# Μαθηματικοί και άλλοι

## 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…

## Τρίτη, 23 Μαΐου 2017

## Τρίτη, 9 Μαΐου 2017

## Κυριακή, 2 Απριλίου 2017

### How the French Mathematician Sophie Germain Paved the Way for Women in Science and Almost Saved Gauss’s Life – Brain Pickings

How the French Mathematician Sophie Germain Paved the Way for Women in Science and Almost Saved Gauss’s Life – Brain Pickings

A century after the trailblazing French mathematician Émilie du Châtelet popularized Newton and paved the path for women in science, and a few decades before the word “scientist” was coined for the Scottish mathematician Mary Somerville,

(April 1, 1776–June 27, 1831) gave herself an education using her

father’s books and became a brilliant mathematician, physicist, and

astronomer, who pioneered elasticity theory and made significant

contributions to number theory.

In lieu of a formal education, unavailable to women until more than a century later,

Germain supplemented her reading and her natural gift for science by

exchanging letters with some of the era’s most prominent mathematicians.

Among her famous correspondents was Carl Friedrich Gauss, considered by

many scholars the greatest mathematician who ever lived. Writing under

the male pseudonym M. LeBlanc — “fearing the ridicule attached to a

female scientist,” as she herself later explained — Germain began

sharing with Gauss some of her theorem proofs in response to his magnum

opus

Their correspondence began in 1804, at the peak of the French

occupation of Prussia. In 1806, Germain received news that Napoleon’s

troops were about to enter Gauss’s Prussian hometown of Brunswick.

Terrified that her faraway mentor might suffer the fate of Archimedes,

who was killed when Roman forces conquered Syracuse after a two-year

siege, she called on a family friend — the French military chief M.

Pernety — to find Gauss in Brunswick and ensure his safety. Pernety

tasked one of his battalion commanders with traveling two hundred miles

to the occupied Brunswick in order to carry out the rescue mission.

But Gauss, it turned out, was unscathed by the war. In a letter from

November 27 of 1806, included in the altogether fascinating

Upon receiving the comforting if somewhat comical news, Germain felt

obliged to write to Gauss and clear his confusion about his would-be

savior’s identity. After coming out as the woman behind the M. LeBlanc

persona in a letter from February 20 of 1807, she tells Gauss:

mathematical solutions Germain had shared with him — the same gift which

trailblazing feminist Margaret Fuller bestowed upon Thoreau,

which shaped his career. Although Gauss eventually disengaged from the

exchange, choosing to focus on his scientific work rather than on

correspondence, he remained an admirer of Germain’s genius. He advocated

for the University of Gottingen to award her a posthumous honorary

degree, for she had accomplished, despite being a woman and therefore

ineligible for actually attending the University, “something worthwhile

in the most rigorous and abstract of sciences.”

She was never awarded the degree.

After the end of their correspondence, Germain heard that the Paris Academy of Sciences had announced a

— a gold medal valued at 3,000 francs, roughly $600 then or about

$11,000 now — awarded to whoever could explain an exciting new physical

phenomenon scientists had found in the vibration of thin elastic

surfaces. The winning contestant would have to “give the mathematical

theory of the vibration of an elastic surface and to compare the theory

to experimental evidence.”

The problem appeared so difficult that it discouraged all other

mathematicians except Germain and the esteemed Denis Poisson from

tackling it. But Poisson was elected to the Academy shortly after the

award was announced and therefore had to withdraw from competing. Only

Germain remained willing to brave the problem. She began work on it in

1809 and submitted her paper in the autumn of 1811. Despite being the

only entrant, she lost — the jurors ruled that her proofs were

unconvincing.

Germain persisted — because no solution had been accepted, the

Academy extended the competition by two years, and she submitted a new

paper, anonymously, in 1813. It was again rejected. She decided to try a

third time and shared her thinking with Poisson, hoping he would

contribute some useful insight. Instead, he borrowed heavily from her

ideas and published his own work on elasticity, giving Germain no

credit. Since he was the editor of the Academy’s journal, his paper was

accepted and printed in 1814.

