In addition to some beautiful photos and maps and descriptions of upland challenges in Ireland and abroad, the November issue of *The Summit*, the Mountain Views Quarterly Newsletter for hikers and hillwalkers, describes a method to find the length of a walk based on ideas originating with the French naturalist and mathematician George-Louis Leclerc, Comte de Buffon [TM224 or search for “thatsmaths” at irishtimes.com].

## Archive for the 'Irish Times' Category

### Buffon’s Noodle and the Mathematics of Hillwalking

Published December 2, 2021 Irish Times Leave a CommentTags: Geometry, Geophysics

### Émilie Du Châtelet and the Conservation of Energy

Published November 18, 2021 Irish Times Leave a CommentTags: History, Mechanics

A remarkable French natural philosopher and mathematician who lived in the early eighteenth century, Émilie Du Châtalet, is generally remembered for her translation of Isaac Newton’s *Principia Mathematica*, but her work was much more than a simple translation: she added an extensive commentary in which she included new developments in mechanics, the most important being her formulation of the principle of conservation of energy [TM223 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Émilie Du Châtelet and the Conservation of Energy’

### Topsy-turvy Maths: Proving Axioms from Theorems

Published November 4, 2021 Irish Times Leave a CommentTags: Logic, Philosophy

Mathematics is distinguished from the sciences by the freedom it enjoys in choosing basic assumptions from which consequences can be deduced by applying the laws of logic. We call the basic assumptions axioms and the consequent results theorems. But can things be done the other way around, using theorems to prove axioms? This is a central question of reverse mathematics [TM222 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Topsy-turvy Maths: Proving Axioms from Theorems’

### Mathematical Scandals and Scoundrels

Published October 21, 2021 Irish Times Leave a CommentTags: History

Edna St Vincent Millay’s sonnet “Euclid alone has looked on beauty bare” evokes the ethereal, otherworldly quality of mathematics. Scandalous behaviour is not usually associated with mathematicians, but they are human: pride, overblown ego and thirst for fame have led to skulduggery, plagiarism and even murder. Some of the more egregious scandals are reviewed here [TM221 or search for “thatsmaths” at irishtimes.com].

### A Grand Unification of Mathematics

Published October 7, 2021 Irish Times Leave a CommentTags: Algebra, Analysis, Group Theory, Number Theory

There are numerous branches of mathematics, from arithmetic, geometry and algebra at an elementary level to more advanced fields like number theory, topology and complex analysis. Each branch has its own distinct set of axioms, or fundamental assumptions, from which theorems are derived by logical processes. While each branch has its own flavour, character and methods, there are also strong overlaps and interdependencies. Several attempts have been made to construct a grand unified theory that embraces the entire field of maths [TM220 or search for “thatsmaths” at irishtimes.com].

### Earth System Models simulate the changing climate

Published September 16, 2021 Irish Times Leave a CommentTags: biology, Climate Modelling, Geophysics

The climate is changing, and we need to know what changes to expect and how soon to expect them. Earth system models, which simulate all relevant components of the Earth system, are the primary means of anticipating future changes of our climate [TM219 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Earth System Models simulate the changing climate’

### The Social Side of Mathematics

Published September 2, 2021 Irish Times Leave a CommentTags: Education, Ireland

** **On a cold December night in 1976, a group of mathematicians assembled in a room in Trinity College Dublin for the inaugural meeting of the Irish Mathematical Society (IMS). Most European countries already had such societies, several going back hundreds of years, and it was felt that the establishment of an Irish society to promote the subject, foster research and support teaching of mathematics was timely [TM218 or search for “thatsmaths” at irishtimes.com].

### Changing Views on the Age of the Earth

Published August 19, 2021 Irish Times Leave a CommentTags: Geophysics, History, Ireland

### Phantom traffic-jams are all too real

Published August 5, 2021 Irish Times Leave a CommentTags: modelling

Driving along the motorway on a busy day, you see brake-lights ahead and slow down until the flow grinds to a halt. The traffic stutters forward for five minutes or so until, mysteriously, the way ahead is clear again. But, before long, you arrive at the back of another stagnant queue. Hold-ups like this, with no apparent cause, are known as phantom traffic jams and you may experience several such delays on a journey of a few hours [TM216 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Phantom traffic-jams are all too real’### All Numbers Great and Small

