Paul Erdös 26 Mar 1913 - 20 Sep 1996

Happy birthday to Paul Erdös, who would have been 100 today if he were still with us.

This Hungarian mathematician, was one of the 20th century's top math experts and pioneered the fields of number theory and combinatorics. The type of mathematics he worked on were beautiful problems that were simple to understand, but notoriously difficult to solve. He loved to set problems for others to solve and would often offer cash prizes as rewards for correct solutions to the problems. These rewards ranged from $5 to $10,000 depending on how difficult he judged them to be.

At age 20, Erdös discovered a proof for a classic theorem of number theory that states that there is always at least one prime number between any positive integer and its double. In the 1930s, he studied in England and later moved to the USA. His Jewish origins made a return to Hungary impossible. However, he was affected by McCarthyism in the 1950s and he spent much of the next ten years in Israel.

Having written many hundreds of papers Erdös became history's most prolific mathematician. He wrote over 1,000 research papers, more than any other mathematician. The previous record was held by Arthur Cayley, who wrote 927.

Pi Day Live

Thursday is the annual Pi Day (because Americans would write the date 3.14).


This year, Marcus du Sautoy is hosting Pi Day Live. It's a free interactive online event that is open to all.

The number pi has intrigued mathematicians throughout the ages and this fascination has shown no sign of stopping. In recent times mathematicians have employed super-computers to calculate pi to over a trillion decimal places.

In Pi Day Live, Marcus du Sautoy will be asking whether the techniques used by the ancients to calculate pi can still be used today. And if so, which ones are best? As a part of the interactive audience, you will be a part of answering these questions and more.

To take part, visit the event's online lecture theatre, or go to the event's big screen to watch online. All you need is access to YouTube to get involved.

Brightest Shine Less Brightly At 16

Institute of Education (Photo credit: Wikipedia)

A new study has highlighted the differences in mathematical ability between the children of different countries at different ages. According to researchers at the Institute of Education in London, England's brightest primary school pupils are on a par, mathematically, with the those from Taiwan and Hong Kong. But by the time pupils reach 16, the comparative performance achieved by the top 10% falls. Overall the English pupils came 28th out of 65 countries at this age.

When looking at the average scores of the entire cohort, the pupils from east Asia performed better than those from England at all ages, but the gap didn't widen as the pupils became older.

What is going on here? There is no doubt it is disappointing, but what or who is to blame?

a) The curriculum? Is the curriculum too narrow at secondary school? There is no doubt that the very brightest pupils in UK schools will absorb everything they are taught. So are we simply not teaching enough? Do the top 10% need extra challenges?

b) The teaching? There is a long-standing debate over whether, as a society, we value the work of teachers enough. Would increasing the average pay of teachers encourage better, more inspirational teachers into the classroom? Would this really make a difference in educational standards?

c) The culture? Is there enough of a culture of learning in our schools? Are there schools in which pupils learn little or nothing mathematically? Are there schools in which the poor performance and behaviour of a section of the cohort is adversely affecting the chances for the brightest to progress?

d) The basics? Interestingly, the Institute's report's recommendations suggest taking a new look at the way mathematics is taught in our primary schools, despite the brightest pupils apparently being close to the top of the world rankings at this age. Are we failing to build the foundations of a successful mathematics education with our primary education?

We would be very interested to hear your view. Email info@mathsbank.co.uk .

Is Gove's GCSE U-Turn Enough?

Another week, another controversy in the Department for Education.

After criticism from teaching unions, academics and fellow MPs, Michael Gove has withdrawn his plans to replace the GCSE with English Baccalaureate certificates in key subjects from 2015. The Commons Education committee had said that Mr Gove had been trying to implement "too much too soon". In his Commons speech reversing his plans, Gove did, however, say that he has asked Ofqual to ensure new GCSEs would be in place by 2015 in seven subject areas: English, maths, the sciences, history and geography. GCSEs for all remaining subjects would be reformed by the following year.

Now, the head of England's exam regulator Ofqual has warned that these changes may be too rapid. Glenys Stacey has replied to Mr Gove, saying that she will delay the education secretary's GCSE changes if there are problems with the timetable. She continued "The timetable for qualifications development that you have set out is challenging." She expressed concerns about maintaining the quality of qualifications if drafting new curricula within such a short timeframe and pointed out that she would be conducting her own consultation with the exam boards.

Other criticism has come from the head of the Mathematical Association, Peter Ransom. He pointed out that "The 2015 schedule for implementation is so ambitious that no time will be available for piloting, reflection and refinement."

Dr Kevin Stannard from the Girls' Day School Trust expressed concerns that many aspects of Michael Gove's Baccalaureate plans may still be pushed through in the GCSE reform "on the mistaken assumption that the DfE has done a U-turn."

The Department for Education maintains that it will act quickly in order to address a loss of rigour in GCSEs.

