Archive for the 'Irish Times' Category

Closing the Gap between Prime Numbers

Occasionally, a major mathematical discovery comes from an individual working in isolation, and this gives rise to great surprise. Such an advance was announced by Yitang Zhang six years ago. [TM161 or search for “thatsmaths” at irishtimes.com].

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Yitang Zhang

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A Pioneer of Climate Modelling and Prediction

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Norman Phillips (1923-2019)

Today we benefit greatly from accurate weather forecasts. These are the outcome of a long struggle to advance the science of meteorology. One of the major contributors to that advancement was Norman A. Phillips, who died in mid-March, aged 95. Phillips was the first person to show, using a simple computer model, that mathematical simulation of the Earth’s climate was practicable [TM160 or search for “thatsmaths” at irishtimes.com].

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Joseph Fourier and the Greenhouse Effect

Jean-Baptiste Joseph Fourier, French mathematician and physicist, was born in Auxerre 251 years ago today. He is best known for the mathematical techniques that he developed in his analytical theory of heat transfer. Over the past two centuries, his methods have evolved into a major subject, harmonic analysis, with widespread applications in number theory, signal processing, quantum mechanics, weather prediction and a broad range of other fields [TM159 or search for “thatsmaths” at irishtimes.com].

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Greenhouse Effect [Image Wikimedia Commons]

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Hokusai’s Great Wave and Roguish Behaviour

Hokusai’s woodcut “The Great Wave off Kanagawa”.

“The Great Wave off Kanagawa”, one of the most iconic works of Japanese art, shows a huge breaking wave with foam thrusting forward at its crest, towering over three fishing boats, with Mt Fuji in the background [TM158 or search for “thatsmaths” at irishtimes.com].

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Multiple Discoveries of the Thue-Morse Sequence

It is common practice in science to name important advances after the first discoverer or inventor. However, this process often goes awry. A humorous principle called Stigler’s Law holds that no scientific result is named after its original discoverer. This law was formulated by Professor Stephen Stigler of the University of Chicago in his publication “Stigler’s law of eponymy”. He pointed out that his “law” had been proposed by others before him so it was, in a sense, self-verifying. [TM157 or search for “thatsmaths” at irishtimes.com].

Axel Thue (1863-1922) and Marston Morse (1892-1977)
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Rambling and Reckoning

A walk on the beach, in the hills or along a river bank provides great opportunities for mathematical reflection. How high is the mountain? How many grains of sand are on the beach? How much water is flowing in the river?  [TM156 or search for “thatsmaths” at irishtimes.com].


Daily average flow (cubic metres per second) at Ardnacrusha, on the Shannon near Limerick. Data from the Electricity Supply Board (ESB).

While the exact answers may be elusive, we can make reasonable guesstimates using basic knowledge and simple mathematical reasoning. And we will be walking in the footsteps of some of the world’s greatest thinkers.

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Discoveries by Amateurs and Distractions by Cranks

Do amateurs ever solve outstanding mathematical problems? Professional mathematicians are aware that almost every new idea they have about a mathematical problem has already occurred to others. Any really new idea must have some feature that explains why no one has thought of it before  [TM155 or search for “thatsmaths” at irishtimes.com].

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Pierre de Fermat and Srinivasa Ramanujan, two brilliant “amateur” mathematicians.

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