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Mathematics Quotes

Unless the chemist learns the language of mathematics, he will become a provincial and the higher branches of chemical work, that require reason as well as skill, will gradually pass out of his hands Picture Quote #1

With the exception of the geometrical series, there does not exist in all of mathematics a single infinite series the sum of which has been rigorously determined. In other words, the things which are the most important in mathematics are also those which have the least foundation Picture Quote #1

... while there is such a thing as correctness in ethics, in interpretation, in mathematics, the way to understand that is not by trying to model it on the ways in which we get things right in physics Picture Quote #1

The most distinctive characteristic which differentiates mathematics from the various branches of empirical science, and which accounts for its fame as the queen of the sciences, is no doubt the peculiar certainty and necessity of its results Picture Quote #1

Women have a passion for mathematics. They divide their age in half, double the price of their clothes, and always add at least five years to the age of their best friend Picture Quote #1

Mathematics is one of the deepest and most powerful expressions of pure human reason, and, at the same time, the most fundamental resource for description and analysis of the experiential world Picture Quote #1

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It is impossible to overstate the imporance of problems in mathematics. It is by means of problems that mathematics develops and actually lifts itself by its own bootstraps... Every new discovery in mathematics, results from an attempt to solve some problem Picture Quote #1

All mathematicians share... a sense of amazement over the infinite depth and the mysterious beauty and usefulness of mathematics Picture Quote #1

It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts Picture Quote #1

I love mathematics... principally because it is beautiful; because man has breathed his spirit of play into it, and because it has given him his greatest game the encompassing of the infinite Picture Quote #1

Mathematics, in the common lay view, is a static discipline based on formulas... But outside the public view, mathematics continues to grow at a rapid rate... the guid to this growth is not calculation and formulas, but an open ended search for pattern Picture Quote #1

What humans do with the language of mathematics is to describe patterns... To grow mathematically children must be exposed to a rich variety of patterns appropriate to their own lives through which they can see variety, regularity, and interconnections Picture Quote #1

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As one reads mathematics, one needs to have an active mind, asking questions, forming mental connections between the current topic and other ideas from other contexts, so as to develop a sense of the structure, not just familiarity with a particular tour through the structure Picture Quote #1

The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking Picture Quote #1

... the discipline of economics has yet to get over its childish passion for mathematics and for purely theoretical and often highly ideological speculation, at the expense of historical research and collaboration with the other social sciences Picture Quote #1

Modern economics is sick. Economics has increasingly become an intellectual game played for its own sake and not for its practical consequences for understanding the economic world. Economists have converted the subject into a sort of social mathematics in which analytical rigour is everything and practical relevance is nothing Picture Quote #1

May not music be described as the mathematics of the sense, mathematics as music of the reason? Picture Quote #1

I feel that what mathematics needs least are pundits who issue prescriptions or guidelines for presumably less enlightened mortals Picture Quote #1

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Solving a problem for which you know there’s an answer is like climbing a mountain with a guide, along a trail someone else has laid. In mathematics, the truth is somewhere out there in a place no one knows, beyond all the beaten paths. And it’s not always at the top of the mountain. It might be in a crack on the smoothest cliff or somewhere deep in the valley Picture Quote #1

Neglect of mathematics work injury to all knowledge, since he who is ignorant of it cannot know the other sciences or things of this world. And what is worst, those who are thus ignorant are unable to perceive their own ignorance, and so do not seek a remedy Picture Quote #1

The rejection of all abstract formalism. Materialism reminds every science of its real source: the world men transform. No science can, whether in its history or its object, grasp its own origins within itself or constitute itself as a closed world, exhaustively defined by internal rules. Materialism refers every science and every activity to the reality they depend on, even if this dependence is masked by a great many abstract mediations: mathematics as well as logic, aesthetics as well as ethics and politics Picture Quote #1

If a nonnegative quantity was so small that it is smaller than any given one, then it certainly could not be anything but zero. 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. These supposed mysteries have rendered the calculus of the infinitely small quite suspect to many people. Those doubts that remain we shall thoroughly remove in the following pages, where we shall explain this calculus Picture Quote #1

The main duty of the historian of mathematics, as well as his fondest privilege, is to explain the humanity of mathematics, to illustrate its greatness, beauty and dignity, and to describe how the incessant efforts and accumulated genius of many generations have built up that magnificent monument, the object of our most legitimate pride as men, and of our wonder, humility and thankfulness, as individuals. The study of the history of mathematics will not make better mathematicians but gentler ones, it will enrich their minds, mellow their hearts, and bring out their finer qualities Picture Quote #1

The introduction of the cipher 0 or the group concept was general nonsense too, and mathematics was more or less stagnating for thousands of years because nobody was around to take such childish steps Picture Quote #1

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Besides language and music, mathematics is one of the primary manifestations of the free creative power of the human mind Picture Quote #1

The student of mathematics must get rid of all arbitrary thinking and follow purely the demands of thought. In thinking in this way, the laws of the spiritual world flow into him. This regulated thinking leads to the most spiritual truths Picture Quote #1

To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion? not because it makes no sense to you, but because you gave it sense and you still don’t understand what your creation is up to Picture Quote #1

A formal manipulator in mathematics often experiences the discomforting feeling that his pencil surpasses him in intelligence Picture Quote #1

The subtleties of mathematics defecate the grossness of our apprehension, and supply the elements of a sounder and severer logic Picture Quote #1

There isn’t an education system on the planet that teaches dance everyday to children the way we teach them mathematics. Why? Picture Quote #1

