The Joy of Maths

'The true spirit of delight

is to be found in mathematics

as surely as in poetry'

Bertrand Russell

If you do not like maths, the reason is that you have not put enough interest to discover them or because your teacher has failed to open up your eyes to them. It is true that mathematics have not the social presence that corresponds to their contribution to civilization, but the queen of sciences has an infinite beauty. I will try to fight against some topics:

Mathematics are useless

It usually happens that the best professionals in most sciences are mathematicians. It is said that the First World War was the war of the chemists (million of casualties by mustard gas), WWII was the war of the physics (atomic bombs) and the third one will be the war of the mathematicians.

For example, thanks to its knowledge we can prevent that politicians and media can cheat us with statistics:

In the debates of the last presidential elections, the opponent-leader showed the graph unemployment versus time taking very few units on the `y´ axis, so that we could see an exaggerated increase in unemployment. On the other hand, the ruling political leader used the same data with a large number of units on the `y' axis, so that the increase in unemployment did not seem significant.

If a newspaper says that homicides have increased by 60%, it will be more shocking than if it says that last year 5 people were killed and this year 8 were killed. We saw another example of deception in the inconsistency between the Consumer Price Index presented by the government and the popular sensitivity to the impact on prices with the introduction of the euro. The media often offer a percentage without reference; unemployment can be said to have dropped from 8.1% to 7.9%, but they do not say that the confidence interval is 1% (so that unemployment could even have increased).

Anyway... mathematics will always be useful to think and...

Once upon a time there was a young man who decided to learn how to hunt dragons. He spent five years studying everything related to dragons (to capture them). He analysed all their habits: where they used to eat, how they reproduced, in what places they preferred to sleep... When he finished his long study and was considered an expert on the dragon hunt, he realized that there were no dragons. Then he dedicated himself to teach how to hunt dragons.

"Mathematics cannot take us out of the labyrinth, but they can tell us at what point of it we are." Galileo.

Mathematics are boring

Only a few things are able to call the attention of human beings as much as mathematical puzzles do:

• A snail is next to a 30-metre-high wall. During the day, it goes up three metres and at night it sleeps, so it slides two metres down. How many days will it need to climb the wall up?

• We have two wicks. They are unbreakable. We know that each one takes an hour to get completely burnt. How would you calculate 45 minutes of time?

• In a race of 100 metres, a runner beats his opponent by 10 metres. Then they decide to run again, but this time the fastest one starts 10 meters behind. If everyone runs at the same speed as before, who wins now?

• We are on an island where there are two kinds of Indians. Some Indians always lie and some always tell the truth. We are going to the village and there is a crossroad with two roads. We find one Indian (we don't know if he is a liar or a sincere). What question do you have to ask to know which of the two roads would lead you to the village?

• You must touch all the points with four straight lines. It is not allowed to lift the pencil from the paper.

• There is a trielo: Mr. Black hits 1 out of 3 shots , Mr. Gray 2 out of 3 and Mr. White does not fail. They shoot in reverse order of their aim. What would you do if you were Mr. Black?

• What number comes next in the series ? 

And paradoxes...

• In one village, there is only one barber. He cuts the hair only to those who are not able to cut it by themselves. Who cuts the barber's hair?

• If all roads lead to Rome, how do I get out of Rome?

• I
 always lie.

• This sentence is false.

• My laziness leaves me no time to do anything.

And the mysteries of nature related to mathematics :

Kepler said 'God is a great mathematician'. Both Π and Φ are peculiar numbers. They appear unexpectedly in the context of science. It could be thought that our universe was designed from a few key numbers. Φ seems to be one of the structural keys. It defines the arrangement of the petals of the rose, the dimensions of the works of Le Corbusier, it is among scores of Debussi and in the Mona Lisa, it defines the dynamics of black holes and the microscopic structure of some crystals. Such timeless and universal coincidences cannot be the result of randomness. In several periods of history, it has been considered sacred. Man has discovered Φ in nature and has used it for aesthetic creation. The logarithmic spiral, which is built from Φ, is common in hurricanes, molluscs, horns and even galaxies. It was widely known in Classical Greece and it was used in the architectural and sculptural designs. It has also inspired artists like Wagner, Dali and Picasso.

The spiral structure is found everywhere in humans. The spiral staircase in the ear, the heart is a spiral formation that facilitates muscle contraction. In the umbilical cord, arteries have a spiral twist to the left and also in the gallbladder. The spiral shape of the seventh rib helps us to breath because it raises the chest. The right humerus have a spiral twist to the right, and the left, to the left. Teeth, nails... The penis of the pigs has a helical structure to ensure penetration and to fix sperm, the digestive spirals valves of the shark allow it to slow the absorption of food (they have inspired engineers). The periodic table is organized in a spiral from the most simple element (hydrogen).