All of this comes on top of stories about bullying by Michael Gove's special advisers and controversial plans for the privatisation of academies.

Gove Lays Out Plans to Overhaul A-Levels

Michael Gove plans to reform A-Levels
and scrap GCSEs. Photo: commons.wikimedia.org

Education Secretary Michael Gove today lays out his long-awaited plans to overhaul the A-Level system in England.

He says that his ideas will make A-Levels more rigorous and reduce the number of exams taken.

The major changes under Gove's reforms will be these:
- AS levels will no longer count towards a full A-level but will become stand-alone qualifications;
- It will no longer be possible to take individual modules; the course will be examined with one final examination;
- There will be a bigger role for universities in monitoring the content of each A-level.

Mr Gove has outlined his plans in a letter to the examination regulator Ofqual. He says A-levels do not provide the solid foundation students need. Mr Gove claims that pupils spend too much time sitting examinations and too little time thinking deeply about their subject. He has previously described the modular system as comprising "bite-sized" units of learning.

The Russell Group of top universities will have a role in supervising the content of A-levels, ensuring they are sufficiently challenging. This is a compromise position that the universities are happy with; Mr Gove had previously consulted with the universities about their being involved in setting the exams.

The new structure will be introduced in England from 2015. Labour's education secretary Stephen Twigg has already accused Mr Gove of "turning the clock back" and narrowing people's options.

Teaching unions have also been quick to express their doubts. Brian Lightman, general secretary of the Association of School and College Leaders (ASCL), said his union was "not convinced" that AS-levels should be separated in this way.

AS-levels, as a stepping-stone qualification to an A-Level, were introduced by the last Labour government under reforms known as Curriculum 2000. The new proposals effectively move the A-level system back to where it was before Curriculum 2000.

Mr Gove's reform of A-Levels come alongside his plans to scrap GCSEs and replace them with English Baccalaureate Certificates (EBCs) from 2015.

As with GCSEs, Northern Ireland and Wales will have to decide whether to stick with their existing A-Level structures, or to follow the new model to be introduced in England. Scotland's schools do not use A-Levels at all.

Isaac Newton 25 December 1642 – 20 March 1727

Isaac Newton, 1689

Christmas Day 2012 marks the 370th anniversary of the birth of Sir Isaac Newton, arguably England's greatest ever mathematician. His achievements in maths and the sciences are wide-ranging and monumental.

Newton made seminal discoveries in several areas of science, and was considered the leading scientist of his era. His study of optics included using a prism to show white light could be split into a spectrum of colours. The statement of his three laws of motion are fundamental in the study of mechanics. He was the first to suggest that the moon is falling in a circle around the earth, under the same influence of gravity as a falling apple, as described by his law of universal gravitation.

As a mathematician, Newton devised infinitesimal calculus to make the calculations needed in his studies, which he published in his greatest work, Philosophiae Naturalis Principia Mathematica in 1687. In the development of differential and integral calculus, Newton shares credit with the German mathematician Gottfried Leibniz, who made similar discoveries independently, at around the same time. In the late 17th century, the two men were locked, for some time, in a bitter dispute around these developments, with Newton accusing the German of plagiarism and worse. It is notation more similar to that adopted by Leibniz that is used in modern-day calculus.

Newton's theory of gravitation survived intact until the early 20th century, when Einstein's work on relativity modified, extended or supplanted it to some extent.


The dispute with Leibniz casts a shadow over the great man's life. There was, however, an element of modesty, when he wrote to another rival, Robert Hooke, "If I have seen further, it is by standing on the shoulders of giants."

Isaac Newton's work was remarkable, ground-breaking and wide-ranging. No doubt many others will continue to stand on Newton's own shoulders, in the extraordinary mathematical discoveries that, no doubt, the future will hold.

Turing Competition

There has been a lot of interest in code-breaking recently - cryptography to use the posh word. You may remember the secret message attached to a pigeon's leg, found mysteriously in somebody's chimney, a message that still baffles cryptographers 70 years after it was written.

Alan Turing was one of the finest British code-breakers during World War II. Some of his work, along with the work of others at Bletchley Park, is supposed to have shortened the war by perhaps 2 years.

After the war, Turing went to Manchester University, where he helped to develop one of the country's first computers. To celebrate his life and work, Manchester University are running a code-breaking competition to begin in the New Year.

The competition is open to secondary school pupils up to Year 11 (England and Wales), S4 (Scotland) or Year 12 (Northern Ireland). It runs from January to April 2013 and is based on a story that runs in six episodes. In each episode there is a new code-breaking challenge to solve.

To enter the competition, you will need a team of pupils. The website features a discussion forum and a leaderboard. Prizes are Amazon vouchers, with members of the winning team receiving £30 of vouchers each and a trophy for the school.

If you think you're up to the Turing Challenge, have a go and good luck!