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# Μαθηματικοί και άλλοι

## Σάββατο, 28 Απριλίου 2018

## Σάββατο, 23 Σεπτεμβρίου 2017

### Euler, the Beethoven of Mathematics - OpenMind

Euler, the Beethoven of Mathematics - OpenMind

In the educational studies of every scientist, there are a

few individual names that seem to emerge from course to course. But

above those of

one name that probably surpasses them all as the first to appear—once

children master the four basic arithmetic operations, their approach to

logic begins with set theory and its Venn diagrams. But these are but

one particular case of those invented by a mathematician whose name

designates constants, functions, equations, laws, theorems, and almost

any other type of mathematical entity: Euler.

The Swiss

September 1783) was one of the greatest intellectual supermen in the

history of mankind. The numbers serve to demonstrate his incredible

mental superpowers—over his 76 years of life he published more than 800

works, totalling some 30,000 pages. It has been estimated that

But even the numbers fall short in describing a prodigious mind whose

talent manifested itself in some anecdotes. Perhaps the best known is

that he was able to recite Virgil’s

anticipate our current machines—his computing power was also superhuman.

He spent the last 17 years of his life almost totally

due to a cataract in his left eye and a degenerative lesion in the

right one, whose origin varies according to the versions. But if this

disease affected his output, it was only to increase it; “in this way I

will have fewer distractions,” he once said. At one stage he was writing

an average of one work a week and joked about his enormous production,

claiming that his pencil outperformed him in intelligence. Like a

Beethoven unable to hear his music,

but in his head he counted tables of lunar movements with such clarity

that an apprentice tailor could serve as a secretary without the need

for mathematical training.

On one occasion, two students disagreed over the result of the sum of

17 terms in a series, as the results of the two operations differed in

the fiftieth decimal place. Without a pencil or slate, Euler computed

the correct result in his mind in a few seconds. The anecdote was

referred to by his contemporary and colleague, the Frenchman Nicolas de

Condorcet, who at Euler’s death wrote a lengthy eulogy to “one of the

greatest and most extraordinary men that Nature ever produced.”

Curiously, that genius might have been lost to mathematics if Euler

had followed in the footsteps of his father to serve as pastor of the

Reformed Church, as planned. The advice of the mathematician Johann

Bernoulli, a friend of the family, was key in directing Euler’s

footsteps definitively towards mathematics and science.

Precocious in his studies and in his career, he soon began to stand out, which led him to travel

The most prolific mathematician in history was not only the main

founder of what we now know as classical mathematics, exploring a wide

variety of fields and introducing much of the notation used today, but

he also explored other disciplines such as astronomy, optics,

engineering, magnetism, ballistics, navigation, shipbuilding, philosophy

and music. It is said that his musical theory did not triumph because

it was too advanced in mathematical computations for musicians, and too

musical for mathematicians.

dedicated himself professionally to teaching. Proof of this is the

publication that was a best seller in its time—

a work in three volumes that began to be published in 1768 and that

collects the letters written by Euler to his pupil, Friederike Charlotte

of Brandenburg-Schwedt, princess of Anhalt-Dessau and niece of the King

of Prussia Federico the Great.

In fact, Euler’s correspondence is also a treasure trove—the famous

Goldbach Conjecture, one of the oldest yet unsolved mathematical

problems, first appeared in 1742 in a letter addressed to Euler by the

German mathematician Christian Goldbach, his friend since they met each

other at the St. Petersburg Academy.

It was in this Russian city that, on September 18, 1783, Euler was

calculating the ascent of hot air balloons—which at that time were

causing a furore in Europe—and argued over dinner with his colleague

Anders Johan Lexell about the orbit of the newly discovered planet

Uranus. As Condorcet wrote, it was later, while drinking tea and playing

with his grandson, when “all of a sudden the pipe that he was smoking

slipped from his hand and he ceased to calculate and live.”

# Euler, the Beethoven of Mathematics

- 18 September 2017
- Mathematics, Science

few individual names that seem to emerge from course to course. But

above those of

**Newton, Galileo, or Einstein**, there isone name that probably surpasses them all as the first to appear—once

children master the four basic arithmetic operations, their approach to

logic begins with set theory and its Venn diagrams. But these are but

one particular case of those invented by a mathematician whose name

designates constants, functions, equations, laws, theorems, and almost

any other type of mathematical entity: Euler.

