Quotes of All Topics . Occasions . Authors
Even when I was studying mathematics, physics, and computer science, it always seemed that the problem of consciousness was about the most interesting problem out there for science to come to grips with.
To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be.
The development of mathematics towards greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules.
We will always have STEM with us. Some things will drop out of the public eye and will go away, but there will always be science, engineering, and technology. And there will always, always be mathematics.
To start with invention is the mark of the fertile mind ... and leads later to the interpretation of experience; to start with the reproduction of experience is the infallible index of a barren invention.
In mathematics and science, there is no difference in the intelligence of men and women. The difference in genes between men and women is simply the Y chromosome, which has nothing to do with intelligence.
In many cases, mathematics is an escape from reality. The mathematician finds his own monastic niche and happiness in pursuits that are disconnected from external affairs. Some practice it as if using a drug.
I still remember the realization in college at Flinders University in Australia that mathematics was not just an abstract game of symbols but could be used as a tool to analyze and understand the modern world.
My father's family hails from Banaras. My grandfather taught mathematics at Banaras Hindu University. Banaras is also dedicated to Lord Shiva, home to one of the great jyotirlings, the Kashi Vishwanath temple.
I believe there are 15, 747, 724, 136, 275, 002, 577, 605, 653, 961, 181, 555, 468, 044, 717, 914, 527, 116, 709, 366, 231, 425, 076, 185, 631, 031, 296 protons in the universe and the same number of electrons.
It is indubitable that a 50-year-old mathematician knows the mathematics he learned at 20 or 30, but has only notions, often rather vague, of the mathematics of his epoch, i.e. the period of time when he is 50.
Poincaré was a vigorous opponent of the theory that all mathematics can be rewritten in terms of the most elementary notions of classical logic; something more than logic, he believed, makes mathematics what it is.
Many who have had an opportunity of knowing any more about mathematics confuse it with arithmetic, and consider it an arid science. In reality, however, it is a science which requires a great amount of imagination.
What affected me most profoundly was the realization that the sciences of cryptography and mathematics are very elegant, pure sciences. I found that the ends for which these pure sciences are used are less elegant.
When I was in Cambridge reading mathematics, I went to Amsterdam for the International Mathematics Congress. There I saw M.C. Escher's fascinating work. That inspired me to try my hand at drawing such impossibilities.
I'd like to take some calculus, too. I have absolutely no ability in that direction and not much interest, either, but there's something going on in mathematics that I don't understand, and I'd like to find out what it is.
We know that nature is described by the best of all possible mathematics because God created it. So there is a chance that the best of all possible mathematics will be created out of physicists' attempts to describe nature.
How many of you have broken no laws this month? That's the kind of society I want to build. I want a guarantee - with physics and mathematics, not with laws - that we can give ourselves real privacy of personal communications.
We can... treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth of geometrical axioms and that no special geometrical visualization exists in mathematics.
To many, mathematics is a collection of theorems. For me, mathematics is a collection of examples; a theorem is a statement about a collection of examples and the purpose of proving theorems is to classify and explain the examples.
Wherever Mathematics is mixed up with anything, which is outside its field, you will find attempts to demonstrate these merely conventional propositions a priori, and it will be your task to find out the false deduction in each case.
When Europeans first came to Africa, they considered the architecture very disorganized and thus primitive. It never occurred to them that the Africans might have been using a form of mathematics that they hadn't even discovered yet.
Even the simplest calculation in the purest mathematics can have terrible consequences. Without the invention of the infinitesimal calculus most of our technology would have been impossible. Should we say therefore that calculus is bad?
Making mathematics accessible to the educated layman, while keeping high scientific standards, has always been considered a treacherous navigation between the Scylla of professional contempt and the Charybdis of public misunderstanding.
I became an atheist because, as a graduate student studying quantum physics, life seemed to be reducible to second-order differential equations. Mathematics, chemistry and physics had it all. And I didn't see any need to go beyond that.
In terms of mathematics textbooks, why can't you have the scale of a national market? Right now, we have a Texas textbook that's different from a California textbook that's different from a Massachusetts textbook. That's very expensive.
Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality.
Although I liked especially physics and mathematics for which I had considerable talent, I decided to study medicine. This profession had for me a strong emotional appeal, which was reinforced by having an uncle who was an excellent surgeon.
