For many centuries, mathematicians struggled to derive Euclid’s fifth postulate as a theorem following from the other axioms. All attempts failed and, in the early nineteenth century, three mathematicians, working independently, found that consistent geometries could be constructed without the fifth postulate. Carl Friedrich Gauss (c. 1813) was first, but he published nothing on the topic. Nikolai Ivanovich Lobachevsky, around 1830, and János Bolyai, in 1832, published treatises on what is now called hyperbolic geometry.
A Model for Elliptic Geometry
Published May 13, 2021 Occasional Leave a CommentTags: Geometry, Spherical Trigonometry
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].
The characteristic butterfly pattern for solutions of Lorenz’s equations [Image credit: source unknown].
Can You Believe Your Eyes?
Published April 29, 2021 Occasional Leave a CommentTags: Numerical Analysis
Scene from John Ford’s Stagecoach (1939).
Remember the old cowboy movies? As the stage-coach comes to a halt, the wheels appear to spin backwards, then forwards, then backwards again, until the coach stops. How can this be explained?
In Euclidean geometry, all lengths, areas and volumes are relative. Once a unit of length is chosen, all other lengths are given in terms of this unit. Classical geometry could determine the lengths of straight lines, the areas of polygons and the volumes of simple solids. However, the lengths of curved lines, areas bounded by curves and volumes with curved surfaces were mostly beyond the scope of Euclid. Only a few volumes — for example, the sphere, cylinder and cone — could be measured using classical methods.
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].
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Circles, polygons and the Kepler-Bouwkamp constant
Published April 8, 2021 Occasional Leave a CommentTags: Analysis
If circles are drawn in and around an equilateral triangle (a regular trigon), the ratio of the radii is 
Kepler was unable to construct an accurate model using polygons, but he noted that, if successive polygons with an increasing number of sides were inscribed within circles, the ratio did not diminish indefinitely but appeared to tend towards some limiting value. Likewise, if the polygons are circumscribed, forming successively larger circles (see Figure below), the ratio tends towards the inverse of this limit. It is only relatively recently that the limit, now known as the Kepler-Bouwkamp constant, has been established.
Continue reading ‘Circles, polygons and the Kepler-Bouwkamp constant’Was Space Weather the cause of the Titanic Disaster?
Published April 1, 2021 Occasional Leave a CommentTags: Geophysics
Space weather, first studied in the 1950’s, has grown in importance with recent technological advances. It concerns the influence on the Earth’s magnetic field and upper atmosphere of events on the Sun. Such disturbances can enhance the solar wind, which interacts with the magnetosphere, with grave consequences for navigation. Space weather affects the satellites of the Global Positioning System, causing serious navigation problems [TM208 or search for “thatsmaths” at irishtimes.com].
The Dimension of a Point that isn’t there
Published March 25, 2021 Occasional Leave a CommentTags: Topology
A slice of Swiss cheese has one-dimensional holes;
a block of Swiss cheese has two-dimensional holes.
What is the dimension of a point? From classical geometry we have the definition “A point is that which has no parts” — also sprach Euclid. A point has dimension zero, a line has dimension one, a plane has dimension two, and so on.
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Making the Best of Waiting in Line
Published March 18, 2021 Irish Times Leave a CommentTags: Applied Maths
Queueing system with several queues, one for each serving point [Wikimedia Commons].
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].
Differential Forms and Stokes’ Theorem
Published March 11, 2021 Occasional Leave a CommentTags: Analysis
Elie Cartan (1869–1951).
The theory of exterior calculus of differential forms was developed by the influential French mathematician Élie Cartan, who did fundamental work in the theory of differential geometry. Cartan is regarded as one of the great mathematicians of the twentieth century. The exterior calculus generalizes multivariate calculus, and allows us to integrate functions over differentiable manifolds in 
The fundamental theorem of calculus on manifolds is called Stokes’ Theorem. It is a generalization of the theorem in three dimensions. In essence, it says that the change on the boundary of a region of a manifold is the sum of the changes within the region. We will discuss the basis for the theorem and then the ideas of exterior calculus that allow it to be generalized. Finally, we will use exterior calculus to write Maxwell’s equations in a remarkably compact form.
