Gh Quotes

The world's continual breathing is what we hear and call silence.

And I want to be held down. I don't know what to do with the horrifying freedom that can destroy me.

It is not worth an intelligent man's time to be in the majority. By definition, there are already enough people to do that.

Angel is right,"said Dr. G-H quickly. "This is my clumsy way of demonstrating." "Demonstrating what?" I was barely able to keep a snarl out of my voice. "How to get yourself beat up in one easy step?

What I want is to live of that initial and primordial something that was what made some things reach the point of aspiring to be human.

Reality prior to my language exists as an unthinkable thought. . . . life precedes love, bodily matter precedes the body, and one day in its turn language shall have preceded possession of silence.

A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.

The mystery of human destiny is that we are fated, but that we have the freedom to fulfill or not fulfill our fate: realization of our fated destiny depends on us. While inhuman beings like the cockroach realize the entire cycle without going astray because they make no choices.

Claire was going to hate me. Our son was sucked into the pits of hell while I was watching General Hospital. God damn you Brenda and Sonny for making me lose focus.

Holding someone's hand was always my idea of joy. Often before falling asleep - in that small struggle not to lose consciousness and enter the greater world - often, before having the courage to go toward the greatness of sleep, I pretend that someone is holding my hand and I go, go toward the enormous absence of form that is sleep. And when even then I can't find the courage, then I dream.

Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

Real mathematics must be justified as art if it can be justified at all.

I' is merely one of the world's instantaneous spasms.

I spend roughly $80 per year watching bananas go brown.

I'm so frightened that I shall be able to accept the notion that I have lost myself only if I imagine that someone is holding my hand.

I don't want beauty, I want identity.

In the world there exists no aesthetic plane, not even the aesthetic plane of goodness.

Reality is the raw material, language is the way I go in search of it - and the way I do not find it. But it is from searching and not finding that what I did not know was born, and which I instantly recognise. Language is my human effort. My destiny is to search and my destiny is to return empty-handed. But - I return with the unsayable. The unsayable can only be given to me through the failure of my language. Only when the construction fails, can I obtain what I could not achieve.

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. “Immortality” may be a silly word, but probably a mathematician has the best chance of whatever it may mean.

Perder-se é um achar-se perigoso.

Would it be simplistic to think the moral problem with regards to others consists in behaving as one ought to, and the moral problem with regards to oneself is managing to feel what one ought to?

The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.

Never again shall I understand anything I say. Since how could I speak without the word lying for me? How could I speak except timidly like this: life just is for me. Life just is for me, and I don't understand what I'm saying. And so I adore it.

Real life is so secret that not even I, who am dying of it, have been given the password, I am dying without knowing of what.

If a man has any genuine talent he should be ready to make almost any sacrifice in order to cultivate it to the full.

A note exists between two notes of music, between two facts exists a fact, between two grains of sand no matter how close together there exists an interval of space, a sense that exists between senses — in the interstices of primordial matter is the line of mystery and fire that is the breathing of the world, and the continual breathing of the world is what we hear and call silence.

I, who called love my hope for love.

Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. Appearances suggest the contrary, but there are easy explanations. Music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable, whereas most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity

Depersonalization like the deposing of useless individuality— the loss of everything that can be lost, while still being. To take away from yourself little by little, with an effort so attentive that no pain is felt, to take away from yourself like one who gets free of her own skim, her own characteristics. Everything that characterizes me is just the way I am most easily viewed by others and end up being superficially recognizable to myself.

Oh, don't pull your hand away from me, I've promised myself that maybe by the end of this impossible narrative I shall understand, oh maybe it will be on Hell's road that I shall be able to find what we need—but don't pull your hand away, even though I now know that the finding has to come on the road of what we are, if I can succeed in not sinking completely into what we are.

Exposition, criticism, appreciation, is work for second-rate minds. I

—————— I’m searching, I’m searching. I’m trying to understand. Trying to give what I’ve lived to somebody else and I don’t know to whom, but I don’t want to keep what I lived. I don’t know what to do with what I lived, I’m afraid of that profound disorder. I don’t trust what happened to me. Did something happen to me that I, because I didn’t know how to live it, lived as something else? That’s what I’d like to call disorganization, and I’d have the confidence to venture on, because I would know where to return afterward: to the previous organization. I’d rather call it disorganization because I don’t want to confirm myself in what I lived — in the confirmation of me I would lose the world as I had it, and I know I don’t have the fortitude for another.

Estou tão assustada que só poderei aceitar que me perdi se imaginar que alguém me está dando a mão.

It (proof by contradiction) is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

A mathematical proof should resemble a simple and clear-cut constellation, not a scattered cluster in the Milky Way.

Life was taking its vengeance on me, and that vengeance consisted merely in coming back, nothing more. Every case of madness involves something coming back. People who are possessed are not possessed by something that just comes but instead by something that comes back. Sometimes life comes back. If in me everything crumbled before that power, it is not because that power was itself necessarily an overwhelming one: it in fact had only to come, since it had already become too full-flowing a force to be controlled or contained - when it appeared it overran everything. And then, like after a flood, there floated a wardrobe, a person, a loose window, three suitcases. And that seemed like Hell to me, that destruction of layers and layers of human archaeology.

Dá-me a tua mão desconhecida, que a vida está me doendo, e não sei como falar – a realidade é delicada demais, só a realidade é delicada, minha irrealidade e minha imaginação são mais pesadas.

At the same time, Dad was working on a book arguing the case for phonetic spelling. He called it 'A Ghoti out of Water.' "Ghoti," he liked to point out, could be pronounced like "fish." The "gh" had the "f" sound in "enough," the "o" had the short "i" sound in "women," and "ti" had the "sh" sound in "nation.

I am the cockroach, I am my leg, I am my hair, I am the section of brightest light on the wall plaster—I am every Hellish piece of myself—life is so pervasive in me that if they divide me in pieces like a lizard, the pieces will keep on shaking and writhing. I am the silence etched on a wall, and the most ancient butterfly flutters in and looks at me: just the same as always. From birth to death is what I call human in myself, and I shall never actually die. But this is not eternity, it is condemnation. How opulent this silence is. It is the accumulation of centuries. It is the silence of the cockroach looking. The world looks at itself in me. Everything looks at everything, everything experiences the other; in this desert things know things.

No mathematician should ever allow him to forget that mathematics, more than any other art or science, is a young man's game. … Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work later; … [but] I do not know of a single instance of a major mathematical advance initiated by a man past fifty. … A mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas.

I shall never be able to understand it, but there must be someone who can. And I shall have to create that someone who can inside myself.