Still, Germain persisted. On January 8, 1816, she submitted a third

paper under her own name. Her solution was still imperfect, but the

jurors decided that it was as good as it gets given the complexity of

the problem and awarded her the prize, which made her the first woman to

win an accolade from the Paris Academy of Sciences.

But even with the prize in tow, Germain was not allowed to attend

lectures at the Academy — the only women permitted to audit were the

wives of members. She decided to self-publish her winning essay, in

large part in order to expose Poisson’s theft and point out errors in

his proof. She went on to do foundational mathematical work on

elasticity, as well as work in philosophy and psychology a century

before the latter was a formal discipline. Like Rachel Carson,

Germain continued to work as she was dying of breast cancer. A paper

she published shortly before her terminal diagnosis precipitated the

discovery the laws of movement and equilibrium of elastic solids.

Her unusual life and enduring scientific legacy are discussed in great detail in the biography

### By Maria Popova

A century after the trailblazing French mathematician Émilie du Châtelet popularized Newton and paved the path for women in science, and a few decades before the word “scientist” was coined for the Scottish mathematician Mary Somerville,

**Sophie Germain**

(April 1, 1776–June 27, 1831) gave herself an education using her

father’s books and became a brilliant mathematician, physicist, and

astronomer, who pioneered elasticity theory and made significant

contributions to number theory.

In lieu of a formal education, unavailable to women until more than a century later,

Germain supplemented her reading and her natural gift for science by

exchanging letters with some of the era’s most prominent mathematicians.

Among her famous correspondents was Carl Friedrich Gauss, considered by

many scholars the greatest mathematician who ever lived. Writing under

the male pseudonym M. LeBlanc — “fearing the ridicule attached to a

female scientist,” as she herself later explained — Germain began

sharing with Gauss some of her theorem proofs in response to his magnum

opus

*Disquisitiones Arithmeticae*.

Their correspondence began in 1804, at the peak of the French

occupation of Prussia. In 1806, Germain received news that Napoleon’s

troops were about to enter Gauss’s Prussian hometown of Brunswick.

Terrified that her faraway mentor might suffer the fate of Archimedes,

who was killed when Roman forces conquered Syracuse after a two-year

siege, she called on a family friend — the French military chief M.

Pernety — to find Gauss in Brunswick and ensure his safety. Pernety

tasked one of his battalion commanders with traveling two hundred miles

to the occupied Brunswick in order to carry out the rescue mission.

But Gauss, it turned out, was unscathed by the war. In a letter from

November 27 of 1806, included in the altogether fascinating

**(**

*Sophie Germain: An Essay in the History of the Theory of Elasticity**public library*), the somewhat irate battalion commander reports to his chief:

Just arrived in this town and have bruised myself with

your errand. I have asked several persons for the address of Gauss, at

whose residence I was to gather some news on your and Sophie Germain’s

behalf. M. Gauss replied that he did not have the honor of knowing you

or Mlle. Germain… After I had spoken of the different points contained

in your order, he seemed a little confused and asked me to convey his

thanks for your consideration on his behalf.

Upon receiving the comforting if somewhat comical news, Germain felt

obliged to write to Gauss and clear his confusion about his would-be

savior’s identity. After coming out as the woman behind the M. LeBlanc

persona in a letter from February 20 of 1807, she tells Gauss:

The appreciation I owe you for the encouragement you haveGauss responds a few weeks later:

given me, in showing me that you count me among the lovers of sublime

arithmetic whose mysteries you have developed, was my particular

motivation for finding out news of you at a time when the troubles of

the war caused me to fear for your safety; and I have learned with

complete satisfaction that you have remained in your house as

undisturbed as circumstances would permit. I hope, however, that these

events will not keep you too long from your astronomical and especially

your arithmetical researches, because this part of science has a

particular attraction for me, and I always admire with new pleasure the

linkages between truths exposed in your book.

Mademoiselle,With this, Gauss extends the gift of constructive criticism on some

Your letter … was for me the source of as much pleasure as surprise.

How pleasant and heartwarming to acquire a friend so flattering and

precious. The lively interest that you have taken in me during this war

deserves the most sincere appreciation. Your letter to General Pernety

would have been most useful to me, if I had needed special protection on

the part of the French government.