Goldbach’s Conjecture: if it’s Unprovable, it must be True
Published March 4, 2021 Irish Times Leave a CommentTags: Euler, Logic, Number Theory
Image © easycalculation.com
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’
Mamikon’s Theorem and the area under a cycloid arch
Published February 25, 2021 Occasional Leave a CommentTags: Analysis, Geometry
The cycloid, the locus of a point on the rim of a rolling disk.
The Cycloid
The cycloid is the locus of a point fixed to the rim of a circular disk that is rolling along a straight line (see figure). The parametric equations for the cycloid are
where 
* * * * *
That’s Maths II: A Ton of Wonders
by Peter Lynch now available.
Full details and links to suppliers at
http://logicpress.ie/2020-3/
>> Review in The Irish Times <<
* * * * *
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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].
Schematic diagram of some key physical processes in the climate system.
Continue reading ‘Machine Learning and Climate Change Prediction’
A ring torus (or, simply, torus) is a surface of revolution generated by rotating a circle about a coplanar axis that does not intersect it. We let 
Generating a ring torus by rotating a circle of radius
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].
Al Khwarizmi, Persian polymath (c. 780 – 850) [image, courtesy of Prof. Irfan Shahid].
Continue reading ‘Complexity: are easily-checked problems also easily solved?’
Euler’s Product: the Golden Key
Published January 28, 2021 Occasional Leave a CommentTags: Analysis, Euler
The Golden Key
The Basel problem was solved by Leonhard Euler in 1734 [see previous post]. His line of reasoning was ingenious, with some daring leaps of logic. The Basel series is a particular case of the much more general zeta function, which is at the core of the Riemann hypothesis, the most important unsolved problem in mathematics.
Euler treated the Taylor series for 
This enabled him to deduce the remarkable result
which he described as an unexpected and elegant formula.
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.
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The Basel Problem: Euler’s Bravura Performance
Published January 14, 2021 Occasional Leave a CommentTags: Analysis, Euler
The Basel problem was first posed by Pietro Mengoli, a mathematics professor at the University of Bologna, in 1650, the same year in which he showed that the alternating harmonic series sums to 
It is not immediately clear that this series converges, but this can be proved without much difficulty, as was first shown by Jakob Bernoulli in 1689. The sum is approximately 1.645 which has no obvious interpretation.
* * * * *
That’s Maths II: A Ton of Wonders
by Peter Lynch has just appeared.
Full details and links to suppliers at
http://logicpress.ie/2020-3/
* * * * *
Continue reading ‘The Basel Problem: Euler’s Bravura Performance’
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].
Derangements and Continued Fractions for e
Published December 31, 2020 Occasional Leave a CommentTags: Combinatorics, Number Theory
We show in this post that an elegant continued fraction for 
Continue reading ‘Derangements and Continued Fractions for e’
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’
Will RH be Proved by a Physicist?
Published December 10, 2020 Occasional Leave a CommentTags: Analysis, Number Theory
The Riemann Hypothesis (RH) states that all the non-trivial (non-real) zeros of the zeta function lie on a line, the critical line, 
The non-trivial zeros of 
eigenvalues of a hermitian operator.
Is there a Riemann operator? What could this operater be? What dynamical system would it represent? Are prime numbers and quantum mechanics linked? Will RH be proved by a physicist?
This last question might make a purest-of-the-pure number theorist squirm. But it is salutary to recall that, of the nine papers that Riemann published during his lifetime, four were on physics!
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].
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Laczkovich Squares the Circle
Published November 26, 2020 Occasional Leave a CommentTags: Analysis, Logic
The phrase `squaring the circle’ generally denotes an impossible task. The original problem was one of three unsolved challenges in Greek geometry, along with trisecting an angle and duplicating a cube. The problem was to construct a square with area equal to that of a given circle, using only straightedge and compass.
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].
Transverse Mercator projection with central meridian at Greenwich.