The seriousness of a theorem, of course, does not lie in its consequences, which are merely the evidence for its seriousness.

I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our "creations," are simply our notes of our observations. This view has been held, in one form or another, by many philosophers of high reputation from Plato onwards, and I shall use the language which is natural to a man who holds it.

her short stories read like perfect songs.

Sou: o que vi.

...things are very delicate. People tread upon them with too many human feet, with too many sentiments. Only the delicacy of innocence or only the delicacy of the initiate senses its almost nonexistent taste. Before, I needed seasoning for everything, and in that way I skipped over the thing and tasted the taste of the seasoning.

I was advised to read Jordan's 'Cours d'analyse'; and I shall never forget the astonishment with which I read that remarkable work, the first inspiration for so many mathematicians of my generation, and learnt for the first time as I read it what mathematics really meant.

I'm blinder than before. I did see, I really did. I was terrified by the raw truth of a world whose greatest horror is that it is so alive that for me to admit that I am as alive as it is - and my most hideous discovery is that I am as alive as it is - I shall have to raise my consciousness of life outside to so high a point that it would amount to a crime against my personal life.

I am going to create what happened to me. Only because living isn't tellable. Living isn't livable. I shall have to create upon life. And without lying. Yes to creation, no to lying. Creation isn't imagination, it's running the huge risk of coming face to face with reality.

Ambition is a noble passion which may legitimately take many forms; there was something noble in the ambitions of Attila or Napoleon; but the noblest ambition is that of leaving behind something of permanent value.

One rather curious conclusion emerges, that pure mathematics is on the whole distinctly more useful than applied. ... For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.

The beauty of a mathematical theorem depends a great deal on its seriousness, as even in poetry the beauty of a line may depend to some extent on the significance of the ideas which it contains.

Oh, but to reach silence, what a huge effort of voice. My voice is the way I go seek reality; reality prior to my language exists as an unthinkable thought, but I was and am fatefully impelled to have to know what thought thinks. Reality precedes the voice that seeks it, but like the earth precedes the tree, but like the world precedes the man, but like the sea precedes the view of the sea, life precedes love, bodily matter precedes the body, and one day in its turn language shall have preceded possession of silence. - Clarice Lispector, The Passion According to G.H.

Ignorance of the law of irreducibility was no excuse. I could no longer excuse myself with the claim that I didn't know the law -- for knowledge of self and of the world is the law that, even though unattainable, cannot be broken, and no one can excuse himself by saying that he doesn't know it. . . . The renewed originality of the sin is this: I have to carry out my unknowing, I shall be sinning originally against life.

And my fear, too, was different now: not the fear of someone who is still about to go in but the so much greater fear of someone who has gone in.

Se não tivesse sido eu, eu não saberia, e tendo sido eu, eu soube.

Ouve, por eu ter mergulhado no abismo é que estou começando a amar o abismo de que sou feita.

The truly transformative power of language occurs when these descriptive root terms are used to form words that convey abstract concepts. A three-letter root compound used to name the spine (Q-W-M) is adapted to describe “flexibility.” The root term for a heated pot boiling over (Gh-Dh-B) constructs a word meaning “hot-headed.” A root term describing the process of carefully separating grains (D-R-S) evolves to express “analyzing” or “interpreting.” From physical sources emerge words for the intangible, like the Qur’an’s parable of the healthy tree with roots anchored in the ground while branches stretch toward the heavens.

Night is our latent state. And it is so moist that plants are born. In houses the lights go out in order to hear the crickets more clearly, and so the grasshoppers can walk atop the leaves almost without touching them, the leaves, the leaves, the leaves—in the night the soft anxiety is transmitted through the hollow of the air, the void is a means of transport.

I've always liked putting things in their places. I think it's my only true calling. By ordering things I create and understand at the same time ... Ordering is finding the best form.

Ah, meu amor, não tenhas medo da carência: ela é o nosso destino maior. O amor é tão mais fatal do que eu havia pensado, o amor é tão inerente quanto a própria carência, e nós somos garantidos por uma necessidade que se renovará continuamente. O amor já está, está sempre. Falta apenas o golpe da graça - que se chama paixão.

Poetry is more valuable than cricket, but Bradman would be a fool if he sacrificed his cricket in order to write second-rate minor poetry (and I suppose that it is unlikely that he could do better).

And giving myself over with the confidence of belonging to the unknown. For I can pray only to what I do not know. And I can love only the unknown evidence of things and can add myself only to what I do not know. Only that is a real giving of oneself.

At the same time, Dad was working on a book arguing the case for phonetic spelling. He called it A Ghoti out of Water. “Ghoti,” he liked to point out, could be pronounced like “fish.” The “gh” had the “f” sound in “enough,” the “o” had the short “i” sound in “women,” and “ti” had the “sh” sound in “nation.” Dad

Regarding mathematics, there are now few studies more generally recognized, for good reasons or bad, as profitable and praiseworthy. This may be true; indeed it is probable, since the sensational triumphs of Einstein, that stellar astronomy and atomic physics are the only sciences which stand higher in popular estimation.

I do not think that G. H. Hardy was talking nonsense when he insisted that the mathematician was discovering rather than creating... The world for me is a necessary system, and in the degree to which the thinker can surrender his thought to that system and follow it, he is in a sense participating in that which is timeless or eternal.

Depersonalization as the great objectification of oneself. The greatest exteriorization one can reach. Whoever gets to oneself through depersonalization shall recognize the other in any disguise: the first step in relation to the other is finding inside oneself the man of all men. Every woman is the woman of all women, every man is the man of all men, and each of them could appear wherever man is judged. But only in immanence, because only a few reach the point of, in us, recognizing themselves. And then, by the simple presence of their existence, revealing ours.

Se eu me confirmar e me considerar verdadeira, estarei perdida porque não saberei onde engastar meu novo modo de ser - se eu for adiante nas minhas visões fragmentárias, o mundo inteiro terá que se transformar para eu caber nele.

Life just is for me, and I don’t understand what I’m saying. And so I adore it. ——————

My old life was necessary to me because it was precisely its error that made me take up imagining a hope that, without the life that I led, I wouldn't have known.

I had reached nothingness, and the nothingness was live and moist.

Toda compreensão súbita é finalmente a revelação de uma aguda incompreensão. Todo momento de achar é um perder-se a si próprio.

