Top 1200 Mathematical Problems Quotes & Sayings

I combat the errors of ages; I meet the violence of mobs; I cope with illegal proceedings from executive authority; I cut the gordian knot of powers, and I solve mathematical problems of universities, with truth-diamond truth; and God is my 'right hand man'.

Theoretical physicists accept the need for mathematical beauty as an act of faith... For example, the main reason why the theory of relativity is so universally accepted is its mathematical beauty.

An old French mathematician said: "A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street." This clearness and ease of comprehension, here insisted on for a mathematical theory, I should still more demand for a mathematical problem if it is to be perfect; for what is clear and easily comprehended attracts, the complicated repels us.

I sell my problems. I'm a woman with problems. I've had problems since the day I was born. And I have found a way to turn my problems into assets.

Most people will solve the problems they know how to solve. Roughly speaking they will solve B+ problems instead of A+ problems. A+ problems are high impact problems for your company but they're difficult problems.

If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming.

One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. We have a natural opportunity to investigate the connections of a problem when looking back at its solution.

My reasons are the same as for any mathematical conjecture: (1) It is a legitimate mathematical possibility, and (2) I do not know.

In mathematical analysis we call x the undetermined part of line a: the rest we don't call y, as we do in common life, but a-x. Hence mathematical language has great advantages over the common language.

To do any important work in physics a very good mathematical ability and aptitude are required. Some work in applications can be done without this, but it will not be very inspired. If you must satisfy your "personal curiosity concerning the mysteries of nature" what will happen if these mysteries turn out to be laws expressed in mathematical terms (as they do turn out to be)? You cannot understand the physical world in any deep or satisfying way without using mathematical reasoning with facility.

Formal logic is mathematics, and there are philosophers like Wittgenstein that are very mathematical, but what they're really doing is mathematics - it's not talking about things that have affected computer science; it's mathematical logic.

In fact, I barely missed being number one in France in both schools. In particular I did very well in mathematical problems.

The validity of mathematical propositions is independent of the actual world-the world of existing subject-matters-is logically prior to it, and would remain unaffected were it to vanish from being. Mathematical propositions, if true, are eternal verities.

It can be shown that a mathematical web of some kind can be woven about any universe containing several objects. The fact that our universe lends itself to mathematical treatment is not a fact of any great philosophical significance.

The attempt to apply rational arithmetic to a problem in geometry resulted in the first crisis in the history of mathematics. The two relatively simple problems -- the determination of the diagonal of a square and that of the circumference of a circle -- revealed the existence of new mathematical beings for which no place could be found within the rational domain.

[Referring to Fourier's mathematical theory of the conduction of heat] ... Fourier's great mathematical poem.

What a mathematical proof actually does is show that certain conclusions, such as the irrationality of , follow from certain premises, such as the principle of mathematical induction. The validity of these premises is an entirely independent matter which can safely be left to philosophers.

Many persons entertain a prejudice against mathematical language, arising out of a confusion between the ideas of a mathematical science and an exact science. ...in reality, there is no such thing as an exact science.

At the end of the day, I sit down for about five minutes and review all the problems I'm working on, research problems or writing problems, and I go to sleep. Then when I wake up in the morning, I've trained myself to not open my eyes and to just lie there and recall the problems and see if there's anything there.

The emphasis on mathematical methods seems to be shifted more towards combinatorics and set theory - and away from the algorithm of differential equations which dominates mathematical physics.

The constructs of the mathematical mind are at the same time free and necessary. The individual mathematician feels free to define his notions and set up his axioms as he pleases. But the question is will he get his fellow mathematician interested in the constructs of his imagination. We cannot help the feeling that certain mathematical structures which have evolved through the combined efforts of the mathematical community bear the stamp of a necessity not affected by the accidents of their historical birth.

Technology causes problems as well as solves problems. Nobody has figured out a way to ensure that, as of tomorrow, technology won't create problems. Technology simply means increased power, which is why we have the global problems we face today.

Mathematics is about problems, and problems must be made the focus of a student's mathematical life. Painful and creatively frustrating as it may be, students and their teachers should at all times be engaged in the process - having ideas, not having ideas, discovering patterns, making conjectures, constructing examples and counterexamples, devising arguments, and critiquing each other's work.

The mathematical question is "Why?" It's always why. And the only way we know how to answer such questions is to come up, from scratch, with these narrative arguments that explain it. So what I want to do with this book is open up this world of mathematical reality, the creatures that we build there, the questions that we ask there, the ways in which we poke and prod (known as problems), and how we can possibly craft these elegant reason-poems.

I imagine that whenever the mind perceives a mathematical idea, it makes contact with Plato's world of mathematical concepts... When mathematicians communicate, this is made possible by each one having a direct route to truth, the consciousness of each being in a position to perceive mathematical truths directly, through the process of 'seeing'.

My brother is a genius. When we went to Italy, he was on the local television channel as a prodigy, who could solve very sophisticated mathematical equations. He was only seven or eight years old but he could solve mathematical problems for fourteen year olds.

Mathematical Mark all mathematical heads, which be only and wholly bent to those sciences, how solitary they be themselves, how unfit to live with others, and how unapt to serve in the world.

The "seriousness" of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects.

When you have different kinds of scientific and mathematical minds approaching problems, you will get more solutions. This leads to more innovation and more creative design.

Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit of chemistry.... if mathematical analysis should ever hold a prominent place in chemistry -- an aberration which is happily almost impossible -- it would occasion a rapid and widespread degeneration of that science.

Before a kid learns how to use a computer that can solve mathematical problems, he or she should know how to do arithmetic without a computer.

The mathematical is that evident aspect of things within which we are always already moving and according to which we experience them as things at all, and as such things. The mathematical is this fundamental position we take toward things by which we take up things as already given to us, and as they must and should be given. Therefore, the mathematical is the fundamental presupposition of the knowledge of things.

