, at a fundamental level, mathematics is the primary means of describing the physical world. … Continue reading A New Window on the World
Thank Heaven for Turbulence
The chaotic flow of water cascading down a mountainside is known as turbulence. It is complex, irregular and unpredictable, but we should count our blessings that it exists. Without turbulence, we would gasp for breath, struggling to absorb oxygen or be asphyxiated by the noxious fumes belching from motorcars, since pollutants would not be dispersed … Continue reading Thank Heaven for Turbulence
A Ton of Wonders
Every number is interesting. Suppose there were uninteresting numbers. Then there would be a smallest one. But this is an interesting property, contradicting the supposition. By reductio ad absurdum, there are none! This is the hundredth “That's Maths” article to appear in The Irish Times [TM100, or search for “thatsmaths” at irishtimes.com]. To celebrate the … Continue reading A Ton of Wonders
The next Hamilton
William Rowan Hamilton was Ireland's greatest mathematician. His name is heard thousands of times every day throughout the world when researchers use the Hamiltonian function that encapsulates the dynamics of a vast range of physical systems. He achieved fame early in life and remains one of the all-time great scientists. [TM099, or search for “thatsmaths” at … Continue reading The next Hamilton
The Tunnel of Eupalinos in Samos
The tunnel of Eupalinos on the Greek island of Samos, over one kilometre in length, is one of the greatest engineering achievements of the ancient world [TM098, or search for “thatsmaths” at irishtimes.com]. Approximate course of the tunnel of Eupalinos in Samos. Modern Tunnels The Gotthard Base Tunnel opened in June and will be fully … Continue reading The Tunnel of Eupalinos in Samos
Recreational Mathematics is Fun
We all love music, beautiful paintings and great literature without being trained musicians, talented artists or accomplished writers. It is the same with mathematics: we can enjoy the elegance of brilliant logical arguments and appreciate the beauty of mathematical structures and symmetries without being skilled creators of new theorems. [See TM097, or search for “thatsmaths” … Continue reading Recreational Mathematics is Fun
Can Mathematics Keep Us Secure?
The National Security Agency is the largest employer of mathematicians in America. Mathematics is a core discipline at NSA and mathematicians work on signals intelligence and information security (US citizenship is a requirement for employment). Why is NSA so interested in mathematics? [See TM096, or search for “thatsmaths” at irishtimes.com]. Many actions are easy to … Continue reading Can Mathematics Keep Us Secure?
Computers Speaking in Irish
Most of us use computer terminals, tablets and smart phones, absorbing information quickly and easily. How do the many thousands of Irish people who are blind or visually impaired manage to interact with computers? For them, entering data by keyboard or voice is easy, but special software is needed to convert the text on screen … Continue reading Computers Speaking in Irish
Lateral Thinking in Mathematics
Many problems in mathematics that appear difficult to solve turn out to be remarkably simple when looked at from a new perspective. George Pólya, a Hungarian-born mathematician, wrote a popular book, How to Solve It, in which he discussed the benefits of attacking problems from a variety of angles [see TM094, or search for “thatsmaths” … Continue reading Lateral Thinking in Mathematics
Bloom’s attempt to Square the Circle
The quadrature of the circle is one of the great problems posed by the ancient Greeks. This “squaring of the circle” was also an issue of particular interest to Leopold Bloom, the central character in James Joyce’s novel Ulysses, whom we celebrate today, Bloomsday, 16 June 2016 [see TM093, or search for “thatsmaths” at irishtimes.com]. The challenge … Continue reading Bloom’s attempt to Square the Circle
Big Data: the Information Explosion
The world is awash with data. Large data sets have been available for many decades but in recent years their volumes have grown explosively. With mobile devices and internet connections data capture is simple and with powerful computers the analysis of “big data” is feasible [see TM092, or search for “thatsmaths” at irishtimes.com]. But there are … Continue reading Big Data: the Information Explosion
Andrew Wiles wins 2016 Abel Prize
A recent post described the Abel Prize, effectively the Nobel Prize for Mathematics, and promised a further post when the 2016 winner was announced. This is the follow-up post [also at TM091, or search for “thatsmaths” at irishtimes.com]. Next Tuesday, HRH Crown Prince Haakon will present the Abel Medal to Sir Andrew Wiles at a ceremony … Continue reading Andrew Wiles wins 2016 Abel Prize
Modelling Rogue Waves
There are many eyewitness accounts by mariners of gigantic waves – almost vertical walls of water towering over ocean-going ships – that appear from nowhere and do great damage, sometimes destroying large vessels completely. Oceanographers, who have had no way of explaining these 'rogue waves', have in the past been dismissive of these reports [TM090, or search for … Continue reading Modelling Rogue Waves
The Inexorable Rise in Life Expectancy
Life expectancy has increased in a spectacular fashion over the past 150 years. There has been a four-decade increase in average length of life over the period since 1850. World life expectancy has more than doubled, from about 25 years to around 65 years for men and 70 years for women. [TM089, or search for … Continue reading The Inexorable Rise in Life Expectancy
The Search is on for Planet Nine
Then felt I like some watcher of the skies When a new planet swims into his ken. John Keats: On First Looking into Chapman's Homer Pluto, discovered in 1930, orbits in the Kuiper Belt, a ring of asteroids and icy debris beyond Neptune. About ten years ago, it was reclassified as a "dwarf planet", so … Continue reading The Search is on for Planet Nine
Computus: Dating the Resurrection
Whatever the weather, St Patrick's Day occurs on the same date every year. In contrast, Easter springs back and forth in an apparently chaotic manner. The date on which the Resurrection is celebrated is determined by a complicated convolution of astronomy, mathematics and theology, an algorithm or recipe that fixes the date in accordance with … Continue reading Computus: Dating the Resurrection
