GCSE Maths Revision Papers
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Pierre de Fermat

Pierre de Fermat

Pierre de Fermat was a French mathematician, born in 1601, in Beaumont de Lomagne. He made many important discoveries in mathematics.

Fermat developed his career in the legal profession but loved mathematics and worked on it as a hobby. He kept in contact with many of the leading mathematicians of his day through writing letters.

 

Fermat would often scribble notes in the margins of books that he read. On one occasion he stated that the equation xn + yn = zn would have no solutions with whole number values for x, y,z and n whenever n is greater than 2. He also said that he had discovered the most remarkable proof of this result, but that the margin was too small to hold it.

This statement became known as Fermat’s last theorem. His proof was never found and many scholars attempted to either prove or disprove the result. In 1908 (around 250 years after Fermat made his statement) the German mathematician P.Wolfskehl offered a prize of 100000 marks as a prize for the first complete proof. Many attempts have been made and a lot of new mathematics has been produced in the process.

In June 1993 the British-born mathematician Andrew Wiles presented a proof to a conference at Cambridge. His proof ran to 1000 pages but turned out to be incomplete. Wiles re-submitted his proof in November 1994 and this version has been accepted.

You can find out much more about Pierre de Fermat by following this link.

 


Andrew Wiles

Andrew Wiles

 

Andrew Wiles was born in Cambridge, England, in April 1953 and is famous for producing the first accepted proof of Fermat’s last theorem.

Attempts at proving the theorem had baffled mathematicians for over 300 years before Wiles tackled the problem!

Wiles was just 10 years old when he first found out about Fermat’s last theorem. He found it in a book and, when he realised that he understood what the theorem said, he decided that he wanted to be the first person to prove it.

The theorem states that the equation xn + yn = zn has no solutions with whole number values for x, y,z and n whenever n is greater than 2. Fermat had written in the margin of a book that he had discovered the most remarkable proof of this result, but that the margin was too small to hold it.

Wiles studied mathematics at Oxford University for his degree and then transferred to Cambridge University to do further work for a doctorate. He was tempted to work on Fermat’s theorem as a part of this, but he decided that there was too big a risk that he would have little to show for all his efforts.

He did eventually have the chance to devote his full attention to finding a proof but the problem was so complex that, after seven years of study, he nearly gave up. Then, one day, all of the key ideas that he needed suddenly fell into place and he could see the solution. He achieved his childhood dream and proved Fermat’s last theorem.

You can find out much more about Andrew Wiles by following this link.

 


The wall

Here is an addition wall.
Adding two numbers next to each other on the same row gives the number above.
Enter all of the missing numbers then press Check.
Click New for another wall.

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Top Score

Try this game and test your mental abilities.

Click start to reveal some numerical expressions. The object is to click the matching pairs as quickly as possible.

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Grid Game – Multiplication 01

Play the Grid Game below – this time it’s basic multiplication. Fill out the answers and check your score…. Try to get 100%!

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Grid Game – Addition 02

Play the Grid Game below – this time it’s basic addition. Fill out the answers and check your score…. Try to get 100%!

Sorry, either Adobe flash is not installed or you do not have it enabled

Grid Game – Addition 01

Play the Grid Game below – this time it’s basic addition.  Fill out the answers and check your score…. Try to get 100%!

Sorry, either Adobe flash is not installed or you do not have it enabled

Ramanujan

This week’s look in the vaults tells us about Srinivasa Ramanujan…….

Srinivasa Ramanujan

Srinivasa Ramanujan was born into a poor family from Madras Province, India in 1887.
He had a great gift for mathematics.

He came across a book containing about 6000 theorems in mathematics that would normally just be used for reference. Ramanujan read it and then set about proving the results for himself.

He planned to study at the University of Madras but missed a lot of work due to illness. As a result, he failed all of the entrance exams apart from mathematics and was not allowed on the course.

Ramanujan continued to teach himself mathematics and developed many results of his own without any guidance. In 1913 he sent a letter to a number of British mathematicians stating some of his results. The only one to respond was the Cambridge mathematician G.H. Hardy. Hardy was so impressed with what Ramanujan had achieved that he invited him to Cambridge. They later worked together on some important papers on number theory.

There is a story that Hardy and Ramanujan were travelling by taxi when Hardy noticed the number of the taxi in front was 1729. He couldn’t think of anything special about the number and said so. Ramanujan replied that it is the smallest number that can be written as the sum of two cubes in two different ways!
(1729 = 1³ + 12³ = 9³ + 10³).

You can find out much more about Ramanujan by following this link.


William Rowan Hamilton

This look in the vaults tells us about William Rowan Hamilton……..

William Rowan Hamilton

William Rowan Hamilton was born on August 3, 1805, in Dublin, Ireland.
He showed outstanding ability from an early age. He could read and write at the age of three and translated Latin, Greek, and Hebrew into English by the time he was five.

As a teenager he was fluent in 14 different languages.

He studied for his degree at Trinity College in Dublin. At the age of 21, he wrote a paper using mathematics to produce his theory about rays of light. This work was so impressive that he was made professor of astronomy even though he hadn’t applied for the post!

Hamilton went on to develop new theories in mathematics. He spent 10 years working on something called quaternions in algebra. He struggled for a long time to make the theory work. Then, one day, he was walking along a canal when the solution came to him.

He was so overjoyed that he wanted to record the result immediately. He used a knife to cut i² = j² = k² = ijk = -1 into a stone of Brougham Bridge as he passed it.

You can find out much more about Hamilton by following this link.


Sir Isaac Newton

This look in the vaults tells us about the English mathematician Isaac Newton.

Sir Isaac Newton

Isaac Newton was born on Christmas day 1642 at the manor house of Woolsthorpe, near Grantham in Lincolnshire.

Newton’s father died three months before he was born and,when his mother remarried two years later, he was brought up by his grandmother. It seems that he didn’t have a happy childhood and showed little promise in his early years at school.

He was taken out of school at the age of 17 to manage the family estate….he hated it! Fortunately his headmaster persuaded his mother to allow him to return to school and prepare for university.

He went to Cambridge university in 1662 to study law. The story goes that he first developed an interest in mathematics when he bought a book on astrology and struggled to understand the mathematics in it. Just a few years later, during the time of the plague, he made his own major discoveries in mathematics, optics, physics and astronomy. He became known as one of the world’s greatest mathematicians.

You can find out much more about Newton by following this link.