Ivory-Handled

Wild Geese

You do not have to be good.

You do not have to walk on your knees

for a hundred miles through the desert repenting.

You only have to let the soft animal of your body

love what it loves.

Tell me about despair, yours, and I will tell you mine.

Meanwhile the world goes on.

Meanwhile the sun and the clear pebbles of the rain

are moving across the landscapes,

over the prairies and the deep trees,

the mountains and the rivers.

Meanwhile the wild geese, high in the clean blue air,

are heading home again.

Whoever you are, no matter how lonely,

the world offers itself to your imagination,

calls to you like the wild geese, harsh and exciting -

over and over announcing your place

in the family of things.

Mary Oliver, 1935-2019

You will hear thunder and remember me

Услышишь гром и вспомнишь обо мне,

Подумаешь: она грозы желала...

Полоска неба будет твердо-алой,

А сердце будет как тогда - в огне.

Случится это в тот московский день,

Когда я город навсегда покину

И устремлюсь к желанному притину,

Свою меж вас еще оставив тень.

Anna Akhmatova, 1889-1966

Fig Tree

I saw my life branching out before me like the green fig tree in the story.

From the tip of every branch, like a fat purple fig, a wonderful future beckoned and winked.

One fig was a husband and a happy home and children,

and another fig was a famous poet

and another fig was a brilliant professor,

and another fig was Ee Gee, the amazing editor,

and another fig was Europe and Africa and South America,

and another fig was Constantin and Socrates and Attila and a pack of other lovers with queer names and offbeat professions,

and another fig was an Olympic lady crew champion,

and beyond and above these figs were many more figs I couldn't quite make out.

I saw myself sitting in the crotch of this fig tree, starving to death, just because I couldn't make up my mind which of the figs I would choose.

I wanted each and every one of them, but choosing one meant losing all the rest, and, as I sat there, unable to decide, the figs began to wrinkle and go black, and, one by one, they plopped to the ground at my feet.

Sylvia Plath, 1932-1963

Thread

There's a thread you follow.

It goes among things that change.

But it doesn't change.

People wonder about what you are pursuing.

You have to explain about the thread.

But it is hard for others to see.

While you hold it you can't get lost.

Tragedies happen; people get hurt or die; and you suffer and get old.

Nothing you do can stop time's unfolding.

You don't ever let go of the thread.

William Stafford, 1914-1993

Twice-Told Tales

Mostly, we authors must repeat ourselves-that's the truth. We have two or three great and moving experiences in our lives-experiences so great and moving that it doesn't seem at the time that anyone else has been so caught up and pounded and dazzled and astonished and beaten and broken and rescued and illuminated and rewarded and humbled in just that way ever before.

Then we learn our trade, well or less well, and we tell our two or three stories-each time in a new disguise-maybe ten times, maybe a hundred, as long as people will listen.

If this were otherwise, one would have to confess to having no individuality at all. And each time I honestly believe that, because I have found a new background and a novel twist, I have really got away from the two or three fundamental tales I have to tell. But it is rather like Ed Wynn's famous anecdote about the painter of boats who was begged to paint some ancestors for a client. The bargain was arranged, but with the painter's final warning that the ancestors would all turn out to look like boats.

When I face the fact that all my stories are going to have a certain family resemblance, I am taking a step toward avoiding false starts. If a friend says he's got a story for me and launches into a tale of being robbed by Brazilian pirates in a swaying straw hut on the edge of a smoking volcano in the Andes, with his fiancee bound and gagged on the roof, I can well believe there were various human emotions involved; but having successfully avoided pirates, volcanoes and fiancees who get themselves bound and gagged on roofs, I can't feel them. Whether it's something that happened twenty years ago or only yesterday, I must start out with an emotion-one that's close to me and that I can understand.

Francis Scott Key Fitzgerald, 1896-1940

In a word, the calculations are impractical.

Si maintenant vous me donnez une équation que vous aurez choisie à votre gré et que vous désirez connaître si elle est ou non soluble par radicaux, je n'aurais rien à y faire que de vous indiquer le moyen de répondre à votre question, sans vouloir charger ni moi ni personne de la faire. En un mot les calculs sont impracticables.

Évariste Galois, 1811-1832

from Mémoire sur les conditions de résolubilité des équations par radicaux.
Copyright © 1830 by Journal de mathématiques pures et appliquées, 417-433.
All rights reserved.

You stop thinking about the meaning.

Algebra is the offer made by the devil to the mathematician.

The devil says : "I will give you this powerful machine,

and it will answer any question you like.

All you need to do is give me your soul :

give up geometry and you will have this marvellous machine."