Published July 15, 2021 Irish Times Leave a CommentTags: Number Theory, Physics

Is space continuous or discrete? Is it smooth, without gaps or discontinuities, or granular with a limit on how small a distance can be? What about time? Can time be repeatedly divided into smaller periods without any limit, or is there a shortest interval of time? We don’t know the answers. There is much we do not know about physical reality: is the universe finite or infinite? Are space and time arbitrarily divisible? Does our number system represent physical space and time? [TM215 or search for “thatsmaths” at irishtimes.com]. Continue reading ‘All Numbers Great and Small’

### Kalman Filters: from the Moon to the Motorway

Published July 1, 2021 Irish Times Leave a CommentTags: Algorithms

Before too long, we will be relieved of the burden of long-distance driving. Given the desired destination and access to a mapping system, electronic algorithms will select the best route and control the autonomous vehicle, constantly monitoring and adjusting its direction and speed of travel. The origins of the methods used for autonomous navigation lie in the early 1960s, when the space race triggered by the Russian launch of Sputnik I was raging [TM214 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Kalman Filters: from the Moon to the Motorway’

### Seeing beyond the Horizon

Published June 17, 2021 Irish Times Leave a CommentTags: Geometry, Geophysics

From a hilltop, the horizon lies below the horizontal level at an angle called the “dip”. Around AD 1020, the brilliant Persian scholar al-Biruni used a measurement of the dip, from a mountain of known height, to get an accurate estimate of the size of the Earth. It is claimed that his estimate was within 1% of the true value but, since he was not aware of atmospheric refraction and made no allowance for it, this high precision must have been fortuitous [TM213 or search for “thatsmaths” at irishtimes.com].

### The Simple Arithmetic Triangle is full of Surprises

Published June 3, 2021 Irish Times Leave a CommentTags: Arithmetic, Number Theory

Pascal’s triangle is one of the most famous of all mathematical diagrams, simple to construct and yet rich in mathematical patterns. These can be found by a web search, but their discovery by study of the diagram is vastly more satisfying, and there is always a chance of finding something never seen before [TM212 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘The Simple Arithmetic Triangle is full of Surprises’

### Multi-faceted aspects of Euclid’s Elements

Published May 20, 2021 Irish Times Leave a CommentTags: Geometry

*Elements*was the first major work to organise mathematics as an axiomatic system. Starting from a set of clearly-stated and self-evident truths called axioms, a large collection of theorems is constructed by logical reasoning. For some, the

*Elements*is a magnificent triumph of human thought; for others, it is a tedious tome, painfully prolix and patently pointless [TM211 or search for “thatsmaths” at irishtimes.com]. Continue reading ‘Multi-faceted aspects of Euclid’s Elements’

### Improving Weather Forecasts by Reducing Precision

Published May 6, 2021 Irish Times Leave a CommentTags: Numerical Weather Prediction

Weather forecasting relies on supercomputers, used to solve the mathematical equations that describe atmospheric flow. The accuracy of the forecasts is constrained by available computing power. Processor speeds have not increased much in recent years and speed-ups are achieved by running many processes in parallel. Energy costs have risen rapidly: there is a multimillion Euro annual power bill to run a supercomputer, which may consume something like 10 megawatts [TM210 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Improving Weather Forecasts by Reducing Precision’### Entropy and the Relentless Drift from Order to Chaos

Published April 15, 2021 Irish Times Leave a CommentTags: History, Physics

In a famous lecture in 1959, scientist and author C P Snow spoke of a gulf of comprehension between science and the humanities, which had become split into “two cultures”. Many people in each group had a lack of appreciation of the concerns of the other group, causing grave misunderstandings and making the world’s problems more difficult to solve. Snow compared ignorance of the Second Law of Thermodynamics to ignorance of Shakespeare [TM209 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Entropy and the Relentless Drift from Order to Chaos’

### Making the Best of Waiting in Line

Published March 18, 2021 Irish Times Leave a CommentTags: Applied Maths

Queueing is a bore and waiting to be served is one of life’s unavoidable irritants. Whether we are hanging onto a phone, waiting for response from a web server or seeking a medical procedure, we have little choice but to join the queue and wait. It may surprise readers that there is a well-developed mathematical theory of queues. It covers several stages of the process, from patterns of arrival, through moving gradually towards the front, being served and departing [TM207 or search for “thatsmaths” at irishtimes.com].