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Unless the chemist learns the language of mathematics, he will become a provincial and the higher branches of chemical work, that require reason as well as skill, will gradually pass out of his hands (Mathematics Quotes) With the exception of the geometrical series, there does not exist in all of mathematics a single infinite series the sum of which has been rigorously determined. In other words, the things which are the most important in mathematics are also those which have the least foundation (Mathematics Quotes) ... while there is such a thing as correctness in ethics, in interpretation, in mathematics, the way to understand that is not by trying to model it on the ways in which we get things right in physics (Mathematics Quotes) The most distinctive characteristic which differentiates mathematics from the various branches of empirical science, and which accounts for its fame as the queen of the sciences, is no doubt the peculiar certainty and necessity of its results (Mathematics Quotes) Women have a passion for mathematics. They divide their age in half, double the price of their clothes, and always add at least five years to the age of their best friend (Mathematics Quotes) Mathematics is one of the deepest and most powerful expressions of pure human reason, and, at the same time, the most fundamental resource for description and analysis of the experiential world (Mathematics Quotes) It is impossible to overstate the imporance of problems in mathematics. It is by means of problems that mathematics develops and actually lifts itself by its own bootstraps... Every new discovery in mathematics, results from an attempt to solve some problem (Mathematics Quotes) All mathematicians share... a sense of amazement over the infinite depth and the mysterious beauty and usefulness of mathematics (Mathematics Quotes) It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts (Mathematics Quotes) I love mathematics... principally because it is beautiful; because man has breathed his spirit of play into it, and because it has given him his greatest game the encompassing of the infinite (Mathematics Quotes) Mathematics, in the common lay view, is a static discipline based on formulas... But outside the public view, mathematics continues to grow at a rapid rate... the guid to this growth is not calculation and formulas, but an open ended search for pattern (Mathematics Quotes) What humans do with the language of mathematics is to describe patterns... To grow mathematically children must be exposed to a rich variety of patterns appropriate to their own lives through which they can see variety, regularity, and interconnections (Mathematics Quotes) As one reads mathematics, one needs to have an active mind, asking questions, forming mental connections between the current topic and other ideas from other contexts, so as to develop a sense of the structure, not just familiarity with a particular tour through the structure (Mathematics Quotes) The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking (Mathematics Quotes) ... the discipline of economics has yet to get over its childish passion for mathematics and for purely theoretical and often highly ideological speculation, at the expense of historical research and collaboration with the other social sciences (Mathematics Quotes) Modern economics is sick. Economics has increasingly become an intellectual game played for its own sake and not for its practical consequences for understanding the economic world. Economists have converted the subject into a sort of social mathematics in which analytical rigour is everything and practical relevance is nothing (Mathematics Quotes) May not music be described as the mathematics of the sense, mathematics as music of the reason? (Mathematics Quotes) I feel that what mathematics needs least are pundits who issue prescriptions or guidelines for presumably less enlightened mortals (Mathematics Quotes) Solving a problem for which you know there’s an answer is like climbing a mountain with a guide, along a trail someone else has laid. In mathematics, the truth is somewhere out there in a place no one knows, beyond all the beaten paths. And it’s not always at the top of the mountain. It might be in a crack on the smoothest cliff or somewhere deep in the valley (Mathematics Quotes) Neglect of mathematics work injury to all knowledge, since he who is ignorant of it cannot know the other sciences or things of this world. And what is worst, those who are thus ignorant are unable to perceive their own ignorance, and so do not seek a remedy (Mathematics Quotes) The rejection of all abstract formalism. Materialism reminds every science of its real source: the world men transform. No science can, whether in its history or its object, grasp its own origins within itself or constitute itself as a closed world, exhaustively defined by internal rules. Materialism refers every science and every activity to the reality they depend on, even if this dependence is masked by a great many abstract mediations: mathematics as well as logic, aesthetics as well as ethics and politics (Mathematics Quotes) If a nonnegative quantity was so small that it is smaller than any given one, then it certainly could not be anything but zero. 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. These supposed mysteries have rendered the calculus of the infinitely small quite suspect to many people. Those doubts that remain we shall thoroughly remove in the following pages, where we shall explain this calculus (Mathematics Quotes) The main duty of the historian of mathematics, as well as his fondest privilege, is to explain the humanity of mathematics, to illustrate its greatness, beauty and dignity, and to describe how the incessant efforts and accumulated genius of many generations have built up that magnificent monument, the object of our most legitimate pride as men, and of our wonder, humility and thankfulness, as individuals. The study of the history of mathematics will not make better mathematicians but gentler ones, it will enrich their minds, mellow their hearts, and bring out their finer qualities (Mathematics Quotes) The introduction of the cipher 0 or the group concept was general nonsense too, and mathematics was more or less stagnating for thousands of years because nobody was around to take such childish steps (Mathematics Quotes) Besides language and music, mathematics is one of the primary manifestations of the free creative power of the human mind (Mathematics Quotes) The student of mathematics must get rid of all arbitrary thinking and follow purely the demands of thought. In thinking in this way, the laws of the spiritual world flow into him. This regulated thinking leads to the most spiritual truths (Mathematics Quotes) To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion? not because it makes no sense to you, but because you gave it sense and you still don’t understand what your creation is up to (Mathematics Quotes) A formal manipulator in mathematics often experiences the discomforting feeling that his pencil surpasses him in intelligence (Mathematics Quotes) The subtleties of mathematics defecate the grossness of our apprehension, and supply the elements of a sounder and severer logic (Mathematics Quotes) There isn’t an education system on the planet that teaches dance everyday to children the way we teach them mathematics. Why? (Mathematics Quotes)

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