Continue reading ‘Ireland’s Mapping Grid in Harmony with GPS’
Aleph, Beth, Continuum
Published November 12, 2020 Occasional Leave a CommentTags: Logic, Set Theory
Georg Cantor developed a remarkable theory of infinite sets. He was the first person to show that not all infinite sets are created equal. The number of elements in a set is indicated by its cardinality. Two sets with the same cardinal number are “the same size”. For two finite sets, if there is a one-to-one correspondence — or bijection — between them, they have the same number of elements. Cantor extended this equivalence to infinite sets.
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].
Anomaly correlation of ECMWF 500 hPa height forecasts over three decades [Image from ECMWF].
The p-Adic Numbers (Part 2)
Published October 29, 2020 Occasional Leave a CommentTags: Number Theory
Kurt Hensel (1861-1941)
Kurt Hensel, born in Königsberg, studied mathematics in Berlin and Bonn, under Kronecker and Weierstrass; Leopold Kronecker was his doctoral supervisor. In 1901, Hensel was appointed to a full professorship at the University of Marburg. He spent the rest of his career there, retiring in 1930.
Hensel is best known for his introduction of the p-adic numbers. They evoked little interest at first but later became increasingly important in number theory and other fields. Today, p-adics are considered by number theorists as being “just as good as the real numbers”. Hensel’s p-adics were first described in 1897, and much more completely in his books, Theorie der algebraischen Zahlen, published in 1908 and Zahlentheorie published in 1913.
The p-Adic Numbers (Part I)
Published October 22, 2020 Occasional Leave a CommentTags: Number Theory
Image from Cover of Katok, 2007.
The motto of the Pythagoreans was “All is Number”. They saw numbers as the essence and foundation of the physical universe. For them, numbers meant the positive whole numbers, or natural numbers 
If we arrange the rational numbers on a line, there are gaps everywhere. We can fill these gaps by introducing additional numbers, which are the limits of sequences of rational numbers. This process of completion gives us the real numbers 
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].
Fields Medalist Professor Terence Tao.
Continue reading ‘Terence Tao to deliver the Hamilton Lecture’
From Impossible Shapes to the Nobel Prize
Published October 8, 2020 Occasional 1 CommentTags: Astronomy, Geometry
Roger Penrose, British mathematical physicist, mathematician and philosopher of science has just been named as one of the winners of the 2020 Nobel Prize in Physics. Penrose has made major contributions to general relativity and cosmology.
Impossible triangle sculpture in Perth, Western Australia [image Wikimedia Commons].
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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].
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Doughnuts and Dumplings are Distinct: Homopoty-101
Published September 24, 2020 Occasional Leave a CommentTags: Topology
As everyone knows, a torus is different from a sphere. Topology is the study of properties that remain unchanged under continuous distortions. A square can be deformed into a circle or a sphere into an ellipsoid, whether flat like an orange or long like a lemon or banana.
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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?’
Donald E Knuth, designer of the \TeX mathematical typesetting system.
Mathematicians owe a great debt of gratitude to Donald Knuth. A renowned American computer scientist and mathematician, Knuth is an emeritus professor at Stanford University. He is author of many books, including the multi-volume work, The Art of Computer Programming.
Knuth is the author of the powerful and versatile mathematical typesetting system called TeX. The original version, designed and written by Knuth, was released in 1978.
TeX is a powerful system for typesetting mathematical formulae. It is ideal both for simple mathematical notes with few formulas and for more complex documents and books involving subtle and sophisticated mathematical typography. TeX is used by almost all research mathematicians. It is also popular in computer science, engineering, physics, statistics, and and many other sciences.
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].
Jung’s Theorem: Enclosing a Set of Points
Published August 27, 2020 Occasional Leave a CommentTags: Geometry
Let us imagine that we have a finite set 
Left: a set P of points in the real plane. Right: The span s is the maximum distance between two points of P.
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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].
A plaque commemorating the first appearance of the Drake Equation at a conference at the National Radio Astronomy Observatory, Green Bank, West Virginia in 1961.
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Think of a Number: What are the Odds that it is Even?
Published August 13, 2020 Occasional Leave a CommentTags: Number Theory, Probability
Pick a positive integer at random. What is the chance of it being 100? What or the odds that it is even? What is the likelihood that it is prime?