I shall need to courage to do what I'm about to do: speak. And risk the enormous surprise I shall feel at the poverty of the spoken thing. As soon as it's out of my mouth, I'll have to add: that's not it, that's not it! But I cannot be afraid of being ridiculous, I always preferred less to more also out of fear of the ridiculous: because there's also the shattering of modesty. I'm putting off having to speak to myself. Out of fear? And because I don't have a word to say. I don't have a word to say. So why don't I shut up? But if I do not force out the word muteness will swallow me forever in waves.

when art is good it is because it touched upon the inexpressive, the worst art is expressive, that art which trangresses the piece of iron and the piece of glass, and the smile, and the scream.

I still say to myself when I am depressed, and find myself forced to listen to pompous and tiresome people, 'Well, I have done one thing you could never have done, and that is to have collaborated with both Littlewood and Ramanujan on something like equal terms.

But I’m afraid to begin composing in order to be understood by the imaginary someone, I’m afraid to start to “make” a meaning, with the same tame madness that till yesterday was my healthy way of fitting into a system. Will I need the courage to use an unprotected heart and keep talking to the nothing and the no one? as a child thinks about the nothing. And run the risk of being crushed by chance.

The Greeks were the first mathematicians who are still ‘real’ to us to-day. Oriental mathematics may be an interesting curiosity, but Greek mathematics is the real thing. The Greeks first spoke a language which modern mathematicians can understand: as Littlewood said to me once, they are not clever schoolboys or ‘scholarship candidates’, but ‘Fellows of another college’. So Greek mathematics is ‘permanent’, more permanent even than Greek literature. Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. ‘Immortality’ may be a silly word, but probably a mathematician has the best chance of whatever it may mean.

Billy and Aaron found their way beyond the rain. Anyone who reads this story: Have faith in the resilience of the human spirit.........if I can tell you just one thing, please believe in yourself. God made you to be beautiful. You can find your way to the other side too. Just never give up! GH

Plenty of mathematicians, Hardy knew, could follow a step-by-step discursus unflaggingly—yet counted for nothing beside Ramanujan. Years later, he would contrive an informal scale of natural mathematical ability on which he assigned himself a 25 and Littlewood a 30. To David Hilbert, the most eminent mathematician of the day, he assigned an 80. To Ramanujan he gave 100.

Eu tenho à medida que designo – e este é o esplendor de se ter uma linguagem . Mas eu tenho muito mais à medida que não consigo designar. A realidade é a matéria-prima, a linguagem é o modo como vou buscá-la – e como não acho. Mas é do buscar e não achar que nasce o que eu não conhecia, e que instantaneamente reconheço. A linguagem é o meu esforço humano. Por destino tenho que ir buscar e por destino volto com as mãos vazias. Mas – volto com o indizível . O indizível só me poderá ser dado através do fracasso de minha linguagem. Só quando falha a construção, é que obtenho o que ela não conseguiu.

A MAN who sets out to justify his existence and his activities has to distinguish two different questions. The first is whether the work which he does is worth doing; and the second is why he does it, whatever its value may be.

The geometer offers to the physicist a whole set of maps from which to choose. One map, perhaps, will fit the facts better than others, and then the geometry which provides that particular map will be the geometry most important for applied mathematics.

I'm stalling. I know that everything I say is just to put it off-to put off the moment when I'll have to start talking, knowing that there is nothing more for me to say. I'm putting off my silence. Have I been putting off silence for my whole life? but now, in my disparagement of the word, perhaps I'll finally be able to start talking." (14)

Twentieth-century British mathematician G.H. Hardy also believed that the human function is to "discover or observe" mathematics rather than to invent it. In other words, the abstract landscape of mathematics was there, waiting for mathematical explorers to reveal it.

Am lucky my cloud can't store all my chat..me i don't keep/stare our chat

E nunca antes eu me havia deixado levar, a menos que soubesse para o quê.

Now I understand what a trial is. Trial: it means that life is trying me. But trial: means that I too am trying. And trying can become an ever more insatiable thirst.

I'm going to start my exercise in courage, living isn't courage, knowing that you're living, that's courage.

Hoje me exige hoje mesmo.

O erro é um dos meus modos fatais de trabalho.

The best mathematics is serious as well as beautiful—‘important’ if you like, but the word is very ambiguous, and ‘serious’ expresses what I mean much better

Let the Angels lead me to you, if only they fly in this land.

¿Qué soy? Soy: estar de pie ante un espanto. Soy: lo que he visto. No entiendo y temo entender, la materia del mundo me espanta, con sus planetas y sus cucarachas

Good work is no done by ‘humble’ men. It is one of the first duties of a professor, for example, in any subject, to exaggerate a little both the importance of his subject and his own importance in it. A man who is always asking ‘Is what I do worth while?’ and ‘Am I the right person to do it?’ will always be ineffective himself and a discouragement to others.

Good work is no done by ‘humble’ men. It is one of the first duties of a professor, for example, in any subject, to exaggerate a little both the importance of his subject and his own importance in it. A man who is always asking ‘Is what I do worth while?’ and ‘Am I the right person to do it?’ will always be ineffective himself and a discouragement to others.

UggGH!

Nostalgia is not for the God who is missing to us, it is a nostalgia for ourselves, for we do not sustain ourselves; we miss our impossible grandeur - my unreachable nowness is my paradise lost.

Never, until then, had life happened to me by day. Never in sunlight. Only in my nights did the world slowly revolve. Only that, whatever happened in the dark of night itself, would also happen at the same time in my own entrails, and my dark wasn't differentiated from the dark outside, and in the morning, when I opened my eyes, the world was still a surface: the secret life of the night soon reduced in my mouth to the taste of a nightmare that disappears. but now life was happening by day. undeniable and to be seen. unless I averted my eyes. and I could still avert my eyes.

Real life is so secret that not even I, who am dying of it, have been given the password, I am dying without knowing of what. And the secret is such that only if the mission is finally carried out do I, all of a sudden, see that I was born entrusted with it - all of life is a secret mission.

I remembered you, when I kissed your man face, slowly, slowly kissed it, and when the time came to kiss your eyes—I remembered that then I had tasted the salt in my mouth, and that the salt of tears in your eyes was my love for you. But, what bound me most of all in a fright of love, had been, in the depth of the depths of the salt, your saltless and innocent and childish substance: with my kiss your deepest insipid life was given to me, and kissing your face was the saltless and busy patient work of love, it was woman weaving a man, just as you had woven me, neutral crafting of life.

Life, my love, is a great seduction in which all that exists seduces. That room that was deserted and for that reason primally alive. I had reached the nothing, and the nothing was living and moist.