The rare and significant numbers are those whose divisors add up to exactly their value, and those are called perfect. The 6 has divisors 1, 2 and 3, so it is a perfect number because 1 +2 +3 = 6. The perfect number that follows is 28. The perfection of 6 and 28 has been recognized by many cultures. The moon's cycle is 28 days, God created the world in 6...

The lives of the mathematicians are serious

Alfred Nobel felt guilty for having invented dynamite (it has been used in so many wars), so he decided to create the prizes that bear his name. There are a lot of disciplines in these prizes, but there is not a nobel prize for maths. There is a legend that explains why. At that time, one of the most important candidates to receive this prize was the Sweddish Gösta Mittag-Leffler. But, it seems that he had an affair with Nobel's wife. So he decided not to create a prize for this discipline.

Ramanujan was a poor Indian boy who, by chance, found a book of maths. He learned by himself. Later, he was able to develop theorems and proofs that had escaped to the Western mathematicians. He wrote to Hardy (an important English mathematician) who was deeply impressed with his knowledge. Hardy took Ramanujan to England to work with him. Unfortunately, English winters were too much for him. He contracted tuberculosis. Hardy went to visit him to the hospital. He travelled by taxi. «I think my cab number was 1729. It seems a rather dull number» . And Ramanujan replied: «No, Hardy! No, Hardy! It is a very interesting number because it is the smallest number that can be expressed as a sum of two cubes in two different ways». Ramanujan died at 33.

Galois was a mathematical genius of dissolute life: jail, alcohol, prostitutes... At the age of twenty, he was involved in a problem with women. He was challenged to a duel by the military fencing champion. The night before of the duel, aware of his few chances, he tried desperately to record all his mathematic findings, but he did not have enough time. On the right side of his notes, he wrote: «Je n'ai pas le temps». The next day he was defeated and he died.

Fermat, the best amateur mathematician in all history, had a hard job. He was a member of the Inquisition and condemned people to die at the stake. He had a hobby: mathematics. He wrote down in a notebook that he had found a wonderful test to prove a theorem, but he could not write that test in that space because it was too small. This statement would haunt generations of mathematicians. Hardy, another great mathematician, used to say every time he was going to travel in a ship that he had the solution of another famous theorem. He was afraid of dying in the sea, but he believed that God would never let him drown because, in that case, the mathematicians would be harassed by a second and terrible ghost.

Euler wrote mathematical papers without wasting a second of his life. He used to do it and at the same time he could cradle his child, he ate soup with one hand and he wrote with the other... When he lost an eye, he exclaimed: «This is good for me: now I will be less distracted». In the court of Catherine the Great they mocked him because he believed in God and was very rustic. One day, he stood before Diderot with a formula that proved the existence of God: «Sir, (a + bn ) / n = x and therefore God exists. Refute it!»

Alan Turing played a very important role in the defeat of Germany in World War II. He discovered the secret code by which they communicated. A few years later, the British government convicted him for being homosexual. He was condemned and he had to inject hormones to himself. Later, he decided to commit suicide. Quietly, he ate an apple where he had injected cyanide.

Misako Suzuki wrote a suicide note where he described methodically things like the books he had to return to the library and to his friends, he explained which lesson he had come to in his course in calculus and algebra for the substitute teacher to continue from there, and ended up apologizing to his colleagues for any inconvenience that his act would cause to them.

Norbert Wiener was the typical absent-minded mathematician. His wife repeated him many times that they would move that day. That morning, before going to work at university, he wrote on a piece of paper the new address. But he used the paper to solve an issue to a student. In the afternoon, Norbert returned to his old home. He had forgotten the move. Then he remembered, but he did not know the new address. He went out and saw a girl worried approaching: «Excuse me, but I lived here before and I cannot remember...». «Do not worry, dad, mom sent me to pick you up».

Taniyama was the perfect example of the absent-minded genius and it was reflected in his appearance. He was unable to make a knot. Therefore, he decided that instead of tying the laces of his shoes a dozen times a day, he would never tie them. He always wore the same green suit with a strange peculiar metallic glow. The rest of his family had rejected it because it was made of a very striking fabric.

An astronomer, a physicist and a mathematician were having holidays in Scotland. Looking out of the train window, they distinguished a black sheep in the middle of a meadow. «How interesting, the sheep in Scotland are black!» The astronomer said. The physicist answered: «No, no, some Scottish sheep are black». The mathematician looked pleadingly at the sky and then mouthed: «In Scotland, there is at least one field that has at least one sheep with at least one of its sides black».