Statements about mathematics as an abstract science can be found not only in historical sources, but also in everyday conditions, where you need to make calculations and measurements. We perform operations of describing objects in terms of volume and shape every day. Starting with the number of spoons of sugar put in coffee, to the exact deduction of the interest rate of the loan.
Definition
The first definitions and statements about mathematics can be found in the French philosopher Rene Descartes: “It is necessary to unite under the old, well-known concept of universal mathematics, everything that needs to be put in order, or measure the measure. And it doesn't matter what measurements will be taken, numbers or sounds, stars or figures.”
In the Soviet Union, A. N. Kolmogorov's statement was considered traditional: “This is a science where the quantitative relation is closely connected with the real form of the surrounding world. But only inextended and completely abstract concept.”
Nicolas Bourbaki is a group of French scientists who have written several books on modern science. The group was created in 1935, statements about mathematics were in the epigraph of the first edition: “The essence of this great science can be called the doctrine of the impact of objects on each other. Some properties of objects may not be known, but they can be calculated using known, fundamental qualities. It is a set of abstract structures.”
Hermann Weyl doubted that it was possible to give a clear definition of mathematics at all: “The question of the foundations can be considered open. It is hard to imagine that over time we will find a definition of mathematics that will suit everyone. Since it is rather not a science, but a creative activity, like music or versification.”
Science Quotes
Sayings about mathematics by great mathematicians and short quotes ask more questions than answer them:
- "This is the tool of any scientist, like a scalpel for a surgeon" (N. Abel).
- "There is only beauty on earth, the main thing in beauty is form, the ideal form is ideal proportions, proportions consist of numbers. Conclusion: beauty is numbers" (A. Augustine).
- "The main benefit of mathematics for ordinary people is that it is difficult" (A. Alexandrov).
- "This is the science of rigor and clarity. In moral terms, it can be considered a truth that is clear and does not like fog" (L. Behrs).
- "Mathematics is an unshakable structure and a true prophecy" (L. Behrs).
Mistakes and miscalculations
Sayings about mathematics by great mathematicians remind us that this science excludes the possibility of errors in any field of activity:
- "Math does not tolerate mistakes" (E. Bell).
- "There is no such thing as 'obvious'" (E. Bell).
- "Even the ancient Greeks said "mathematics", but meant "proof"" (N. Bourbaki).
- "Five terms - point, angle, body, line and surface - this is mathematics. But the perspective of artists is decided by these concepts" (L. da Vinci).
- "A mathematician's mistake can cost the life of not only one person, but the whole civilization" (N. Bourbaki).
- "We get flour from grain. But the millstones grind what is put into them. You fill up the quinoa, you won't bake bread. So it is in mathematics, if you make a mistake at the beginning, you won't get the right conclusions" (T. Huxley).
- "There are no incompetent in this science. So, you just treated learning carelessly" (I. Herbart).
Aphorisms about algebra
The statements about mathematics by great mathematicians are not only a broad concept of computation, but also a narrow focus on algebra, geometry and physics:
- "Algebra is more than science, it's a way of talking about science" (N. Bohr).
- "This can't be hard work, algebra is made for fun and to help people" (R. Bringhurst).
- "Art is hidden algebra. It takes all the time andlife itself for those who want to penetrate its secret "(E. Bourdelle).
- "Practice is born from the union of algebra, physics and geometry" (R. Bacon).
- "You can't really understand algebra without being a poet" (K. Weierstrass).
- "Algebra and the natural sciences need to establish the deepest interaction. It is often perceived as an auxiliary discipline. But it is necessary to consider deeper issues" (K. Weierstrass).
- "Solving problems in algebra means capturing an enemy fortress and placing your own flag on the towers of a defeated city" (N. Vilenkin).
Geometry as visual reasoning
The sayings of great people about mathematics and geometry can be created by yourself or you can see the truth with your own eyes.
- "If you look closely, everything that surrounds us is geometry" (A. Alexandrov).
- "Aren't there contradictions, mysteries and troubles in geometry?" (D. Berkeley).
- "Geometry and logic are two miracles. Here, all definitions are clear, no one disputes the postulates, clear reasoning translates into an observational process to identify the properties of the figure, and the figure is always in front of you. All this forms the habit of thinking sequentially" (D. Berkeley).
- "Elementary geometry makes you use unusual, even witty tricks" (E. Borel).
- "We carry on our shoulders the whole burden of Greek scientific thought, we follow the path of the heroes of the Renaissance, since civilization cannotexist without geometry" (A. Weyl).