Immortality is often ridiculous or cruel: few of us would have chosen to be Og or Ananias or Gallio. Even in mathematics, history sometimes plays strange tricks; Rolle figures in the textbooks of elementary calculus as if he had been a mathematician like Newton; Farey is immortal because he failed to understand a theorem which Haros had proved perfectly fourteen years before; the names of five worthy Norwegians still stand in Abel’s Life, just for one act of conscientious imbecility, dutifully performed at the expense of their country’s greatest man. But on the whole the history of science is fair, and this is particularly true in mathematics. No other subject has such clear-cut or unanimously accepted standards, and the men who are remembered are almost always the men who merit it. Mathematical fame, if you have the cash to pay for it, is one of the soundest and steadiest of investments.

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This book is like any other book. But I would be happy if it were only read by people whose souls are already formed. Those who know that the approach, of whatever it may be, happens gradually and painstakingly — even passing through the opposite of what it approaches. They who, only they, will slowly come to understand that this book takes nothing from no one. To me, for example, the character G. H. gave bit by bit a difficult joy; but it is called joy. C.

I was now so much greater that I could no longer see myself. As great as a far-off landscape. I was far off. But perceptible in my furthest mountains and in my remotest rivers: the simultaneous present no longer scared me, and in the furthest extremity of me I could finally smile without even smiling. At last I was stretching beyond my sensibility.

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. ‘Immortality’ may be a silly word, but probably a mathematician has the best chance of whatever it may mean. G.H. Hardy 23

If I had a statue on a column in London, would I prefer the columns to be so high that the statue was invisible, or low enough for the features to be recognizable? I would choose the first alternative, Dr Snow, presumably, the second.

It is a tiny minority who can do something really well, and the number of men who can do two things well is negligible. If a man has any genuine talent he should be ready to make almost any sacrifice in order to cultivate it to the full

There is no treasure but Truth, there is no Truth but Wisdom. There is no Wisdom, but from Learning, and Learning is won by the devotion of hours, years, days and nights to the works of Nature and the Treasures of Truth that others have gathered.

I want the material of things. Humanity is drenched with humanization, as if that were necessary; and that false humanization trips up man and trips up his humanity. A thing exists that is fuller, deafer, deeper, less good, less bad, less pretty. Yet that thing too runs the risk, in our coarse hands, of becoming transformed into "purity", our hands that are coarse and full of words.

It is hardly possible to maintain seriously that the evil done by science is not altogether outweighed by the good. For example, if ten million lives were lost in every war, the net effect of science would still have been to increase the average length of life.

The mathematician’s patterns, like the painter’s or the poet’s, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics. G.H. Hardy

I had better say something here about this question of age, since it is particularly important for mathematicians. No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game. To take a simple illustration at a comparatively humble level, the average age of election to the Royal Society is lowest in mathematics. We can naturally find much more striking illustrations. We may consider, for example, the career of a man who was certainly one of the world's three greatest mathematicians. Newton gave up mathematics at fifty, and had lost his enthusiasm long before; he had recognized no doubt by the time he was forty that his greatest creative days were over. His greatest idea of all, fluxions and the law of gravitation, came to him about 1666 , when he was twentyfour—'in those days I was in the prime of my age for invention, and minded mathematics and philosophy more than at any time since'. He made big discoveries until he was nearly forty (the 'elliptic orbit' at thirty-seven), but after that he did little but polish and perfect. Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work a good deal later; Gauss's great memoir on differential geometry was published when he was fifty (though he had had the fundamental ideas ten years before). I do not know an instance of a major mathematical advance initiated by a man past fifty. If a man of mature age loses interest in and abandons mathematics, the loss is not likely to be very serious either for mathematics or for himself.

My life had been as continuous as death. Life is so continuous that we divide it into stages and call one of them death. I had always been in life, it mattered little that it was not I properly speaking, not that thing that I customarily call "I." I had always been in life.

The proof is by reductio ad absurdum, and reductio ad absurdum, which Euclid loved so much, is one of a mathematician’s finest weapons5. It is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

When authors write best, or at least, when they write most fluently, an influence seems to waken in them which becomes their master, which will have its own way, putting out of view all behests but its own, dictating certain words, and insisting on their being used, whether vehement or measured in their nature; new moulding characters, giving unthought-of turns to incidents, rejecting carefully elaborated old ideas, and suddenly creating and adopting new ones. Is it not so? And should we try to counteract this influence? Can we indeed counteract it? from a letter to G.H. Lewes, 12 January 1848

The world had reclaimed its own reality, and, just like after a catastrophe, my culture had ended: I was merely a historical fact. Everything in me had been reclaimed by the beginning of time and by my own beginning. I had passed on to a first, primary plane, I was in the silence of the winds and in the age of tin and copper - at the first age of life.

It’s not a story that leads the reader to philosophical thoughts. And it’s not a philosophical treatise that needs a story to convey them. Instead, it is a vivifying experience that leads a person to the most ambitious philosophical discoveries. An experience transformed into literary art, in which harmony and disorder are the price of the revelation. A

No one should ever be bored. One can be horrified, or disgusted, but one can't be bored.

Que não se acorde quem está todo ausente, quem está absorto está sentindo o pesos das coisas.

Ultrapassar a dor é a pior crueldade

Cuando se comprende a fondo el vivir, uno se pregunta: pero ¿era solo esto? Y la respuesta es: no es solo esto, es exactamente esto.

Como, pois, inaugurar agora em mim o pensamento? E talvez só o pensamento me salvasse, tenho medo da paixão.

When living comes to pass, one wonders: but was that it? And the answer is: that is not only it, that is exactly it.

Perhaps I now knew that I would never be equal to life myself, but that my life was equal to life. I would never reach my root, but my root did exist.

It is half about what you want to be and the other half is what destiny lets you to be.

A dream is a reality when conceived with the mindset of an achiever.

The play is independent of the pages on which it is printed, and ‘pure geometries’ are independent of lecture rooms, or of any other detail of the physical world.

We are merely explorers of infinity in the pursuit of absolute perfection.

Nunca saberei entender mas há de haver quem entenda. E é em mim que tenho de criar esse alguém que entenderá.

Ние решаваме да отидем до луната или да направим друго нещо не защото е лесно, а защото е трудно.

Writing is easy, good writing is hard and excellent writing is hard work.

I always liked to arrange things. I guess it’s my only real vocation. By putting things in order, I create and understand at the same time.

My expectations closed the world to me.

Como se explica que o meu maior medo seja exatamente o de ir vivendo o que for sendo?

We have concluded that the trivial mathematics is, on the whole, useful, and that the real mathematics, on the whole, is not.

a respiração contínua do mundo é aquilo que ouvimos e chamamos de silêncio.