The Swiss

**Leonhard Euler**(15 April 1707 – 18September 1783) was one of the greatest intellectual supermen in the

history of mankind. The numbers serve to demonstrate his incredible

mental superpowers—over his 76 years of life he published more than 800

works, totalling some 30,000 pages. It has been estimated that

**almost a third of all the science and mathematics written in the eighteenth century bears his signature.**After his death, his obituary required 56 pages to list all his publications.But even the numbers fall short in describing a prodigious mind whose

talent manifested itself in some anecdotes. Perhaps the best known is

that he was able to recite Virgil’s

*Aeneid*from beginning to end, detailing in what line every page of the edition he owned began and ended.## Superhuman computing power

Memory was not the only ability in which his brain seemed toanticipate our current machines—his computing power was also superhuman.

He spent the last 17 years of his life almost totally

**blind**,due to a cataract in his left eye and a degenerative lesion in the

right one, whose origin varies according to the versions. But if this

disease affected his output, it was only to increase it; “in this way I

will have fewer distractions,” he once said. At one stage he was writing

an average of one work a week and joked about his enormous production,

claiming that his pencil outperformed him in intelligence. Like a

Beethoven unable to hear his music,

**Euler could hardly see his calculations**,but in his head he counted tables of lunar movements with such clarity

that an apprentice tailor could serve as a secretary without the need

for mathematical training.

On one occasion, two students disagreed over the result of the sum of

17 terms in a series, as the results of the two operations differed in

the fiftieth decimal place. Without a pencil or slate, Euler computed

the correct result in his mind in a few seconds. The anecdote was

referred to by his contemporary and colleague, the Frenchman Nicolas de

Condorcet, who at Euler’s death wrote a lengthy eulogy to “one of the

greatest and most extraordinary men that Nature ever produced.”

Curiously, that genius might have been lost to mathematics if Euler

had followed in the footsteps of his father to serve as pastor of the

Reformed Church, as planned. The advice of the mathematician Johann

Bernoulli, a friend of the family, was key in directing Euler’s

footsteps definitively towards mathematics and science.

Precocious in his studies and in his career, he soon began to stand out, which led him to travel

**to occupy prestigious positions in the Academies of Saint Petersburg and Berlin.**The most prolific mathematician in history was not only the main

founder of what we now know as classical mathematics, exploring a wide

variety of fields and introducing much of the notation used today, but

he also explored other disciplines such as astronomy, optics,

engineering, magnetism, ballistics, navigation, shipbuilding, philosophy

and music. It is said that his musical theory did not triumph because

it was too advanced in mathematical computations for musicians, and too

musical for mathematicians.

## A Gift for Dissemination

Euler was also endowed with a gift for dissemination, without havingdedicated himself professionally to teaching. Proof of this is the

publication that was a best seller in its time—

*Letters to a German Princess, On Different Subjects in Physics and of Philosophy*,a work in three volumes that began to be published in 1768 and that

collects the letters written by Euler to his pupil, Friederike Charlotte

of Brandenburg-Schwedt, princess of Anhalt-Dessau and niece of the King

of Prussia Federico the Great.

In fact, Euler’s correspondence is also a treasure trove—the famous

Goldbach Conjecture, one of the oldest yet unsolved mathematical

problems, first appeared in 1742 in a letter addressed to Euler by the

German mathematician Christian Goldbach, his friend since they met each

other at the St. Petersburg Academy.

It was in this Russian city that, on September 18, 1783, Euler was

calculating the ascent of hot air balloons—which at that time were

causing a furore in Europe—and argued over dinner with his colleague

Anders Johan Lexell about the orbit of the newly discovered planet

Uranus. As Condorcet wrote, it was later, while drinking tea and playing

with his grandson, when “all of a sudden the pipe that he was smoking

slipped from his hand and he ceased to calculate and live.”

**Javier Yanes**## Τετάρτη, 23 Αυγούστου 2017

## Παρασκευή, 7 Ιουλίου 2017

### Women in Maths - Δημοσιεύσεις

Women in Maths - Δημοσιεύσεις

Claire

Voisin (Professor at Collège de France, member of the

Académie des Sciences, Paris, recipient of CNRS Gold medal

2016):``... I would not say that I chose math as a career; I got

interested, so I started, then I continued and it was a sort of

addiction. I never really 'thought' of doing this, it's like

this was simply obvious and also the easiest way. How can I say;

once I started seriously doing maths, there was no alternative. I

got used to it, I had to do this. Since I started, I never wanted to

do something different. I would even say I find it more and more

interesting over time...

The fact is that my family did

not care so much, because I come from a very large family: I have

eight sisters and three brothers. My parents were very happy if we

were independent and earned money. I left my family's home when I

was 17, I got a scholarship and, starting from this point, I

never had to ask money from my parents. I should say that when I

was a child I had some contacts with maths, especially geometry, but

my parents did not care so much about our future careers; if I

had been a teacher in high school they would have been happy.