- "Geometry brings order to the chaos of everything that surrounds us" (N. Wiener).
- "Our whole world can be calculated geometrically" (N. Wiener).
The beauty of computing
Sayings about mathematics by great mathematicians confirm that the beauty of figures and numbers can be compared with true art:
- "Number is the first perception of the ideal. Pleasure is in the very feeling that certain numbers can welcome equal intervals and disapprove of disorderly ones" (A. Augustine).
- "Intuition can be legitimized in mathematical rigor" (J. Hadamard).
- "The science of computing forms the character and personality of a person by the clarity of thought and logical truths that can be proved" (A. Alexandrov).
- "Numbers, despite their external severity, are full of internal heat of knowledge" (A. Alexandrov).
- "The Pythagoreans considered mathematics to be the beginning of all things" (Aristotle).
- "When solving one problem with the analysis of a specific action, it is possible to formulate general techniques that will be useful for solving such problems where there is an unknown" (M. Bashmakov).
- "Science has developed in such a way that today's solid stone of knowledge can turn into a web in a few years" (E. Bell).
Profession or life
A. V. Voloshinov's statements about mathematics introduce us to the great science. Allow us to perceive it as part of ourlife:
- “Mathematics will always be the mistress of all directions and disciplines. The purity of mathematics has no peaks, it is infinite. It is the link that links art and computing.”
- “Only this computational science in its development was devoid of materiality. This property makes her omnipotent. Today, every person who is not related to mathematics knows that this is a great force, the influence of which has no limits.”
- "Only those who are truly in love with science can afford true statements in mathematics."
- "Mathematics found a meaningful and systematic application to art in music, as well as in the work of Pythagoras and his students."
- "Mathematics is beautiful in itself, but when it brings this beauty to the development of civilization, it becomes a search for perfection."
Pythagoras's statements about mathematics as a science of the beginnings
The most famous saying of Pythagoras sounds like a slogan for followers: "Everything is a number."
Other of his statements, more philosophical, can be interpreted as you like:
- "Do great things, but don't promise great things."
- "To learn the laws of mathematics, try to learn the language of numbers first."
- "Explore everything you see, let your mind come first."
Lomonosov's statements about mathematics
Russian scientist Mikhail Vasilyevich was not only a great scientist, he explored all branches of science: from chemistry to versification. Mostthe quoted statement of Lomonosov about mathematics is the following: “Mathematics should be known already because it puts the mind in order.”
You can also find statements about specific disciplines in Lomonosov:
- "Geometry is the queen of all thoughtful research".
- "Chemistry is the hands of physics, and the eyes are mathematics itself."
- "A physicist is blind without the science of calculation".
- "Everything that is doubtful in such sciences as aerometry, hydraulics and optics, mathematical calculation will make clear, obvious and true."
Witty reasoning
Sayings about mathematics of great mathematicians sometimes look like witty sayings. Some can only be understood by knowledgeable people, but there are quotes available to everyone:
- "Different objects and things can be named the same thanks to calculations and formulas" (A. Poincaré).
- "A person who is not familiar with the basics of the science of numbers cannot succeed in any business" (R. Bacon).
- "Mathematics is the study of different formulas and their relationship, only there is no content" (D. Hilbert).
- "If no one could prove a theorem, they call it an axiom" (Euclid).
- "Mathematics can do everything! Only what is needed right now cannot" (A. Einstein).
Adapted Sayings for Children
We remember statements about mathematics for children from school years, when under each portrait of a scientist his thoughts and attitude toScience:
- "It is not enough to have a penetrating mind, you need to find a use for it" (R. Descartes).
- "The hardest thing is to know yourself" (Felas).
- "Before you start solving a problem, you need to carefully read the conditions" (J. Hadamard).
Quotes from the greats
The statements of scientists about mathematics and science in general once again prove that one simply cannot do without the rudiments of elementary knowledge in the modern world:
- "In any science one can find the percentage of truth that is contained in the science of calculation" (Kant).
- "Mathematicians are like Italians. You tell them something, they immediately translate into their own language, and we get back something opposite" (Goethe).
- "The laws of computation that are relevant to the real world are unreliable. And the most reliable laws are abstract" (A. Einstein).
- "Since the time mathematicians began to calculate the theory of relativity, I myself do not understand it anymore" (A. Einstein).
The sayings of great people about mathematics are not always flattering. But we have to admit that our civilization cannot exist without the science of numbers.