I lost something that was essential to me, and that no longer is. I no longer need it, as if I’d lost a third leg that up till then made it impossible for me to walk but that turned me into a stable tripod. I lost that third leg. And I went back to being a person I never was. I went back to having something I never had: just two legs. I know I can only walk with two legs. But I feel the useless absence of that third leg and it scares me, it was the leg that made me something findable by myself, and without even having to look for myself.

I, neutral cockroach body, I with a life that at last is not eluding me because I finally see it outside of myself -- I am the cockroach, I am my leg, I am my hair, I am the section of brightest light on the wall plaster -- I am every Hellish piece of myself -- life is so pervasive in me that if they divide me in pieces like a lizard, the pieces will keep on shaking and writhing.

And solitude is not needing. Not needing leaves a person alone, all alone. Oh, needing doesn't isolate a person, things need things: it's enough to see a chick walking to see that its destiny will be what lack will make of it, its destiny is to join, like drops of mercury cling to other drops of mercury, even though, like all drops of mercury, it has a complete and rounded existence in itself.

And I shall not wander “from thought to thought,” but from mood to mood. We shall be inhuman — as the loftiest conquest of man. Being is being beyond human. Being man does not work, being man has been a constraint. The unknown awaits us, but I feel that this unknown is a totalization and will be the true humanization for which we longed. Am I speaking of death? no, of life. It is not a state of happiness, it is a state of contact.

Mas é a mim que caberá impedir-me de dar nome à coisa. O nome é um acréscimo e impede o contato com a coisa. O nome da coisa é um intervalo para a coisa. A vontade do acréscimo é grande — porque a coisa nua é tão tediosa

She was working as a waitress in a cocktail bar when she decided to summon the devil and sell her soul for fame. As you do. Hell, we’ve all been there… Of course, things didn’t go according to plan. Never have, never will…

My world today is raw, it is a world of great vital difficulty. Because, more than a star, today I want the thick and black root of the stars, I want the source that always seems dirty, and is dirty, and that is always incomprehensible. It is with pain that I bid farewell even to the beauty of a child - I want the adult who is more primitive and ugly and drier and more difficult, and who became a child-seed that cannot be broken between the teeth.

...E nós sabemos Deus. E o que precisamos Dele, extraímos. (Não sei o que chamo de Deus, mas assim pode ser chamado.) Se só sabemos muito pouco de Deus, é porque precisamos pouco: só temos Dele o que fatalmente nos basta, só temos de Deus o que cabe em nós. (A nostalgia não é do Deus que nos falta, é a nostalgia de nós mesmos que não somos bastante; sentimos falta de nossa grandeza impossível - minha atualidade inalcançável é o meu paraíso perdido.)

The last time I came down from the enchanted saddle, my human sadness was so great that I swore never to again. The ride, however, continues on in me. I converse, I clean the house, I smile, but I know that the ride is within me.

I am the priestess of a secret that I no longer know. And I serve out of blissful ignorance. I found out something I was unable to understand, my lips became sealed, and I retained only the incomprehensible fragments of a ritual.

It isn't for us that cows' milk comes forth, but we drink it. Flowers weren't made for us to look at or for us to smell, and we look at them and smell them. The Milky Way doesn't exist for us to know if its existence, but we know.

And He not only allows but needs to be used, used is a way of being understood. (In all religions God demands to be loved.) For us to have, all we need is to need. To need is always the supreme moment. Just as the most daring happiness between a man and a woman comes when needing becomes so great that it is felt in agony and wonder: without you I will be unable to live. Love's revelation is a revelation of lacking—blessed be the poor of spirit for the sundering realm of life is theirs.

We must guard against a fallacy common among apologists of science, the fallacy of supposing that the men whose work most benefits humanity are thinking much of that while they do it, that physiologists, for example, have particularly noble souls.

se eu gritasse acordaria milhares de seres gritantes que iniciariam pelos telhados um coro de gritos e horror. Se eu gritasse desencadearia a existência - a existência de quê? a existência do mundo. Com reverência eu temia a existência do mundo para mim.

An eye looked over my life. I probably called that eye sometimes "truth", sometimes morality, sometimes human law, sometimes "God", sometimes "myself". For the most part I lived inside a mirror. Two minutes after I was born I had already lost my beginnings.

Ne olduğumu bilmediğimden, "olmamak" gerçeğe en yakın olduğum yerdi: en azından madalyonun öteki yüzü kontrolümde: en azından "-mamak"a sahiptim, tersime sahiptim. O zaman benim için neyin iyi olduğunu bilmiyordum; benim için kötü olana da böylece ısınmış oldum.

Até então eu nunca fora dona de meus poderes - poderes que eu não entendia nem queria entender, mas a vida em mim os havia retido para que um dia enfim desabrochasse essa matéria desconhecida e feliz e inconsciente que era finalmente: eu! eu, o que quer que seja.

It is not for us that the cow’s milk flows, but we drink it. The flower was not made for us to look at it or for us to smell its fragrance, and we look at it and smell it. The Milky Way does not exist for us to know of its existence, but we know of it. And we know God. And what we need from Him, we elicit. (I don’t know what I am calling God, but thus he may be called.) If we only know very little of God, that is because we need little: we only have of Him whatever is inevitably enough for us, we only have of God whatever fits inside us.

It is the dull and elementary parts of applied mathematics, as it is the dull and elementary parts of pure mathematics, that work for good or ill. Time may change all this. No one foresaw the applications of matrices and groups and other purely mathematical theories to modern physics, and it may be that some of the 'highbrow' applied mathematics will become 'useful' in as unexpected a way; but the evidence so far points to the conclusion that, in one subject as in the other, it is what is commonplace and dull that counts for practical life.

Mas tenho medo do que é novo e tenho medo de viver o que não entendo quero sempre ter a garantia de pelo menos estar pensando que entendo, não sei me entregar à desorientação. Como é que se explica que o meu maior medo seja exatamente em relação: a ser? e no entanto não há outro caminho. Como se explica que o meu maior medo seja exatamente o de ir vivendo o que for sendo? como é que se explica que eu não tolere ver, só porque a vida não é o que eu pensava e sim outra como se antes eu tivesse sabido o que era! Por que é que ver é uma tal desorganização?

- Dá-me a tua mão, não me abandones, juro que também eu não queria: eu também vivia bem, eu era uma mulher de quem se pode dizer "vida e amores de G.H.". Não posso pôr em palavras qual era o sistema, mas eu vivia num sistema. Era como se eu me organizasse dentro do fato de ter dor de estômago porque, se eu não a tivesse mais, também perderia a maravilhosa esperança de me livrar um dia da dor de estômago: minha vida antiga me era necessária porque era exatamente o seu mal que me fazia usufruir da imaginação de uma esperança que, sem essa vida que eu levava, eu não conheceria.