Happily, the events and consequences of war have not affected me so

much up until now, although I am convinced that they will have a large

influence on the future course of my life. But how I can describe my

astonishment and admiration on seeing my esteemed correspondent M.

LeBlanc metamorphosed into this celebrated person, yielding a copy so

brilliant it is hard to believe? The taste for the abstract sciences in

general and, above all, for the mysteries of numbers, is very rare: this

is not surprising, since the charms of this sublime science in all

their beauty reveal themselves only to those who have the courage to

fathom them. But when a woman, because of her sex, our customs and

prejudices, encounters infinitely more obstacles than men in

familiarizing herself with their knotty problems, yet overcomes these

fetters and penetrates that which is most hidden, she doubtless has the

most noble courage, extraordinary talent, and superior genius. Nothing

could prove me in a more flattering and less equivocal way that the

attractions of that science, which have added so much joy to my life,

are not chimerical, than the favor with which you have honored it.

The scientific notes which your letters are so richly filled have

given me a thousand pleasures. I have studied them with attention, and I

admire the ease with which you penetrate all branches of arithmetic,

and the wisdom with which you generalize and perfect. I ask you to take

it as proof of my attention if I dare to add a remark to your last

letter.

mathematical solutions Germain had shared with him — the same gift which

trailblazing feminist Margaret Fuller bestowed upon Thoreau,

which shaped his career. Although Gauss eventually disengaged from the

exchange, choosing to focus on his scientific work rather than on

correspondence, he remained an admirer of Germain’s genius. He advocated

for the University of Gottingen to award her a posthumous honorary

degree, for she had accomplished, despite being a woman and therefore

ineligible for actually attending the University, “something worthwhile

in the most rigorous and abstract of sciences.”

She was never awarded the degree.

After the end of their correspondence, Germain heard that the Paris Academy of Sciences had announced a

*prix extraordinaire*

— a gold medal valued at 3,000 francs, roughly $600 then or about

$11,000 now — awarded to whoever could explain an exciting new physical

phenomenon scientists had found in the vibration of thin elastic

surfaces. The winning contestant would have to “give the mathematical

theory of the vibration of an elastic surface and to compare the theory

to experimental evidence.”

The problem appeared so difficult that it discouraged all other

mathematicians except Germain and the esteemed Denis Poisson from

tackling it. But Poisson was elected to the Academy shortly after the

award was announced and therefore had to withdraw from competing. Only

Germain remained willing to brave the problem. She began work on it in

1809 and submitted her paper in the autumn of 1811. Despite being the

only entrant, she lost — the jurors ruled that her proofs were

unconvincing.

Germain persisted — because no solution had been accepted, the

Academy extended the competition by two years, and she submitted a new

paper, anonymously, in 1813. It was again rejected. She decided to try a

third time and shared her thinking with Poisson, hoping he would

contribute some useful insight. Instead, he borrowed heavily from her

ideas and published his own work on elasticity, giving Germain no

credit. Since he was the editor of the Academy’s journal, his paper was

accepted and printed in 1814.

Still, Germain persisted. On January 8, 1816, she submitted a third

paper under her own name. Her solution was still imperfect, but the

jurors decided that it was as good as it gets given the complexity of

the problem and awarded her the prize, which made her the first woman to

win an accolade from the Paris Academy of Sciences.

But even with the prize in tow, Germain was not allowed to attend

lectures at the Academy — the only women permitted to audit were the

wives of members. She decided to self-publish her winning essay, in

large part in order to expose Poisson’s theft and point out errors in

his proof. She went on to do foundational mathematical work on

elasticity, as well as work in philosophy and psychology a century

before the latter was a formal discipline. Like Rachel Carson,

Germain continued to work as she was dying of breast cancer. A paper

she published shortly before her terminal diagnosis precipitated the

discovery the laws of movement and equilibrium of elastic solids.

Her unusual life and enduring scientific legacy are discussed in great detail in the biography

**. Complement it with the stories of how Ada Lovelace became the world’s first computer programmer, how physicist Lise Meitner discovered nuclear fission, was denied the Nobel Prize, but led the way for women in science anyway, and how Harvard’s unsung 19th-century female astronomers revolutionized our understanding of the universe decades before women could vote.**

*Sophie Germain*
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