Bernhard Riemann Quotes

It is well known that geometry presupposes not only the concept of space but also the first fundamental notions for constructions in space as given in advance. It only gives nominal definitions for them, while the essential means of determining them appear in the form of axioms. The relationship of these presumptions is left in the dark; one sees neither whether and in how far their connection is necessary, nor a priori whether it is possible. From Euclid to Legendre, to name the most renowned of modern writers on geometry, this darkness has been lifted neither by the mathematicians nor the philosophers who have laboured upon it. ~ Bernhard Riemann

Nash's genius was of that mysterious variety more often associated with music and art than with the oldest of all sciences. It wasn't merely that his mind worked faster, that his memory was more retentive, or that his power of concentration was greater. The flashes of intuition were non-rational. Like other great mathematical intuitionists - Georg Friedrich Bernhard Riemann, Jules Henri Poincaré, Srinivasa Ramanujan - Nash saw the vision first, constructing the laborious proofs long afterward. ~ Sylvia Nasar

If only I had the Theorems! Then I should find the proofs easily enough. ~ Bernhard Riemann

Does anyone believe that the difference between the Lebesgue and Riemann integrals can have physical significance, and that whether say, an airplane would or would not fly could depend on this difference? If such were claimed, I should not care to fly in that plane. ~ Richard Hamming

We have relinquished and abandoned and left behind and forgotten what we believed we had to relinquish, abandon and leave behind and ultimately forget; we have let ourselves go and we have gone away and we have gone under, but we have relinquished nothing and abandoned nothing and left behind nothing and forgotten nothing; we have in reality extinguished nothing whatsoever, because our parents did not inform us of or enlighten us about the fact that our life-process is in reality nothing but a process of illness. We were up above, in the company of our parents, locked up in our walls and in our rooms and in our books and papers and everything around us and in us was nothing but lethal and we are down below, without our parents, again locked up in these walls and in our rooms and in our books and papers and everything around us and in us is nothing but lethal. ~ Thomas Bernhard

I have no regrets about my work. To be a photographer was a gift of the gods. I can't imagine anything that would have been better. ~ Ruth Bernhard

I have tried to avoid long numerical computations, thereby following Riemann's postulate that proofs should be given through ideas and not voluminous computations. ~ David Hilbert

The whole process of life is a process of deterioration in which everything - and this is the most cruel law - continually gets worse. ~ Thomas Bernhard

If you come home to a household of chaos and anger and fear, you're not going to feel protected from the world. ~ Sandra Bernhard

Philosophy has forgotten about children ~ Bernhard Schlink

I really thought I wanted to be a musical-comedy star, but I lived in Phoenix and didn't want to go all the way to New York and be that far away from home. So I thought maybe I'd be a rock 'n' roll singer or an opera singer. ~ Sandra Bernhard

We must allow ourselves to think, we must dare to think, even though we fail. It is in the nature of things that we always fail, because we suddenly find it impossible to order our thoughts, because the process of thinking requires us to consider every thought there is, every possible thought. Fundamentally we have always failed, like all the others, whoever they were, even the greatest minds. At some point, they suddenly failed and their system collapsed, as is proved by their writings, which we admire because they venture farthest into failure. To think is to fail, I thought. ~ Thomas Bernhard

Be decisive. A wrong decision is generally less disastrous than indecision. ~ Bernhard Langer

You know, as you get older, the first thing you lose is memory. It seems to be happening with me. ~ Bernhard Langer

Sometimes the memory of happiness cannot stay true because it ended unhappily.. ~ Bernhard Schlink

I learned early on that if I was to get attention, I would have to be charming. Even the models I've photographed are often like that. Some of them are not beautiful. But, if you catch them in the right light, they glow. ~ Ruth Bernhard

Everything is ridiculous if one thinks of death ~ Thomas Bernhard

He was just scraps of words and dislocated phrases. ~ Thomas Bernhard

Unfortunately, most college kids these days aren't coming from any place-they seem to ask the same kind of questions over and over again. ~ Sandra Bernhard

