SCIENCE AND CHRISTIANITY
QUEEN OF SCIENCE
About the fallen universe and where they come from
priests with academic degrees
Why do people involved in science, especially physics and mathematics, so often come to believe in God? Is it possible that their critical mind, their reliance on an accurate, experimentally verified fact, is capable of perceiving the unprovable - that which is beyond human understanding?
I have come across very different explanations for this. This is what, for example, Professor S.B. Stechkin wrote about mathematics. He jokingly divided all sciences into four groups: natural sciences (such as physics, chemistry, biology, geology), unnatural (history, art history), unnatural (“scientific communism”) and supernatural. To the latter, along with theology, the professor also included mathematics, which he studied all his life.
His colleague G.A. Kalyabin, no longer jokingly, but quite seriously, developed this idea - about the affinity of mathematics and theology. He noted that the most famous mathematical term“theorem” means “said by God” (“theos” is Greek for God), and the main provisions of mathematical theories are called “axioms”; at the same time, “axios” (worthy) is the exclamation of the bishop upon ordination to the clergy. Mathematics is the queen of all sciences (“mathematics” in Greek means “science”, “reliable knowledge”), and it is no coincidence that over the course of thousands of years it has not undergone a single “revolution”, unlike, say, physics or biology. In the same way, theological sciences are solid and unchanging, since they proceed from a small number of axioms-dogmas, the slightest error in which can lead to huge distortions of Divine truth. The new realities and needs of church life are verified once and for all by established church dogmas. In the same way, mathematical apparatus is used to describe natural phenomena and verify the truth of new scientific results.
I came across these interesting statements on the website of a Physics candidate. mathematical sciences Nikolai P. (he does not indicate his full last name). P. himself illustrates them with his own observations - how theology and science are connected.
For example, the dogma of the trinity of God, in his opinion, is surprisingly revealed in modern model material world. The nucleus of an atom, as is known, consists of protons and neutrons. The proton, in turn, consists of two u-quarks and one d-quark. Electric charge The u-quark is “+2/3”, and the d-quark is “-1/3”. All together it looks like this: 2/3+2/3-1/3=1. Total proton charge equal to one and is positive. That is, the trinity of quarks is identical to one, as in the dogma of the Trinity.
Now let's look at the neutron. It consists of two d-quarks and one u-quark (2/3-1/3-1/3=0), that is, the neutron has zero charge. “It is said that “faith without works is dead” (James 2:20), - comments P. - So a neutron with zero charge decays in a free state in 15 minutes. But now let's look at the proton, which has a charge of one. The proton lives, essentially, forever. It is clear that through the properties of the proton, the promise of God for the righteous of the Kingdom of God is written..."
Here is another example that struck me with its obviousness. I used to think that the loss of our Earth in the depths of space was somehow inconsistent with Biblical history. If man is the crown of God’s creation, then why didn’t the Creator place him at the center of the universe? Here is what P. writes about this:
“The fact of the “material” (but not “spiritual”!) abandonment of humanity as a result of the Fall can be illustrated with the help of such drawings. On one of them we see that our solar system nestled at the very edge of the galaxy. On the other is our galaxy in the expanding Universe (it is shown as a cellular grid expanding in all directions, consisting of many galaxies). Look how small and lost our world is! The very structure of the Universe seems to show and symbolize to us that we cannot get out of the state of the Fall on our own: we definitely need a Savior.”
Something in the reasoning of Nikolai P., candidate of physical and mathematical sciences, who wished to remain incognito, seemed familiar to me. I remembered Nikolai Nikolaevich Popov, also a Ph.D. candidate, whom I had the chance to meet in Moscow at the “Science and Christianity” conference. The scientist’s modesty surprised me even then: his most interesting report on six-dimensional space-time was read from the pulpit by a priest friend, and the author himself sat in the “Kamchatka” lecture hall like a student (see article "Axis of Time") . And so, going to this annual conference today, I decided to ask the scientist in more detail about the theory of the “fallen universe.” N.N. Popov was not there this time, but I still received answers to my questions.
