Costa, A. and Kallick, B. (2000) Habits of Mind. A Developmental Series. Alexandria, VA: Association

for Supervision and Curriculum Development

Andrew Wiles was the first mathematician to prove Fermat’s Last Theorem, a theorem that mathematicians had been trying to solve since the 17th century.

It took him 7 years to complete, during which time he was never sure that he would be able to complete the proof where numerous other mathematicians had failed.

When he announced the proof in 1993 it was 150 pages long. Unfortunately it was found that there was a ‘hole’ in the proof which Wiles worked with another mathematician to fix. Finally, after 350 years the Theorem was proved.

Euclid worked as a tutor of mathematics in the royal household of King Ptolemy I. One day the king complained about the difficulty of the theorems which Euclid expected him to learn, and asked whether there might be an easier way to approach the subject

Euclid replied: "Sire," he said, "there is no royal road to geometry."

Emmy Noether was a very talented mathematician who found it difficult to be taken seriously as she was a woman. Fortunately fellow mathematician David Hilbert allowed Noether to deliver lectures for courses listed under his name.

When she was appointed to a lectureship Hilbert's male colleagues objected to the presence of a woman in their midst. Hilbert again came to Noether’s aid: "The faculty," he tartly remarked, "is not a bathing establishment."

"At age 9 Gauss’ teacher set the class the problem of adding the numbers from 1 to 100. In a matter of seconds Gauss wrote an answer on his slate and put in on the teachers desk.

For the next hour the boy sat idly while his classmates continued to work. At the end of the lesson there was a pile of slates on top of Gauss's, all with incorrect answers.

How had he done it so quickly? Instead of adding from 1 to 100 in order, Gauss noticed that he could instead add 1 + 100 then 2 + 99 then 3 + 98 and so calculated the answer by doing 101 * 50 = 5050.

Hypatia is known as the first female mathematician. She was the daughter of Theon, a mathematician who taught at the great school at the Alexandrine Library.

She taught mathematics and natural philosophy at the school in Alexandria, Egypt. Letters written and addressed simply to the philosopher were delivered to her. Hypatia is credited with the writing three major treatises on geometry and algebra and one on astronomy. She wrote of the importance of thinking in mathematics in the quote:

Reserve your right to think, for even to think wrongly is better than not to think at all.

Every day Poincare bought bread from his local baker. Though the bread was supposed to weigh 1 kg, Poincare found that months of careful record keeping produced a nice normal distribution with a mean value of only 950 grams. Poincare called the police who gave the baker a warning...

A year later Poincare again complained to the police: Though his own loaves had increased in size, he accused the baker, of continuing to short-shift his other customers. How could Poincare possibly know that he was always given the largest loaf? Poincare had used his weights from the year to draw a bell shaped curve with max at 950 grams, but truncated on the left side.

The mathematician John von Neumann was renowned for being a great practical joker. Having created his famous "electronic brain" for the US government during World War II, Neumann named the machine a 'Mathematical Analyser, Numerical Integrator, and Computer'.

Several days passed before scientists realised that the name formed a curious anagram: MANIAC.

Blaise Pascal's father wanted his son to be trained in the classical subjects of the day and insisted that his son study readings in ancient languages. When Pascal, at age nine, asked about geometry, he was simply told it was the study of shapes. The boy, intrigued, proceeded to discover, unaided, Euclid's first thirty-two theorems - in the correct order.

His father decided to allow Pascal to pursue his mathematical studies without interruption.

Vaughan Jones is the only New Zealander to win the Fields Medal – the equivalent of the Nobel Prize in mathematics. He won it for his work in Knot Theory, a branch of mathematics where algebra is used to describe the geometry of knots.

Like most mathematicians, Paul Erdos sought simple solutions to complex problems. One day, Erdos learned that a pair of fellow mathematicians had produced a 30-page proof of a certain theorem. Ten minutes later, Erdos had produced a two line solution.

In 1735, the French Academy offered a prize for the solution to a certain astronomical problem. The problem was considered very difficult and they a solution would take several months to produce. Leonhard Euler became obsessed with the problem, and, after working continually for three days, produced a solution, and won the prize.

Unfortunately, poor working conditions and intense stress led to the loss of one of Euler’s eyes when he was still in his twenties. Euler took the loss in stride: "Now," he declared undaunted, "I will have fewer distractions!"

Srinivasa Ramanujan was a mathematical prodigy who taught himself mathematics whilst growing up in India. In later years he was invited to England by the mathematician G. H. Hardy once remarked.

On one occasion when Hardy went to visit Ramanujan Hardy commented that he had ridden in taxicab number 1729, and that the number seemed a rather dull one.

"‘No,’ replied Ramanujan, 'it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.'"

At 13 Sophie began teaching herself mathematics using the books in her father's library. Her parents felt that her interest was inappropriate for a female and did all they could to discourage her.

She began studying at night to escape them, but they went to such measures as taking away her clothes and depriving her of heat and light to make her stay in her bed. Sophie's parents' efforts failed. She would wrap herself in quilts and use candles she had hidden in order to study at night.

Finally her parents realized that Sophie's passion for mathematics was "incurable," and they let her learn. Thus Sophie "spent the years of the French Revolution studying differential calculus.

Emmy Noether made many contributions to the field of mathematics. She spent her time studying abstract algebra, with special attention to rings, groups, and fields. Because of her unique look on topics, she was able to see relationships that traditional algebra experts could not.

She published over 40 papers in her lifetime. She was also a teacher that was able to inspire her students to make their own contributions to the field of mathematics.

Pythagoras’ first pupil was acquired by bribery. The teacher paid his student three oboli for each lesson he attended and noticed that as the weeks passed the boy's initial reluctance to learn was transformed into an enthusiasm for knowledge.

To test his pupil Pythagoras pretended that he could no longer afford to pay the student, claiming that the lessons would have to stop. The boy promptly offered to pay for his education rather than have it ended. The pupil had become Pythagoras’ first disciple.

"Many who have never had occasion to learn what mathematics is confuse it with arithmetic, and consider it a dry and arid science. In reality, however, it is the science which demands the utmost imagination [which is more than just making things up] ..... It seems to me that the poet must see what others do not see, must look deeper than others look. And the mathematician must do the same thing. As for myself, all my life I have been unable to decide for which I had the greater inclination, mathematics or literature."

Reference

• Costa, A. and Kallick, B. (2000) Habits of Mind. A Developmental Series. Alexandria, VA: Association for Supervision and Curriculum Development