But of course the world consists only of absurd ideas. ~ Thomas Bernhard

Those are terrible people who don't like Glenn Gould ... I will have nothing to do with such people, they are dangerous people. ~ Thomas Bernhard

Anyone, any type of story, it doesn't have to be a crime victim, you don't have to let yourself be food for the media. ~ Bernhard Goetz

On the one hand we can't be alone, people like us; on the other we can't stand company. We can't stand male company, which bores us to death, or female company either. I gave up male company for years because it's totally unprofitable, and female company gets on my nerves in no time. ~ Thomas Bernhard

My dear loser, Glenn greeted Wertheimer, with his Canadian-American cold-bloodedness he always called him the loser, he called me quite dryly the philosopher, which didn't bother me. Wertheimer, the loser, was for Glenn always busy losing, constantly losing out, whereas Glenn noticed I had the word philosopher in my mouth at all times and probably with sickening regularity, and so quite naturally we were for him the loser and the philosopher, I said to myself upon entering the inn. The loser and the philosopher went to America to see Glenn the piano virtuoso again, for no other reason. And ~ Thomas Bernhard

Through constant self-sacrifice I had thoroughly ruined life in Desselbrunn for myself, one day it suddenly became unbearable, I thought. The beginning of this self-sacrifice had been the rejection of my Steinway, the triggering moment so to speak for my subsequent inability to tolerate life in Deselbrunn. All at once I could no longer breathe the Desselbrunn air and the walls in Desselbrunn made me sick and the rooms threatened to choke me, one has to remember how cavernous the rooms are there, nine-by-six meter or eight-by-eight meter rooms, I thought. I hated those rooms and I hated what was in those rooms and when I left my house I hated the people outside my house, all at once I was being unjust to all those people, who only wanted the best for me, but precisely that drove me crazy after a while, their constant willingness to be helpful, which I suddenly found profoundly revolting. I barricaded myself and stared out the window, without seeing anything but my own unhappiness. I ran outdoors and cursed at everybody. I ran into the woods and huddled beneath a tree, exhausted. ~ Thomas Bernhard

I feel like you've gotta be able to get up every night in front of a live audience. Whether it's 10 people or 50 people or a hundred people, whether you're in a rock band or doing the comedy circuit. ~ Sandra Bernhard

Did my moral upbrining somehow turn against itself? If looking at someone with desire was as bad as satisfying the desire, if having an active fantasy was as bad as the act you were fantasizing- then why not the satisfaction and the act itself? As the days went on, I discovered that I couldn't stop thinking sinful thoughts. In which case I also wanted the sin itself. ~ Bernhard Schlink

I tend to go against the grain because when I start to see that everybody's trying to shock, I try not to. I just do stuff that's subtler, more emotional, and I think that shocks people. ~ Sandra Bernhard

I've become this sort of icon for the gay community. I don't like the position. ~ Sandra Bernhard

Life is suffering" is misleading for at least two reasons. First, the Buddha used an ancient Indian language similar to Sanskrit called Pali, and the word he used in Pali for the first noble truth, dukkha, is difficult to translate. Dukkha is too multifaceted and nuanced a term to be captured in the one-word translation "suffering." And second, the fact of dukkha in our lives doesn't mean that life is only dukkha. ~ Toni Bernhard

Seen from across the street, he was like someone to whom the world had long since given notice to quit but who was compelled to stay in it, no longer belonging to it, but unable to leave it. ~ Thomas Bernhard

People keep a dog and are ruled by this dog, and even Schopenhauer was ruled in the end not by his head, but by his dog. This fact is more depressing than any other. ~ Thomas Bernhard

Illiteracy is dependence. By finding the courage to learn to read and write, Hanna had advanced from dependence to independence, a step towards liberation. ~ Bernhard Schlink

I don't believe in karma. ~ Sandra Bernhard