We shall be inhuman - as humankind's greatest conquest. To be is to be beyond the human. To be a human being doesn't do it, to be human has been a constraint. The unknown awaits us, but I sense that that unknown is a totalization and will be the true humanization we long for. Am I speaking of death? no, of life.

Ainda que eu seja mais uma ninguém a vagar sem rosto pelas rodas de livros, pelas prateleiras, tenho a sensação de ser uma penetra. Tanta coisa escrita, tanta gente escrevendo. Por que eu escrevo? O que eu tenho a dizer que já não tenha sido dito de milhares de maneiras diferentes? A quem interessa o meu corpo de letras?

Published mathematical papers often have irritating assertions of the type: “It now follows that…,” or: “It is now obvious that…,” when it doesn't follow, and isn't obvious at all, unless you put in the six hours the author did to supply the missing steps and checking them. There is a story about the English mathematician G.H. Hardy, whom we shall meet later. In the middle of delivering a lecture, Hardy arrived at a point in his argument where he said, “It is now obvious that….” Here he stopped, fell silent, and stood motionless with furrowed brow for a few seconds. Then he walked out of the lecture hall. Twenty minutes later he returned, smiling, and began, “Yes, it is obvious that….” If he

What comes out of the roach’s belly is not transcendable—ah, I don’t want to say that it’s the opposite of beauty, “opposite of beauty” doesn’t even make sense—what comes out of the roach is: “today,” blessed be the fruit of thy womb—I want the present without dressing it up with a future that redeems it, not even with a hope—until now what hope wanted in me was just to conjure away the present. But I want much more than that: I want to find the redemption in today, in right now, in the reality that is being, and not in the promise, I want to find joy in this instant—I want the God in whatever comes out of the roach’s belly—even if that, in my former human terms, means the worst, and, in human terms, the infernal.

The room was the opposite of what I'd created in my home, the opposite of the soft beauty I'd made from my talent for arrangement, my talent for living, the opposite of my serene irony, of my sweet and absentminded irony: it was a violation of my quotation marks, the quotation marks that made me a citation of myself. The room was the portrait of an empty stomach.

Perdi alguma coisa que me era essencial, e que já não me é mais. Não me é necessária, assim como se eu tivesse perdido uma terceira perna que até entorno me impossibilitava de andar mas que fazia de mim um tripé estável. Essa terceira perna eu perdi. E voltei a ser uma pessoa que nunca fui. Voltei a ter o que nunca tive: apenas as duas pernas. Sei que momento com duas pernas é que posso caminhar. Mas a ausência inútil da terceira perna me faz falta e me assusta, era ela que fazia de mim uma coisa encontrável por mim mesma, e sem sequer precisar me procurar. Estou desorganizada porque perdi o que não precisava? (…) É difícil perder-se. É tão difícil que provavelmente arrumarei depressa um modo de me achar, mesmo que achar-me seja de novo a mentira de que vivo. Até agora achar-me era já ter uma ideia de pessoa e nela me engastar: nessa pessoa organizada eu me encarnava, e nem mesmo sentia o grande esfoço de construção que era viver. (…) Mas e agora? estarei mais livre? (…) Se tiver coragem, eu me deixarei continuar perdida. Mas tenho medo do que é novo e tenho medo de viver o que não entendo - quero sempre ter a garantia de pelo menos estar pensando que entendo, não sei me entregar à desorientação (…) Talvez desilusão seja o medo de não pertencer mais a um sistema. No entanto se deveria dizer assim: ela está muito feliz porque finalmente foi desiludido. O que eu era antes não era bom. Mas era desse não-bom que eu havia organizado o melhor - a esperança.

O mundo independia de mim - esta era a confiança a que eu tinha chegado: o mundo independia de mim, e não estou entendendo o que estou dizendo, nunca! nunca mais compreenderei o que eu disser. Pois como poderia eu dizer sem que a palavra mentisse por mim? como poderei dizer senão timidamente assim: a vida se me é. A vida se me é, e eu não entendo o que digo. E então adoro.

Everything could be fiercely summed up in never emitting a first scream—a first scream unleashes all the others, the first scream at birth unleashes a life, if I screamed I would awaken thousands of screaming beings who would loose upon the rooftops a chorus of screams and horror. If I screamed I would unleash the existence—the the existence of what? the existence of the world.

In Isaiah’s description of the downfall of Babylon, the city so famed for its astrologers, we find mention of Hobhre Shamayim,[344] that is, dividers of the heavens, astrologers who divide the heavens into houses for the convenience of their prognostications. The same persons are then described as Chozim bakkokhabhim, star-gazers, those who study the stars for the purpose of taking horoscopes.

‎"Беден съм-ти си моето богатство.Мрачен съм-ти си моята светлина.Аз не притежавам нищо-нищо не ми е нужно.И как ли бих могъл да притежавам нещо,след като съществува такова противоречие:който притежава нещо,той не притежава самия себе си.Щастлив съм като дете,което не може и няма нужда да притежава нищо.Аз не притежавам... нищо,защото принадлежа само на тебе,аз не съм,аз съм престанал да бъда,за да бъда само твой" //"Дневникът на прелъстителя",С.Киркегор.

I was being carried off by the demonic. For the inexpressive is diabolic. A person who isn’t committed to hope lives the demonic. A person who has the courage to cast off feelings discovers the ample life of an extremely busy silence, the same that exists in the cockroach, the same in the stars, the same in the self — the demonic precedes the human. And the person who sees that presentness burns as if seeing the God. Prehuman divine life is of a presentness that burns.

The mathematician is in much more direct contact with reality. This may seem a paradox, since it is the physicist who deals with the subject-matter usually described as 'real' ... A chair may be a collection of whirling electrons, or an idea in the mind of God : each of these accounts of it may have its merits, but neither conforms at all closely to the suggestions of common sense. ... neither physicists nor philosophers have ever given any convincing account of what 'physical reality' is, or of how the physicist passes, from the confused mass of fact or sensation with which he starts, to the construction of the objects which he calls 'real'. A mathematician, on the other hand, is working with his own mathematical reality. ... mathematical objects are so much more what they seem. ... 317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is so, because mathematical reality is built that way.

But this is not eternity, it is condemnation. How opulent this silence is. It is the accumulation of centuries. It is the silence of a cockroach looking. The world looks at itself in me. Everything looks at everything, everything experiences the other; in this desert things know things. Things know things as much as this… this something that I shall call pardon, if I wish to save myself within the human plan. It is pardon in itself. Pardon is one of the attributes of living matter.