### Goldbach’s Conjecture: if it’s Unprovable, it must be True

Published March 4, 2021 Irish Times 1 CommentTags: Euler, Logic, Number Theory

The starting point for rigorous reasoning in maths is a system of axioms. An axiom is a statement that is assumed, without demonstration, to be true. The Greek mathematician Thales is credited with introducing the axiomatic method, in which each statement is deduced either from axioms or from previously proven statements, using the laws of logic. The axiomatic method has dominated mathematics ever since [TM206 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Goldbach’s Conjecture: if it’s Unprovable, it must be True’

### Machine Learning and Climate Change Prediction

Published February 18, 2021 Irish Times Leave a CommentTags: Climate Modelling

Current climate prediction models are markedly defective, even in reproducing the changes that have already occurred. Given the great importance of climate change, we must identify the causes of model errors and reduce the uncertainty of climate predictions [TM205 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Machine Learning and Climate Change Prediction’

### Complexity: are easily-checked problems also easily solved?

Published February 4, 2021 Irish Times Leave a CommentTags: Algorithms, Computer Science

From the name of the Persian polymath Al Khwarizmi, who flourished in the early ninth century, comes the term algorithm.* *An algorithm is a set of simple steps that lead to the solution of a problem. An everyday example is a baking recipe, with instructions on what to do with ingredients (input) to produce a cake (output). For a computer algorithm, the inputs are the known numerical quantities and the output is the required solution [TM204 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Complexity: are easily-checked problems also easily solved?’

### Euler: a mathematician without equal and an overall nice guy

Published January 21, 2021 Irish Times 1 CommentTags: Euler

Mathematicians are an odd bunch. Isaac Newton was decidedly unpleasant, secretive and resentful while Carl Friedrich Gauss, according to several biographies, was cold and austere, more likely to criticize than to praise. It is frequently claimed that a disproportionate number of mathematicians exhibit signs of autism and have significant difficulties with social interaction and everyday communication [TM203 or search for “thatsmaths” at irishtimes.com].

It is true that some of the greatest fit this stereotype, but the incomparable Leonhard Euler is a refreshing counter-example. He was described by his contemporaries as a generous man, kind and loving to his 13 children and maintaining his good-natured disposition even after he became completely blind. He is comforting proof that a neurotic personality is not essential for mathematical prowess.

Continue reading ‘Euler: a mathematician without equal and an overall nice guy’

### We are living at the bottom of an ocean

Published January 7, 2021 Irish Times Leave a CommentTags: Geophysics

Anyone who lives by the sea is familiar with the regular ebb and flow of the tides. But we all live at the bottom of an ocean of air. The atmosphere, like the ocean, is a fluid envelop surrounding the Earth, and is subject to the influence of the Sun and Moon. While sea tides have been known for more than two thousand years, the discovery of tides in the atmosphere had to await the invention of the barometer [TM202 or search for “thatsmaths” at irishtimes.com].

### Arrangements and Derangements

Published December 24, 2020 Irish Times Leave a CommentTags: Combinatorics, Number Theory

Six students entering an examination hall place their cell-phones in a box. After the exam, they each grab a phone at random as they rush out. What is the likelihood that none of them gets their own phone? The surprising answer — about 37% whatever the number of students — emerges from the theory of derangements.

### On what Weekday is Christmas? Use the Doomsday Rule

Published December 17, 2020 Irish Times Leave a CommentTags: Algorithms

An old nursery rhyme begins “Monday’s child is fair of face / Tuesday’s child is full of grace”. Perhaps character and personality were determined by the weekday of birth. More likely, the rhyme was to help children learn the days of the week. But how can we determine the day on which we were born without the aid of computers or calendars? Is there an algorithm – a recipe or rule – giving the answer? [TM201 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘On what Weekday is Christmas? Use the Doomsday Rule’

### Decorating Christmas Trees with the Four Colour Theorem

Published December 3, 2020 Irish Times Leave a CommentTags: Geometry, Topology

When decorating our Christmas trees, we aim to achieve an aesthetic balance. Let’s suppose that there is a plenitude of baubles, but that their colour range is limited. We could cover the tree with bright shiny balls, but to have two baubles of the same colour touching might be considered garish. How many colours are required to avoid such a catastrophe? [TM200 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Decorating Christmas Trees with the Four Colour Theorem’

### Ireland’s Mapping Grid in Harmony with GPS

Published November 19, 2020 Irish Times Leave a CommentTags: Geophysics, Maps, Spherical Trigonometry

The earthly globe is spherical; more precisely, it is an oblate spheroid, like a ball slightly flattened at the poles. More precisely still, it is a triaxial ellipsoid that closely approximates a “geoid”, a surface of constant gravitational potential [TM199 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Ireland’s Mapping Grid in Harmony with GPS’

### Weather Forecasts get Better and Better

Published November 5, 2020 Irish Times Leave a CommentTags: Geophysics, Numerical Weather Prediction

Weather forecasts are getting better. Fifty years ago, predictions beyond one day ahead were of dubious utility. Now, forecasts out to a week ahead are generally reliable [TM198 or search for “thatsmaths” at irishtimes.com].