If I were asked to name, in one word, the pole star round which the mathematical firmament revolves, the central idea which pervades the whole corpus of mathematical doctrine, I should point to Continuity as contained in our notions of space, and say, it is this, it is this!

One of the most important tools in critical thinking about numbers is to grant yourself permission to generate wrong answers to mathematical problems you encounter. Deliberately wrong answers!

I want to let you in on a little secret. There are no problems. There are no problems. There never were any problems, there are no problems today, and there will never be any problems. Problems just mean that the world isn't turning the way you want it to. But in truth, there are no problems. Everything is unfolding as it should. Everything is right. You have to forget about yourself and expand your consciousness until you become the whole universe. The Reality in back of the universe is Pure Awareness. It has no problems. And you are That.

The tantalizing and compelling pursuit of mathematical problems offers mental absorption, peace of mind amid endless challenges, repose in activity, battle without conflict, refuge from the goading urgency of contingent happenings, and the sort of beauty changeless mountains present to senses tried by the present day kaleidoscope of events.

Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover.

What distinguishes a mathematical model from, say, a poem, a song, a portrait or any other kind of "model," is that the mathematical model is an image or picture of reality painted with logical symbols instead of with words, sounds or watercolors.

Mathematical demonstrations being built upon the impregnable Foundations of Geometry and Arithmetick are the only truths that can sink into the Mind of Man, void of all Uncertainty; and all other Discourses participate more or less of Truth according as their Subjects are more or less capable of Mathematical Demonstration.

One might think this means that imaginary numbers are just a mathematical game having nothing to do with the real world. From the viewpoint of positivist philosophy, however, one cannot determine what is real. All one can do is find which mathematical models describe the universe we live in. It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless believe in for other reasons. So what is real and what is imaginary? Is the distinction just in our minds?

One of the places where research is needed is all the sensory problems. And you get sensory problems not just with autism, but with dyslexia, learning problems, ADHD, attention deficit, you know, things like sound sensitivity, problems with fluorescent lighting.

Nature seems to take advantage of the simple mathematical representations of the symmetry laws. When one pauses to consider the elegance and the beautiful perfection of the mathematical reasoning involved and contrast it with the complex and far-reaching physical consequences, a deep sense of respect for the power of the symmetry laws never fails to develop.

This common and unfortunate fact of the lack of adequate presentation of basic ideas and motivations of almost any mathematical theory is probably due to the binary nature of mathematical perception. Either you have no inkling of an idea, or, once you have understood it, the very idea appears so embarrassingly obvious that you feel reluctant to say it aloud.

Mathematical thinking is not the same as doing mathematics - at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box - a valuable ability in today's world.

The classes of problems which are respectively known and not known to have good algorithms are of great theoretical interest. [...] I conjecture that there is no good algorithm for the traveling salesman problem. My reasons are the same as for any mathematical conjecture: (1) It is a legitimate mathematical possibility, and (2) I do not know.

The older I get, the more I believe that at the bottom of most deep mathematical problems there is a combinatorial problem.

I believe that no one who is familiar, either with mathematical advances in other fields, or with the range of special biological conditions to be considered, would ever conceive that everything could be summed up in a single mathematical formula, however complex.

The problem with cinema nowadays is that it's a math problem. People can read a film mathematically; they know when this comes or that comes; in about 30 minutes, it's going to be over and have an ending. So film has become a mathematical solution. And that is boring, because art is not mathematical.

The problems we face aren't Democratic problems or Republican problems. These are Maryland's problems.

Mathematics is a logical method. . . . Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.

In some instances even certain social services that normally were supplied, or pre-empted by the state. Take the United States, the [Ronald] Reagan administration is withdrawing assistance, all kinds of welfare programs, and if people don't improvise their own resources to cope with problems of the ageing, problems of the sick, problems of the young, problems of the poor, problems of tenant rights, who will?

In studying mathematics or simply using a mathematical principle, if we get the wrong answer in sort of algebraic equation, we do not suddenly feel that there is an anti-mathematical principle that is luring us into the wrong answers.

America has a lot of problems, believe me. I know what the problems are even better than you do. They're deep problems. They're serious problems. We don't need more.

All the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities by operations with numbers.

... mathematical knowledge ... is, in fact, merely verbal knowledge. "3" means "2+1", and "4" means "3+1". Hence it follows (though the proof is long) that "4" means the same as "2+2". Thus mathematical knowledge ceases to be mysterious.

Cell and tissue, shell and bone, leaf and flower, are so many portions of matter, and it is in obedience to the laws of physics that their particles have been moved, moulded and conformed. They are no exceptions to the rule that God always geometrizes. Their problems of form are in the first instance mathematical problems, their problems of growth are essentially physical problems, and the morphologist is, ipso facto, a student of physical science.

There are no negro problems, or Polish problems, or Jewish problems, or Greek problems, or women's problems, there are HUMAN PROBLEMS”.

The mere formulation of a problem is far more essential than its solution, which may be merely a matter of mathematical or experimental skills. To raise new questions, new possibilities, to regard old problems from a new angle requires creative imagination and marks real advances in science.

For most problems found in mathematics textbooks, mathematical reasoning is quite useful. But how often do people find textbook problems in real life? At work or in daily life, factors other than strict reasoning are often more important. Sometimes intuition and instinct provide better guides; sometimes computer simulations are more convenient or more reliable; sometimes rules of thumb or back-of-the-envelope estimates are all that is needed.

The problems in the world today are not political problems, they are not economic problems, and they are not military problems. The problems in the world today are spiritual problems. They have to do with what people believe. They have to do with our most fervently held thoughts and ideas about Life, about God, and most of all, about ourselves, and our very reason for living.