The Abel Prize – The Nobel Prize for Mathematics
There is no Nobel Prize for mathematics, but there is a close equivalent: The prestigious Abel Medal is awarded every year for outstanding work in mathematics [TM086, or search for “thatsmaths” at irishtimes.com]. This years winner, or winners, will be announced soon. When Alfred Nobel's will appeared, the absence of any provision for a prize … Continue reading The Abel Prize – The Nobel Prize for Mathematics
The Mathematics of Voting
Selection of leaders by voting has a history reaching back to the Athenian democracy. Elections are essentially arithmetical exercises, but they involve more than simple counting, and have some subtle mathematical aspects [TM085, or search for “thatsmaths” at irishtimes.com]. The scientific study of voting and elections, which began around the time of the French Revolution, is called … Continue reading The Mathematics of Voting
Entropy Piano Tuning
An ingenious method of tuning pianos, based on the concept of entropy, has recently been devised by Haye Hinrichsen of Würzburg University. Entropy, which first appeared in the mid-nineteenth century in thermodynamics and later in statistical mechanics, is a measure of disorder. Around 1948 Claude Shannon developed a mathematical theory of communications and used entropy … Continue reading Entropy Piano Tuning
Richardson’s Fantastic Forecast Factory
Modern weather forecasts are made by calculating solutions of the mathematical equations that express the fundamental physical principles governing the atmosphere [TM083, or search for “thatsmaths” at irishtimes.com] The solutions are generated by complex simulation models with millions of lines of code, implemented on powerful computer equipment. The meteorologist uses the computer predictions to produce … Continue reading Richardson’s Fantastic Forecast Factory
How many Christmas Gifts?
We all know the festive carol The Twelve Days of Christmas. Each day, “my true love” receives an increasing number of gifts. On the first day there is one gift, a partridge in a pear tree. On the second, two turtle doves and another partridge, making three. There are six gifts on the third day, … Continue reading How many Christmas Gifts?
The Flight of a Golf Ball
Golf balls fly further today, thanks to new materials and mathematical design. They are a triumph of chemical engineering and aerodynamics. They are also big business, and close to a billion balls are sold every year. [TM081: search for “thatsmaths” at Irish Times ]. The golfer controls the direction and spin of the ball by … Continue reading The Flight of a Golf Ball
Mathematics Solving Crimes
What use is maths? Why should we learn it? A forensic scientist could answer that virtually all the mathematics we learn at school is used to solve crimes. Forensic science considers physical evidence relating to criminal activity and practitioners need competence in mathematics as well as in the physical, chemical and biological sciences [TM080: search … Continue reading Mathematics Solving Crimes
Melencolia: An Enigma for Half a Millennium
Albrecht Dürer, master painter and engraver of the German Renaissance, made his Melencolia I in 1514, just over five centuries ago. It is one of the most brilliant engravings of all time, and amongst the most intensively debated works of art [TM079; or search for “thatsmaths” at irishtimes.com ]. The winged figure, Melancholy, sits in a … Continue reading Melencolia: An Enigma for Half a Millennium
It’s a Small – Networked – World
Networks are everywhere in the modern world. They may be physical constructs, like the transport system or power grid, or more abstract entities like family trees or the World Wide Web. A network is a collection of nodes linked together, like cities connected by roads or people genetically related to each other. Such a system … Continue reading It’s a Small – Networked – World
New Tricks: No Clicks
The quality of music recordings on compact discs or CDs is excellent. In the age of vinyl records, irritating clicks resulting from surface scratches were almost impossible to avoid. Modern recording media are largely free from this shortcoming. But this is curious: there are many reasons why CD music can be contaminated: dirt on the … Continue reading New Tricks: No Clicks
The Ubiquitous Cycloid
Puzzle: However fast a train is travelling, part of it is moving backwards. Which part? For the answer, see the end of this post. Imagine a small light fixed to the rim of a bicycle wheel. As the bike moves, the light rises and falls in a series of arches. A long-exposure nocturnal photograph would … Continue reading The Ubiquitous Cycloid
James Joseph Sylvester
James Joseph Sylvester was born in London to Jewish parents in 1814, just 201 years ago today. The family name was Joseph but, for reasons unclear, Sylvester – the name of an anti-Semitic Pope from the Roman period – was adopted later. [TM075; or search for “thatsmaths” at irishtimes.com ] Sylvester's mathematical talents became evident at … Continue reading James Joseph Sylvester
The Great American Eclipse
Just two years from now, on Monday, August 21, 2017, the Moon's shadow will sweep across the United States at a speed of over 2,000 km/hr. The Great American Eclipse of 2017 will generate a frenzy of activity. [TM074: search for “thatsmaths” at irishtimes.com ]. Solar eclipses are not especially rare, but this one is of … Continue reading The Great American Eclipse
The Bridges of Paris
Leonhard Euler considered a problem known as The Seven Bridges of Königsberg. It involves a walk around the city now known as Kaliningrad, in the Russian exclave between Poland and Lithuania. Since Kaliningrad is out of the way for most of us, let's have a look closer to home, at the bridges of Paris. [TM073: … Continue reading The Bridges of Paris
Pluto’s Unruly Family
An astrodynamical miracle is happening in the sky above. Our ability to launch a space-probe from the revolving Earth to reach a moving target billions of kilometres away almost ten years later with pinpoint accuracy is truly astounding. "New Horizons" promises to enhance our knowledge of the solar system and it may help us to … Continue reading Pluto’s Unruly Family
ThatsMaths 