Careful measurements of forecast accuracy have shown that the range for a fixed level of skill has been increasing by one day every decade. Thus, today’s one-week forecasts are about as good as a typical three-day forecast was in 1980. How has this happened? And will this remarkable progress continue?### Terence Tao to deliver the Hamilton Lecture

Published October 15, 2020 Irish Times Leave a CommentTags: Hamilton

Pick a number; if it is even, divide it by 2; if odd, triple it and add 1. Now repeat the process, each time halving or else tripling and adding 1. Here is a surprise: no matter what number you pick, you will eventually arrive at 1. Let’s try 6: it is even, so we halve it to get 3, which is odd so we triple and add 1 to get 10. Thereafter, we have 5, 16, 8, 4, 2 and 1. From then on, the value cycles from 1 to 4 to 2 and back to 1 again, forever. Numerical checks have shown that all numbers up to one hundred million million million reach the 1–4–2–1 cycle [TM197 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Terence Tao to deliver the Hamilton Lecture’

### Mathematics and the Nature of Physical Reality

Published October 1, 2020 Irish Times 1 CommentTags: Logic, Philosophy

Applied mathematics is the use of maths to address questions and solve problems outside maths itself. Counting money, designing rockets and vaccines, analysing internet traffic and predicting the weather all involve maths. But why does this work? Why is maths so successful in describing physical reality? How is it that the world can be understood mathematically? [TM196, or search for “thatsmaths” at irishtimes.com]. Continue reading ‘Mathematics and the Nature of Physical Reality’

### Will mathematicians be replaced by computers?

Published September 17, 2020 Irish Times Leave a CommentTags: Computer Science

There are ongoing rapid advances in the power and versatility of AI or artificial intelligence. Computers are now producing results in several fields that are far beyond human capability. The trend is unstoppable, and is having profound effects in many areas of our lives. Will mathematicians be replaced by computers? [TM195 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Will mathematicians be replaced by computers?’

### Suitable Names for Large Numbers

Published September 3, 2020 Irish Times Leave a CommentTags: Arithmetic

One year ago, there were just two centibillionaires, Jeff Bezos and Bill Gates. Recently, Facebook’s Mark Zuckerberg has joined the Amazon and Microsoft founders. Elon Musk, CEO of Tesla and SpaceX, is tipped to be next to join this exclusive club [TM194 or search for “thatsmaths” at irishtimes.com].

### Is There Anyone Out There? The Drake Equation gives a Clue

Published August 20, 2020 Irish Times Leave a CommentTags: Astronomy

The Drake Equation is a formula for the number of developed civilizations in our galaxy, the Milky Way. This number is determined by seven factors. Some are known with good accuracy but the values of most are quite uncertain. It is a simple equation comprising seven terms multiplied together [TM193 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Is There Anyone Out There? The Drake Equation gives a Clue’

### Cornelius Lanczos – Inspired by Hamilton’s Quaternions

Published July 16, 2020 Irish Times Leave a CommentTags: Analysis, Applied Maths, Mechanics, Relativity

In May 1954, Cornelius Lanczos took up a position as senior professor in the School of Theoretical Physics at the Dublin Institute for Advanced Studies (DIAS). The institute had been established in 1940 by Eamon de Valera, with a School of Theoretical Physics and a School of Celtic Studies, reflecting de Valera’s keen interest in mathematics and in the Irish language. Later, a School of Cosmic Physics was added. DIAS remains a significant international centre of research today [TM191 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Cornelius Lanczos – Inspired by Hamilton’s Quaternions’

### The Ever-growing Goals of Googology

Published July 2, 2020 Irish Times Leave a CommentTags: Arithmetic, Number Theory

In 1920, a kindergarten class was asked to describe the biggest number that they could imagine. One child proposed to “write down digits until you get tired”. A more concrete idea was to write a one followed by 100 zeros. This number, which scientists would express as ten to the power 100, was given the name “googol” by its inventor [TM190; or search for “thatsmaths” at irishtimes.com ].

