Posts Tagged 'Education'

The Vastness of Mathematics: No One Knows it All

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].


The Princeton Companions to Maths and Applied Maths

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

Learning Maths without even Trying

Children have an almost limitless capacity to absorb knowledge if it is presented in an appealing and entertaining manner. Mathematics can be daunting, but it is possible to convey key ideas visually so that they are instantly accessible. Visiting Explorium recently, I saw such a visual display demonstrating the theorem of Pythagoras, which, according to Jacob Bronowski, “remains the most important single theorem in the whole of mathematics” [TM167 or search for “thatsmaths” at].


Continue reading ‘Learning Maths without even Trying’

Who Uses Maths? Almost Everyone!

In the midst of Maths Week Ireland, many students may be asking “What use is mathematics and what purpose is served by studying it?” Mathematicians often stress the inherent beauty and intellectual charm of the subject, but that is unlikely to persuade many people, who demand to know how mathematics can be of use and value to them. [TM149, or search for “thatsmaths” at].


In reality, mathematics is essential in numerous contexts: the diversity is remarkable, and you may be surprised how maths plays a vital role in the everyday work of so many people.

Continue reading ‘Who Uses Maths? Almost Everyone!’

Tom Lehrer: Comical Musical Mathematical Genius


Tom Lehrer, mathematician, singer, songwriter and satirist, was born in New York ninety years ago. He was active in public performance for about 25 years from 1945 to 1970. He is most renowned for his hilarious satirical songs, many of which he recorded and which are available today on YouTube [see TM147, or search for “thatsmaths” at].

Continue reading ‘Tom Lehrer: Comical Musical Mathematical Genius’

Mathematics at the Science Museum

The new Winton Gallery at London’s Science Museum in South Kensington holds a permanent display on the history of mathematics over the past 400 years. The exhibition shows how mathematics has underpinned astronomy, navigation and surveying in the past, and how it continues to pervade the modern world [see TM139, or search for “thatsmaths” at].


Central Display at the Science Museum

Continue reading ‘Mathematics at the Science Museum’

Learning Maths has never been Easier

Maths is hard: many people find it inscrutable and have negative attitudes towards maths. They may have bad memories of school maths or have been told they lack mathematical talents. This is unfortunate: we all have the capacity to apply reasoning and logic and we can all do maths. Given the vital role mathematics plays in modern society, there is an urgent need to help young people to become more numerate and comfortable with mathematics. With a wealth of online resources, learning maths has never been easier. [TM125 or search for “thatsmaths” at].


Eoin Gill and Sheila Donegan with Jadine Rock of Rutland National School, Dublin , at the launch of Maths Week Ireland. Image: Shane O’Neill, SON Photographic.

Continue reading ‘Learning Maths has never been Easier’

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 answers. For example, Liberty Hall has about 16 floors. With 4 metres per floor we get a height of 64 metres, close enough to the actual height. Problems of this nature are known as Fermi problems. [TM114 or search for “thatsmaths” at].

Continue reading ‘When Roughly Right is Good Enough’

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 into a form for output to a loudspeaker or headphones, or to drive a refreshable Braille display [TM095, or search for “thatsmaths” at].


Braille display (

Continue reading ‘Computers Speaking in Irish’

You Can Do Maths

Bragging about mathematical ineptitude is not cool. There is nothing admirable about ignorance and incompetence. Moreover, everyone thinks mathematically all the time, even if they are not aware of it. Can we all do maths? Yes, we can!  [See this week’s That’s Maths column (TM064) or search for “thatsmaths” at].

Topological map of the London Underground network

When you use a map of the underground network, you are doing topology.

Continue reading ‘You Can Do Maths’

Euclid in Technicolor

 The article in this week’s That’s Maths column in the Irish Times ( TM039 ) is about Oliver Byrne’s amazing technicolor Elements of Euclid, recently re-published by Taschen.

Continue reading ‘Euclid in Technicolor’

Irish Maths Week 2013

This week’s That’s Maths in The Irish Times ( TM028  ) is all about Maths Week, a major event in the calender of mathematics in Ireland. Over the coming weeks information and announcements about the event will appear on the website for the event (click the logo below):


Continue reading ‘Irish Maths Week 2013’

Matholympic Heroes

That’s Maths in the Irish Times this week ( TM025 ) is about the International Mathematical Olympiad (IMO), which takes place in Santa Marta, Columbia next week.
Continue reading ‘Matholympic Heroes’

Wrangling and the Tripos

The Mathematical Tripos examinations, and the Wranglers who achieve honours in them, are the topic of the That’s Maths column ( TM023 ) in the Irish Times this week.
Continue reading ‘Wrangling and the Tripos’

Where Circles are Square

Imagine a world where circles are square and π is equal to 4. Strange as it seems, we live in such a world: urban geometry is determined by the pattern of streets in a typical city grid and distance “as the crow flies” is not the distance that we have to travel from place to place. Continue reading ‘Where Circles are Square’

Khan Academy

This week, That’s Maths (TM005) discusses the large range of maths education videos that are available free of charge from the Khan Academy website.  There are about 3,200 tutorials, covering the whole range of second-level mathematics.

Salman Khan’s Technology, Entertainment and Design (TED) presentation is available on-line: Let’s Use Video to Reinvent Education.

There are several other websites with secondary level maths videos. One of the best is the MathCentre. MathCentre provides second level mathematics support materials to students and teachers. MathCentre team members are also active in university mathematics support centres

More videos on mathematics are available at Udacity. Tutorials are at beginner, intermediate and advanced levels. There are also units on physics and computer science.

The Two Cultures

The Two Cultures

Of course I’ve heard of Beethoven, but who is this guy Gauss?

The “Two Cultures”, introduced by the British scientist and novelist C. P. Snow in an influential Rede Lecture in 1959, are still relevant.

Ludwig von Beethoven and Carl Friedrich Gauss were at the height of their creativity in the early nineteenth century. Beethoven’s music, often of great subtlety and intricacy, is accessible even to those of us with limited knowledge and understanding of it. Gauss, the master of mathematicians, produced results of singular genius, great utility and deep aesthetic appeal. But, although the brilliance and beauty of his work is recognized and admired by experts, it is hidden from most of us, requiring much background knowledge and technical facility for its true appreciation.

There is a stark contrast here. There are many parallels between music and mathematics: both are concerned with structure, symmetry and pattern, but music is accessible to all while maths presents greater obstacles. Perhaps it’s a left versus right brain issue. Music gets into the soul on a high-speed emotional autobahn, while maths has to follow a rational, step-by-step route. Music has instant appeal; maths takes time.

It is regrettable that public attitudes to mathematics are predominantly unsympathetic. The beauty of maths can be difficult to appreciate, and its significance in our lives is often underestimated. But mathematics is an essential thread in the fabric of modern society. We all benefit from the power of maths to model our world and enable technological advances. It is arguable that the work of Gauss has a greater impact on our daily lives than the magnificent creations of Beethoven.

Irish Times Articles

“That’s Maths”,  a new series of articles on mathematics and its importance in society, will be published in the Irish Times, starting on 19 July 2012.

The initial article, at TM001, looks at the statistics of Usain Bolt’s performance in the 100m and the prospects for a new record at the London Olympics.

The column draws on an article,  What is the Speed Limit for Men’s 100 Meter Dash, by Prof Reza Noubary of  Bloomington University, Pennsylvania, available here (PDF).

Last 50 Posts