I can remember Bertrand Russell telling me of a horrible dream. He was in the top floor of the University Library, about A.D. 2100. A library assistant was going round the shelves carrying an enormous bucket, taking down books, glancing at them, restoring them to the shelves or dumping them into the bucket. At last he came to three large volumes which Russell could recognize as the last surviving copy of Principia Mathematica. He took down one of the volumes, turned over a few pages, seemed puzzled for a moment by the curious symbolism, closed the volume, balanced it in his hand and hesitated....

Acum o să-ți povestesc cum am intrat în inexpresivul care a fost întotdeauna căutarea mea oarbă și secretă. Cum am intrat între ceea ce există între numărul unu și numărul doi, cum am văzut linia de mister și foc, care e o linie ascunsă. Între două note muzicale există o notă, între două fapte există un fapt, între două fire de nisip, oricât de apropiate ar fi unul de celălalt, există un interval în spațiu, există un simț care se află între simț; în interstițiile materiei principale se află linia de mister și foc care este respirația lumii, și respirația continuă a lumii este ceea ce auzim și denumim tăcere.

Estou procurando, estou procurando. Estou tentando entender. Tentando dar a alguém o que vivi e não sei a quem, mas não quero ficar com o que vivi. Não sei o que fazer do que vivi, tenho medo dessa desorganização profunda. Não confio no que me aconteceu. Aconteceu-me alguma coisa que eu, pelo fato de não a saber como viver, vivi uma outra? A isso quereria chamar desorganização, e teria a segurança de me aventurar, porque saberia depois para onde voltar: para a organização anterior. A isso prefiro chamar desorganização pois não quero me confirmar no que vivi - na confirmação de mim eu perderia o mundo como eu o tinha, e sei que não tenho capacidade para outro.

Είναι μελαγχολική εμπειρία για έναν κατ' επάγγελμα μαθηματικό να βρεθεί στην θέση να γράφει για τα Μαθηματικά. Η λειτουργία ενός μαθηματικού είναι να δημιουργεί, να αποδεικνύει νέα θεωρήματα, να προσθέτει καινούργια πράγματα στα Μαθηματικά· και όχι να μιλά για τα επιτεύγματα του ίδιου ή άλλων μαθηματικών. Οι δημόσιοι άνδρες απεχθάνονται τους εκδότες, οι ζωγράφοι τους κριτικούς τέχνης, και οι γιατροί, οι φυσικοί, ή οι μαθηματικοί τρέφουν συνήθως για διάφορους παρόμοια συναισθήματα. Δεν υπάρχει πιο μεγάλος ψόγος, ή, εν γένει πιο δικαιολογημένος, από αυτόν που έχουν οι άνθρωποι που δημιουργούν για τους ανθρώπουν που αναλύουν. Η παρουσίαση, η κριτική, η εκτίμηση ενός πράγματος, θεωρείται έργο για μυαλά δευτέρας κατηγορίας.

Judged by all practical standards, the value of my mathematical life is nil; and outside mathematics it is trivial anyhow. I have just one chance of escaping a verdict of complete triviality, that I may be judged to have created something worth creating. And that I have created something is undeniable: the question is about its value. The case for my life, then, or for that of any one else who has been a mathematician in the same sense in which I have been one, is this: that I have added something to knowledge, and helped others to add more; and that these somethings have a value which differs in degree only, and not in kind, from that of the creations of the great mathematicians, or of any of the other artists, great or small, who have left some kind of memorial behind them.

I still felt a little bit sick for needing the help of a Librarian. It was frustrating. Terribly frustrating. In fact, I don’t think I can accurately—through text—show you just how frustrating it was. But because I love you, I’m going to try anyway. Let’s start by randomly capitalizing letters. “We cAn SenD fOr a draGOn to cArry us,” SinG saId As we burst oUt oF the stAirWeLL and ruSHED tHrough ThE roOm aBovE. “ThAT wILl taKe tOO Long,” BaStiLlE saiD. “We’Ll haVe To graB a VeHiCle oFf thE STrEet,” I sAid. (You know what, that’s not nearly frustrating enough. I’m going to have to start adding in random punctuation marks too.) We c! RoS-Sed thrOu? gH t% he Gra## ND e ` nt < Ry > WaY at “A” de-aD Ru) n. OnC $ e oUts/ iDE, I Co* Uld sEe T ^ haT the suN wa + S nEar to s = Ett = ING—it w.O.u.l.d Onl > y bE a co@ uPle of HoU[ rs unTi ^ L the tR} e} atY RATiF ~ iCATiON ha, pPenEd. We nEeDeD!! to bE QuicK?.? UnFOrTu() nAtelY, tHE! re weRe no C? arriA-ges on tHe rOa ^ D for U/ s to cOmMan > < dEer. Not a ON ~ e ~. THerE w + eRe pe/\ Ople wa | lK | Ing aBoUt, BU? t no caRr# iaGes. (Okay, you know what? That’s not frustrating enough either. Let’s start replacing some random vowels with the letter Q.) I lqOk-eD arO! qnD, dE# sPqrA# te, fRq? sTr/ Ated (like you, hopefully), anD aNn | qYeD. Jq! St eaR& lIer, tHqr ^ E hq.d BeeN DoZen! S of cq? RrIqgEs on The rQA! d! No-W tHqRe wA = Sn’t a SqnGl + e oN ^ q. “ThE_rQ!” I eXclai $ mqd, poIntIng. Mqv = Ing do ~ Wn th_e RqaD! a shoRt diStq + + nCe aWay < wAs > a sTrANgq gLaSs cqnTrAPtion. I waSN’t CqrTain What it wAs >, bUt It w! qs MoV? ing—aND s% qmewhat quIc: =) Kly. “LeT’s G_q gRA? b iT!