### The Geography of Europe is Mapped in our Genes

Published June 18, 2020 Irish Times Leave a CommentTags: biology

It may seem too much to expect that a person’s geographic origin can be determined from a DNA sample. But, thanks to a mathematical technique called principal component analysis, this can be done with remarkable accuracy. It works by reducing multi-dimensional data sets to just a few variables [TM189; or search for “thatsmaths” at irishtimes.com ].

Continue reading ‘The Geography of Europe is Mapped in our Genes’

### Pooling Expertise to Tackle Covid-19

Published June 4, 2020 Irish Times Leave a CommentTags: Applied Maths, Epidemiology

Our lives have been severely restricted in recent months. We are assured that the constraints have been imposed following “the best scientific advice”, but what is the nature of this advice? Among the most important scientific tools used for guidance on the Covid-19 outbreak are mathematical models [TM188; or search for “thatsmaths” at irishtimes.com ].

### Changing the way that we look at the world

Published May 21, 2020 Irish Times Leave a CommentTags: Geometry

Albrecht Dürer was born in Nuremberg in 1471, third of a family of eighteen children. Were he still living, he would be celebrating his 549th birthday today. Dürer’s artistic genius was clear from an early age, as evidenced by a self-portrait he painted when just thirteen [TM187; or search for “thatsmaths” at irishtimes.com ].

In 1494, Dürer visited Italy, where he travelled for a year. A novel connection between art and mathematics was emerging around that time. By using rules of perspective, artists could represent objects in three-dimensional space on a plane canvas with striking realism. Dürer was convinced that “the new art must be based upon science; in particular, upon mathematics, as the most exact, logical, and graphically constructive of the sciences”*.*

Continue reading ‘Changing the way that we look at the world’

### John Casey: a Founder of Modern Geometry

Published May 7, 2020 Irish Times Leave a CommentTags: Geometry, Ireland

Next Tuesday – 12th May – is the 200^{th} anniversary of the birth of John Casey, a notable Irish geometer. Casey was born in 1820 in Kilbeheny, Co Limerick. He was educated in nearby Mitchelstown, where he showed great aptitude for mathematics and also had a gift for languages. He became a mathematics teacher, first in Tipperary Town and later in Kilkenny [TM186; or search for “thatsmaths” at irishtimes.com ].

### Exponential Growth must come to an End

Published April 16, 2020 Irish Times Leave a CommentTags: Analysis, Applied Maths

In its initial stages, the Covid-19 pandemic grew at an exponential rate. What does this mean? The number of infected people in a country is growing exponentially if it increases by a fixed multiple R each day: if N people are infected today, then R times N are infected tomorrow. The size of the growth-rate R determines how rapidly the virus is spreading. An example should make this clear [TM185 or search for “thatsmaths” at irishtimes.com].

### The Mathematics of Fair Play in Video Games

Published April 2, 2020 Irish Times Leave a CommentTags: Algorithms, Games, Hamilton

Video games generate worldwide annual sales of about $150 billion. With millions of people confined at home with time to spare, the current pandemic may benefit the industry. At the core of a video game is a computer program capable of simulating a range of phenomena in the real world or in a fantasy universe, of generating realistic imagery and of responding to the actions and reactions of the players. At every level, mathematics is crucial [TM184 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘The Mathematics of Fair Play in Video Games’

### Covid-19: Modelling the evolution of a viral outbreak

Published March 19, 2020 Irish Times Leave a CommentTags: Epidemiology

There is widespread anxiety about the threat of the Covid-19 virus. Mathematics now plays a vital role in combating the spread of epidemics, and will help us to bring this outbreak under control. For centuries, mathematics has been used to solve problems in astronomy, physics and engineering. But now biology and medicine have become topics of mathematical investigation, and applications in these areas are certain to expand in the future [TM183 or search for “thatsmaths” at irishtimes.com].

How rapidly will the viral infection spread? How long will it remain a problem? When will it reach a peak and how quickly will it die out? Most important, what effective steps can we can take to control the outbreak and to minimize the damage caused? When vaccines become available, what is the optimal strategy for their use? Models provide valuable evidence for decision makers.