I am severely dyslexic, so I'm not the person who can do a lot of typing, writing and mathematics. I don't excel in anything except in things that had to do with creativity and things with my hands. I like to build things and take things apart.
From a UX standpoint, the toughest battle is how to make a platform that's really open so kids can use it but has sort of hooks and constraints so it's actually driving towards revealing parts of the world through science or through mathematics.
When a branch of mathematics ceases to interest any but the specialists, it is very near its death, or at any rate dangerously close to a paralysis, from which it can be rescued only by being plunged back into the vivifying source of the science.
All mathematics is is a language that is well tuned, finely honed, to describe patterns; be it patterns in a star, which has five points that are regularly arranged, be it patterns in numbers like 2, 4, 6, 8, 10 that follow very regular progression.
My decision to leave applied mathematics for economics was in part tied to the widely-held popular belief in the 1960s that macroeconomics had made fundamental inroads into controlling business cycles and stopping dysfunctional unemployment and inflation.
If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability.
A nation may be born in a day, but the great truths which make for the glory and uplift of the race only through long ages permeate and control humanity. We must have the divine patience and understand the divine mathematics of a thousand years as one day.
While physics and mathematics may tell us how the universe began, they are not much use in predicting human behavior because there are far too many equations to solve. I'm no better than anyone else at understanding what makes people tick, particularly women.
I can observe the game theory is applied very much in economics. Generally, it would be wise to get into the mathematics as much as seems reasonable because the economists who use more mathematics are somehow more respected than those who use less. That's the trend.
We have such a great depth of human history in all of the arts, whether it's opera or mathematics or painting or classical music or jazz. There's so many things to study, new books to read, and certainly always ways to transform old ideas and to come up with new ones.
The total subject of mathematics is clearly too broad for any of us. I do not think that any mathematician since Gauss has covered it uniformly and fully; even Hilbert did not and all of us are of considerably lesser width quite apart from the question of depth than Hilbert.
Some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve. There's no reason why these problems shouldn't be easy, and yet they turn out to be extremely intricate.
Bitcoin and other cryptocurrencies are a form of money that's a stable field that the government can't destroy and can't distort. Because its creation is governed by the laws of mathematics. It can't happen any faster or slower than a certain rate, and it all sort of self-adjusts.
Imagine life without any algorithms at all, you wouldn't be able to do anything. This is already completely encompassing. We have a habit of over-trusting what mathematics or computer scientists tell us to do, without questioning it, too much faith in the magical power of analysis.
I earned my Ph.D. in philosophy, and one of my specializations was the logic and mathematics of game theory. I've also got a degree in drama, so I know about stories, characterizations, plot arcs, and the like. Lots of game designers can do one or the other: I've got the skills for both.
[Mathematics is] purely intellectual, a pure theory of forms, which has for its objects not the combination of quantities or their images, the numbers, but things of thought to which there could correspond effective objects or relations, even though such a correspondence is not necessary.
One would normally define a "religion" as a system of ideas that contain statements that cannot be logically or observationally demonstrated... Gödels theorem not only demonstrates that meathematics is a religion, but shows that mathematics is the only religion that proves itself to be one!
The problem is that modern fundamental physics is so far from you and me. The mathematics has become so much more complicated that you need at least 10 years to understand it. Fundamental physics has advanced so far from the understanding of most people that there is really a big disconnect.
The Universal Zulu Nation stands to acknowledge wisdom, understanding, freedom, justice, and equality, peace, unity, love, and having fun, work, overcoming the negative through the positive, science, mathematics, faith, facts, and the wonders of God, whether we call him Allah, Jehovah, Yahweh, or Jah.
My high school, the Illinois Mathematics and Science Academy, showed me that anything is possible and that you're never too young to think big. At 15, I worked as a computer programmer at the Fermi National Accelerator Laboratory, or Fermilab. After graduating, I attended Stanford for a degree in economics and computer science.
In Libya, I did well at school because I was clever. In Egyptian public school, I got the highest marks for the basest of reasons. And in the American school, I struggled. Everything - mathematics, the sciences, pottery, swimming - had to be conducted in a language I hardly knew and that was neither spoken in the streets nor at home.