... the danger to our soul is there,

because when you pass over into algebraic calculation, essentially you stop thinking:

you stop thinking geometrically, you stop thinking about the meaning.

Sir Michael Francis Atiyah, 1929-2019

Algebra with a vengeance

Here is algebra with a vengeance;

algebraic austerity could go no further.

"We have not tried to hide (says the author)

our partiality to the algebraic attitude...";

he has not indeed; and, if it were not for a few hints in the introduction and one casual remark at the end of Chapter IV,

one might never suspect him of having ever heard of

algebraic curves or of taking any interest in them.

Fields and only fields are the object of his study.

A field is given, or rather two fields :

one, the function-field R; the other, the field K of constants;

K is algebraically closed in R; and R is finitely generated

and of degree of transcendency 1 over K.

Everything must be "intrinsic,"

i.e. must be born from these by some standard operations.

André Weil, 1906-1998

from Review of Introduction to the theory of algebraic functions of one variable
by Claude Chevalley, Copyright © 1951 by American Mathematical Society,
All rights reserved.

An idea that is fully formed, fully understood

Mr. Saito, this isn't your typical corporate espionage.

You asked me for inception.

I do hope you understand the gravity of that request.

Now, the seed that we plant in this man's mind will grow into an idea.

This idea will define him.

It may come to change...

Well, it may come to change everything about him.

Christopher Nolan, 1970-

This will not suffice. Remember that.

A king may move a man, a father may claim a son,

but remember that even when those who move you be kings, or men of power,

your soul is in your keeping alone.

When you stand before God, you cannot say,

"But I was told by others to do thus," Or that,

"Virtue was not convenient at the time."

This will not suffice. Remember that.

King Baldwin IV, 1161-1185

What is Geometry?

The sight is the richest sensation humanity owns.

When we try to explain something, we often draw a figure to visualize the contents for an explanation.

The role of geometry in mathematics is not so much to give an answer to a problem, since providing an answer to a mathematical question by calculation etc., is usually the role of algebra.

The role of the geometer is to say what the answer (often a number) means.

Geometry in that sense is not so practical since the answer is given anyway.

However, humankind is unable to understand a complicated and chaotic calculation.

We need something-a notion, a concept, or a vision-to understand why we calculate that way.

That is, I think, the role of geometry in mathematics.

Figures appearing in modern mathematics are usually beyond the ability of one's eyesight.

Nevertheless, we visualize important concepts too complicated to understand without geometric meaning.

It is amazing how much we (people studying modern mathematics) came far away from our physical eyesight, free from restriction of the human body, as does modern science and technology.

The frontier of science and technology requires reaching beyond the border of our imagination, which, I believe, modern geometry can provide.

Kenji Fukaya, 1959-

Builder of Cathedrals

Grothendieck a profondément marqué l'histoire des mathématiques.

Salué comme l'un des mathématiciens les plus influents du XXe siècle, il se considérait lui comme un < bâtisseur de cathédrales >.

Son ambitieux programme de fusion entre l'arithmétique, la géométrie algébrique et la topologie continue de structurer les mathématiques contemporaines.

Alexander Grothendieck, 1928-2014

Child's Privilege

Discovery is a child's privilege.

I mean the small child, the child who is not afraid to be wrong, to look silly, to not be serious, and to act differently from everyone else.

He is also not afraid that the things he is interested in are in bad taste or turn out to be different from his expectations, from what they should be, or rather he is not afraid of what they actually are.

He ignores the silent and flawless consensus that is part of the air we breathe - the consensus of all the people who are, or are reputed to be, reasonable.

Alexander Grothendieck, 1928-2014

You see only fragments

A good hunter always climbs the highest dune before his hunt.

He needs to see, as far as he can see.

You need to see.

Frank Herbert, 1920-1986

Рукописи не горят.

О чем, о чем? О ком? — заговорил Воланд, перестав смеяться.

Вот теперь? Это потрясающе! И вы не могли найти другой темы?

Дайте-ка посмотреть, — Воланд протянул руку ладонью кверху.

Я, к сожалению, не могу этого сделать, — ответил мастер, — потому что я сжег его в печке.

Простите, не поверю, — ответил Воланд, — этого быть не может.

Рукописи не горят. — Он повернулся к Бегемоту и сказал: — Ну-ка, Бегемот, дай сюда роман.

Кот моментально вскочил со стула, и все увидели, что он сидел на толстой пачке рукописей.

Mikhail Afanasyevich Bulgakov, 1891-1940

Incommensurable

Even if you could get two such rivals to sit still in

room long enough to listen to one another.

They'd both be trying to overcome their ingrained

resistance to the other's ideas about reality.

In short, then, it doesn't work.

Thomas Kuhn