Anyway... mathematics
will always be useful to think and...
Only a few things
are able to call the attention of human beings as much as
mathematical puzzles do:
- 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?
- 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».