...What is hard are the moments when you lack inspiration to formulate

new ideas, new problems. Also sometimes it happened that I did

some research which was unsuccessful. It is important to be able to stop

something which does not work, not to spend too much time and

energy on an idea that you drive by force. You need to change. I

always found travelling very useful for this, because if you are alone

you tend to stay stuck on a subject, while if you travel you

get some distance and you can try something new, a new subject,

your mind has a new drive, a new energy.

...I had excellent

working conditions, because I had no teaching, I could teach

only when I wanted to, and in high level courses. I had a CNRS

position, so I was able to work at home, no time and energy

wasted in public transportation. Life was made very easy by my CNRS

position; and you know the French system of child care, so I had no

excuse for not working full-time. I should mention that what made

my life so very easy is that my husband is also a

mathematician, so not only the every day schedule is much softer, but

we understood both that we needed time for us. At the weekends,

I used to work in the morning and he in the afternoon. That

was nice, we both agreed that we should do things this way.

...I

like very much the moment I start a new research, I like

very much the moment I have something in my mind: sometimes it

is barely an idea, sometimes it's just the beginning of

something. But there is this quality of the dream, and the fact

that your mind works alone, you do not need to force it.

I also

like to give talks; this is a bit different, but I like it very much. I

have to challenge myself to discuss, because I am what in

French we call ’introvertie’. There is a lot of introversion

in our work, because we are contemplating something. But there

is also a part of our work that is different, discussing,

giving talks, attending conferences, which is also nice. Still, for

me, the very nice part of my job is when I work on something new by

myself.

The bad part....there is some bad part, some

suffering, when you are trying to do something which is

difficult. There are some moments when you spend much energy,

and moments in which the dynamics of research is a little

lost. You don’t feel you are inside of mathematics. But I am afraid this

is especially bad for my family....''

This is a short extract from an interview with Claire by the EWM. For the full interview (worth reading!), please see

http://europeanwomeninmaths.org/…/newsletters/675/newslette…

Voisin (Professor at Collège de France, member of the

Académie des Sciences, Paris, recipient of CNRS Gold medal

2016):``... I would not say that I chose math as a career; I got

interested, so I started, then I continued and it was a sort of

addiction. I never really 'thought' of doing this, it's like

this was simply obvious and also the easiest way. How can I say;

once I started seriously doing maths, there was no alternative. I

got used to it, I had to do this. Since I started, I never wanted to

do something different. I would even say I find it more and more

interesting over time...

The fact is that my family did

not care so much, because I come from a very large family: I have

eight sisters and three brothers. My parents were very happy if we

were independent and earned money. I left my family's home when I

was 17, I got a scholarship and, starting from this point, I

never had to ask money from my parents. I should say that when I

was a child I had some contacts with maths, especially geometry, but

my parents did not care so much about our future careers; if I

had been a teacher in high school they would have been happy.

...What is hard are the moments when you lack inspiration to formulate

new ideas, new problems. Also sometimes it happened that I did

some research which was unsuccessful. It is important to be able to stop

something which does not work, not to spend too much time and

energy on an idea that you drive by force. You need to change. I

always found travelling very useful for this, because if you are alone

you tend to stay stuck on a subject, while if you travel you

get some distance and you can try something new, a new subject,

your mind has a new drive, a new energy.

...I had excellent

working conditions, because I had no teaching, I could teach

only when I wanted to, and in high level courses. I had a CNRS

position, so I was able to work at home, no time and energy

wasted in public transportation. Life was made very easy by my CNRS

position; and you know the French system of child care, so I had no

excuse for not working full-time. I should mention that what made

my life so very easy is that my husband is also a

mathematician, so not only the every day schedule is much softer, but

we understood both that we needed time for us. At the weekends,

I used to work in the morning and he in the afternoon. That

was nice, we both agreed that we should do things this way.

...I

like very much the moment I start a new research, I like

very much the moment I have something in my mind: sometimes it

is barely an idea, sometimes it's just the beginning of

something. But there is this quality of the dream, and the fact

that your mind works alone, you do not need to force it.

I also

like to give talks; this is a bit different, but I like it very much. I

have to challenge myself to discuss, because I am what in

French we call ’introvertie’. There is a lot of introversion

in our work, because we are contemplating something. But there

is also a part of our work that is different, discussing,

giving talks, attending conferences, which is also nice. Still, for

me, the very nice part of my job is when I work on something new by

myself.

The bad part....there is some bad part, some

suffering, when you are trying to do something which is

difficult. There are some moments when you spend much energy,

and moments in which the dynamics of research is a little

lost. You don’t feel you are inside of mathematics. But I am afraid this

is especially bad for my family....''

This is a short extract from an interview with Claire by the EWM. For the full interview (worth reading!), please see

http://europeanwomeninmaths.org/…/newsletters/675/newslette…

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