Probability distribution 
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Resolution of Paradox: a Gateway to Mathematical Progress
Published August 6, 2020 Occasional Leave a Comment
Hermann Weyl (1885-1955)
A paradox is a statement that appears to contradict itself, or that is counter-intuitive. The analysis of paradoxes has led to profound developments in mathematics and logic. One of the richest sources of paradox is the concept of infinity. Hermann Weyl, one of the most brilliant mathematicians of the twentieth century, defined mathematics as “the science of the infinite” [TM192 or search for “thatsmaths” at irishtimes.com].
Ever since there has been time to wonder, humankind has been intrigued by the enigma of infinity. The idea has perplexed philosophers and mystified mathematicians for millennia. The Greeks were contemplating infinity from the time of Pythagoras. Head-on confrontation of infinity led to contradictory conclusions; the paradoxes of Zeno are amongst the most noted of these.
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Berry’s Paradox and Gödel’s Incompleteness Theorem
Published July 30, 2020 Occasional Leave a CommentTags: Logic
Left: Argentine-American mathematician
Gregory Chaitin [image from here]. Right: American philosopher and logician
George Boolos [image Wikimedia Commons].
THE SMALLEST NATURAL NUMBER THAT CANNOT BE
DEFINED IN FEWER THAN TWENTY WORDS.
Continue reading ‘Berry’s Paradox and Gödel’s Incompleteness Theorem’
Does Numerical Integration Reflect the Truth?
Published July 23, 2020 Occasional Leave a CommentTags: Numerical Analysis, Numerical Weather Prediction
Many problems in applied mathematics involve the solution of a differential equation. Simple differential equations can be solved analytically: we can find a formula expressing the solution for any value of the independent variable. But most equations are nonlinear and this approach does not work; we must solve the equation by approximate numerical means. The big question is:
“Does the numerical solution resemble the true solution of the equation?”
The answer is: “Not necessarily”.
There are often specific criteria that must be satisfied to ensure that the answer `crunched out’ by the computer is a reasonable approximation to reality. Although the principles of numerical stability are quite general, they are best illustrated by simple examples. We will look at some of these below.
Smooth curve: True solution. Black dots: stable solution. Red dots: unstable solution (time step too large).
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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’
Jean Buridan (c. 1300-1360).
“Buridan’s Ass” is a paradox in philosophy, in which a hungry donkey, located at the mid-point between two bales of hay, is frozen in indecision about which way to go and faces starvation — he is unable to move one way or the other.
Jean Buridan was a French philosopher who lived in the fourteenth century. He was not interested in donkeys, but in human morality. He wrote that if two courses of action are judged to be morally equal, we must suspend a decision until the right course of action becomes clear. The idea of the paradox can be found in the writings of the ancients, including Aristotle.
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 Online Encyclopedia of Integer Sequences
Published June 25, 2020 Occasional Leave a CommentTags: Analysis, Arithmetic, Number Theory
Suppose that, in the course of an investigation, you stumble upon a string of whole numbers. You are convinced that there must be a pattern, but you cannot find it. All you have to do is to type the string into a database called OEIS — or simply “Slone’s” — and, if the string is recognized, an entire infinite sequence is revealed. If the string belongs to several sequences, several choices are offered. OEIS is a great boon to both professional mathematicians and applied scientists in fields like physics, chemistry, astronomy and biology.
The Home page of OEIS: https://oeis.org
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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 ].
Predicted locations for more than 1200 individuals, based on DNA markers in their genome (figure from Nature).
Continue reading ‘The Geography of Europe is Mapped in our Genes’
Dimension Reduction by PCA
Published June 11, 2020 Occasional Leave a CommentTags: Algebra, Numerical Analysis
We live in the age of “big data”. Voluminous data collections are mined for information using mathematical techniques. Problems in high dimensions are hard to solve — this is called “the curse of dimensionality”. Dimension reduction is essential in big data science. Many sophisticated techniques have been developed to reduce dimensions and reveal the information buried in mountains of data.
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 ].
Prof Philip Nolan, Chairman of IEMAG (Photograph: Tom Honan