Continue reading ‘Covid-19: Modelling the evolution of a viral outbreak’

### Samuel Haughton and the Humane Drop

Published March 5, 2020 Irish Times Leave a CommentTags: Applied Maths, History

Samuel Haughton was born in Co. Carlow in 1821. He entered Trinity College Dublin aged just sixteen and graduated in 1843. He was elected a fellow in 1844 and was appointed professor of geology in 1851. He took up the study of medicine and graduated as a Doctor of Medicine in 1862, aged 40 [TM182 or search for “thatsmaths” at irishtimes.com].

In addition to his expertise in geology and medicine, Haughton was a highly talented applied mathematician. His mathematical investigations included the study of the motion of solid and fluid bodies, solar radiation, climatology, animal mechanics and ocean tides. One of his more bizarre applications of mathematics was to demonstrate a humane method of execution by hanging, by lengthening the drop to ensure instant death.

### How many numbers begin with a 1? More than 30%!

Published February 20, 2020 Irish Times Leave a CommentTags: Probability, Statistics

The irregular distribution of the first digits of numbers in data-bases provides a valuable tool for fraud detection. A remarkable rule that applies to many datasets was accidentally discovered by an American physicist, Frank Benford, who described his discovery in a 1938 paper, “The Law of Anomalous Numbers” [TM181 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘How many numbers begin with a 1? More than 30%!’

### Using Maths to Reduce Aircraft Noise

Published February 6, 2020 Irish Times Leave a CommentTags: Fluid Dynamics, modelling

If you have ever tried to sleep under a flight-path near an airport, you will know how serious the problem of aircraft noise can be. Aircraft noise is amongst the loudest sounds produced by human activities. The noise is over a broad range of frequencies, extending well beyond the range of hearing. The problem of aviation noise has become more severe as aircraft engines have become more powerful [TM180 or search for “thatsmaths” at irishtimes.com].

### The “extraordinary talent and superior genius” of Sophie Germain

Published January 16, 2020 Irish Times Leave a CommentTags: History, Mechanics, Number Theory

When a guitar string is plucked, we don’t see waves travelling along the string. This is because the ends are fixed. Instead, we see a standing-wave pattern. Standing waves are also found on drum-heads and on the sound-boxes of violins. The shape of a violin strongly affects the quality and purity of the sound, as it determines the mixture of standing wave harmonics that it can sustain [TM179 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘The “extraordinary talent and superior genius” of Sophie Germain’

### The knotty problem of packing DNA

Published January 2, 2020 Irish Times Leave a CommentTags: biology, Topology

Soon it will be time to pack away the fairy lights. If you wish to avoid the knotty task of disentangling them next December, don’t just throw them in a box; roll them carefully around a stout stick or a paper tube. Any long and flexible string or cable, squeezed into a confined volume, is likely to become entangled: just think of garden hoses or the wires of headphones [TM178 or search for “thatsmaths” at irishtimes.com].

### Having your Christmas Cake and Eating it

Published December 19, 2019 Irish Times Leave a CommentTags: Algorithms

As Christmas approaches, the question of fair sharing comes into focus. Readers can rejoice that there has been a recent breakthrough in cake-cutting theory. Cake cutting may sound limited, but it is important for many practical problems. A cake is a metaphor for a parcel of land to be divided, broadcast frequencies to be allocated, divorce settlements, chores to be done by flatmates, border resolutions or any other valuable or scarce resource to be shared [TM177 or search for “thatsmaths” at irishtimes.com].

### A New Mathematical Discovery from Neutrino Physics

Published December 5, 2019 Irish Times Leave a CommentTags: Physics

Although abstract in character, mathematics has concrete origins: the greatest advances have been inspired by the natural world. Recently, a new result in linear algebra was discovered by three physicists trying to understand the behaviour of neutrinos [TM176 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘A New Mathematical Discovery from Neutrino Physics’

### Airport Baggage Screening with X-Ray Tomography

Published November 21, 2019 Irish Times Leave a CommentTags: Algorithms

When you check in your baggage for a flight, it must be screened before it is allowed on the plane. Baggage screening detects threats within luggage and personal belongings by x-ray analysis as they pass along a conveyor belt. Hold-baggage and passenger screening systems are capable of detecting contraband materials, narcotics, explosives and weapons [TM175 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Airport Baggage Screening with X-Ray Tomography’

### The Vastness of Mathematics: No One Knows it All

Published November 7, 2019 Irish Times Leave a CommentTags: Education, History

No one person can have mastery of the entirety of mathematics. The subject has become so vast that the best that can be achieved is a general understanding and appreciation of the main branches together with expertise in one or two areas [TM174 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘The Vastness of Mathematics: No One Knows it All’

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