Irruption of fallen angels into the world of men. Then a new and startling event burst upon the world, and fearfully accelerated the already rapid progress of evil. “The sons of God saw the daughters of men that they were fair; and they took them wives of all which they chose.”[264] These words are often explained to signify nothing more than the intermarriage of the descendants of Cain and Seth; but a careful examination of the passage will elicit a far deeper meaning. When men, we are told, began to multiply on the face of the earth, and daughters were born unto them, the sons of God saw the daughters of men.[265] Now by “men” in each case the whole human race is evidently signified, the descendants of Cain and Seth alike. Hence the “sons of God” are plainly distinguished from the generation of Adam. The “sons of God” are angelic beings. Again; the expression “sons of God” (Elohim) occurs but four times in other parts of the Old Testament, and is in each of these cases indisputably used of angelic beings. Twice in the beginning of the Book of Job we read of the sons of God presenting themselves before Him at stated times, and Satan also comes with them as being himself a son of God, though a fallen and rebellious one.[266] For the term sons of Elohim, the mighty Creator, seems to be confined to those who were directly created by the Divine hand, and not born of other beings of their own order. Hence, in Luke’s genealogy of our Lord, Adam is called a son of God.[267] And so also Christ is said to give to them that receive Him power to become the sons of God.[268] For these are born again of the Spirit of God as to their inner man even in the present life. And at the resurrection they will be clothed with a spiritual body, a building of God;[269] so that they will then be in every respect equal to the angels, being altogether a new creation.[270]

But it was Poincare who wrote that what guided him in his unconscious gropings towards the 'happy combinations' which yield new discoveries was 'the feeling of mathematical beauty, of the harmony of number, of forms, of geometric elegance. This is a true aesthetic feeling that all mathematicians know.' The greatest among mathematicians and scientists, from Kepler to Einstein, made similar confessions. 'Beauty is the first test; there is no permanent place in the world for ugly mathematics', wrote G.H. Hardy in his classic, A Mathematician's Apology. Jacques Hadamard, whose pioneer work on the psychology of invention I have quoted, drew the final conclusion: "The sense of beauty as a "drive" for discovery in our mathematical field, seems to be almost the only one.' And the laconic pronouncement of Dirac, addressed to his fellow-physicists, bears repeating: 'It is more important to have beauty in one's equations than to have them fit experiment.

Αν η περιέργεια του πνεύματος, η επαγγελματική υπερηφάνεια και η φιλοδοξία είναι τα κύρια κίνητρα για την έρευνα, τότε σίγουρα κανείς δεν έχει πιο καλή ευκαιρία να τα ικανοποιήσει απ' ό,τι ένας μαθηματικός. Το αντικείμενό του είναι το πιο περίεργο απ' όλα - δεν υπάρχει κανένα άλλο στο οποίο η αλήθεια να παίζει τόσο παράξενα παιγνίδια. Το αντικείμενο αυτό έχει την πιο εκλεπτυσμένη και γοητευτική τεχνική, και δίνει ασυναγώνιστες ευκαιρίες για την επίδειξη μιας ανώτερης επαγγελματικής ικανότητας. Τελικά, όπως αποδεικνύει κατά πολλούς τρόπους η Ιστορία, τα μαθηματικά επιτεύγματα, ανεξάρτητα από την εγγενή τους αξία, αντέχουν στο χρόνο περισσότερο απ' όλα τα άλλα. Μπορούμε να το δούμε αυτό, ακόμη και στους πρώιμους πολιτισμούς της Ιστορίας. Ο Βαβυλωνιακός και ο Ασσυριακός πολιτισμός έχουν χαθεί· ο Χαμουραμπί, ο Σαργκόν και ο Ναβουχοδονόσωρ είναι σκέτα ονόματα. Κι όμως, τα βαβυλωνιακά Μαθηματικά είναι ακόμη και σήμερα ενδιαφέροντα, και το βαβυλωνιακό σύστημα αρίθμησης με βάση το 60 χρησιμοποιείται ακόμη στην Αστρονομία. Αλλά φυσικά, η κρίσιμη περίπτωση είναι εκείνη των Ελλήνων. Οι Έλληνες είναι οι πρώτοι μαθηματικοί που εξακολουθούν να είναι «πραγματικοί» και για μας σήμερα. Τα Μαθηματικά της Ανατολής μπορεί να προκαλούν το ενδιαφέρον, αλλά στα ελληνικά βρίσκεται η ουσία του πράγματος. Οι Έλληνες ήταν οι πρώτοι που μίλησαν με μια μαθηματική γλώσσα που μπορούν να την καταλάβουν οι σύγχρονοι μαθηματικοί. Όπως μου είπε κάποτε ο Littlewood, δεν πρόκειται για έξυπνους μαθητές σχολείου ούτε για «υποψήφιους υποτροφίας», αλλά για «Εταίρους από ένα άλλο πανεπιστήμιο». Έτσι, τα ελληνικά μαθηματικά είναι κάτι «μόνιμο», πιο μόνιμο και από την ελληνική Λογοτεχνία. Τον Αρχιμήδη θα τον θυμούνται ακόμη κι όταν ο Αισχύλος θά 'χει ξεχαστεί, επειδή οι γλώσσες πεθαίνουν ενώ οι μαθηματικές ιδέες όχι. Η «αθανασία» μπορεί να είναι μια ανόητη λέξη αλλά, κατά πάσα πιθανότητα, ένας μαθηματικός έχει περισσότερες ευκαιρίες για ό,τι μπορεί αυτή να σημαίνει. Ο μαθηματικός δε χρειάζεται σοβαρά να φοβάται ότι το μέλλον θα τον αδικήσει. Η αθανασία είναι συχνά γελοία ή βάρβαρη: λίγοι από εμάς θα διάλεγαν να είναι ο Ωγ ή ο Ανανίας ή ο Γαλλίων. Ακόμη και στα Μαθηματικά, η ιστορία παίζει καμιά φορά περίεργες φάρσες. Ο Rolle ποζάρει στα βιβλία του Στοιχειώδους Λογισμού σαν να ήταν ένας μαθηματικός του διαμετρήματος του Νεύτωνα. Ο Farey είναι αθάνατος επειδή απέτυχε να κατανοήσει ένα θεώρημα που ο Haros είχε ήδη αποδείξει πριν από 14 χρόνια. Τα ονόματα πέντε άξιων Νορβηγών βρίσκονται ακόμη στον _Βίο_ του Abel, μόνο εξ αιτίας μιας ενέργειας ενσυνείδητης βλακείας που συνετελέσθη, από τυπολατρεία, εις βάρος του μεγαλύτερου άνδρα της χώρας τους. Αλλά, συνολικά, η ιστορία της επιστήμης είναι δίκαιη, και αυτό ισχύει ιδιαίτερα στα Μαθηματικά. Κανένα άλλο αντικείμενο μελέτης δεν έχει τόσο καθαρά οριοθετημένα ή ομόφωνα αποδεκτά υψηλά κριτήρι, και οι μαθηματικοί που θυμόμαστε είναι σχεδόν πάντα αυτοί που το αξίζουν. Η μαθηματική δόξα, αν μπορούσε να εξαγοραστεί, θα ήταν μια από τις πιο υγιείς και σταθερές επενδύσεις.