I made it to the lecture hall of the Moscow State University physics department towards the end of someone’s report. The speaker spoke precisely on “my” topic:
– What prevents a Christian from unconditionally, literally believing the Biblical text of the book of Genesis? The contradictions between the described picture of creation and ours interfere modern world. But before there were no contradictions! They appeared only when Western theology penetrated us. Catholics, when talking about the origin of the world, made a big mistake - they identified the world that we now see with the first-created world. Unlike them, our fathers Eastern Church, primarily Basil the Great and Gregory the Theologian, argued something else: the world spoken of in the book of Genesis changed radically after the Fall of Adam. We are in a fallen age and fallen space. Therefore, our cosmological standards are not applicable to the Bible. Thank you for attention.
The speaker left the lecture hall to applause. My Kamchatka neighbor, whom I hurriedly sat down with, turned to me:
- He speaks correctly! The Western scholastic school has gotten a lot of things wrong for us. Where did everything come from? From Thomas Aquinas - after all, he decided that the created world and the present world are one and the same. In general, scholasticism is a congenital vice of our mathematicians, physicists and everyone who views the cosmos as an inanimate, soulless mechanism. It doesn’t even occur to them that the universe can be sick...
The speaker himself was clearly experiencing painful sensations - his cheek was swollen with a rounded gumboil, the words he spoke reeked of the smell of a rotting tooth. Tousled hair, a thick sweater and a long scarf, the end of which touched the floor, completed the flavor of the “free explorer” as he presented himself.
– Aren’t you a mathematician?
- Well, what are you talking about! I am a plant physiologist. If you're curious, you can see my work...
The neighbor took from his briefcase a stack of thin brochures with scientific articles. Almost all of them were in physiology, but one seemed interesting to me - “Creation + Evolution”. Despite the abundance of terms (episteme, coherence, chromatin code, etc., etc.), I still understood something. The text provides an interesting diagram:
Symbol T means the Creator ABOUT– organic matter, N- inorganic matter, and the arrows are the vectors of creation and evolution. The surprising thing is that this diagram was compiled by none other than the “father” of atheist evolutionists, Charles Darwin. It turns out that he believed in God and placed the Creator at the beginning of his “evolutionary chain.” But for some reason they didn’t tell us about this at school.
At the end of the brochure on the evolution of fallen matter, a comprehensive conclusion is given:
“...After the incarnation of Adam and the creatures in earthly forms a repeat situation occurs - man again tries to turn all of Nature towards himself. At the same time, sometimes they hypocritically appeal to the Bible, to the Judeo-Christian tradition, saying that man was given power over Nature by the Creator Himself. But such power was given to man in Paradise, when Adam freely talked with God. Nowadays a person in to a greater extent You should follow the rules of the person living in the hostel rather than the owner...”
While I was reading, another latecomer to the conference joined us. A priest of enormous stature, with a bulging forehead, he was somewhat reminiscent of St. Nicholas of Myra.
- No, what is he saying! – “Nikola” suddenly threw up his shovel-like hands.
From the brochure I immediately switched to the report: an old academic-looking priest stood at the pulpit and discussed the topic: “Is it possible for us to know nothingness - that pure nothingness from which God created matter.”
“This is a question beyond the roof,” “Nikola” turned to me, trying to quiet his booming bass voice. – We should somehow cling to the essential, but he is about “nothing”! How can we know this?
“Science is obliged to know everything,” I answer him.
“Well, of course, that’s all,” the priest chuckled. – I have a friend, he defended his candidate’s dissertation on a similar topic: “Silence as the Zero Act.” By the way, he himself is a big silent person.
“And this speaker is a typical scholastic,” the physiologist interjected into our conversation. - A sort of monk in a cassock with scientific degree physical and mathematical sciences. In general, look how many priests have gathered here, and that’s all former physicists. They, physicists, go to church because dry logic eats them up, so they are drawn to the living.
“But I also graduated from the physics department,” the priest laughed. – Only about the logic you are wrong. It seems that Deacon Andrei Kuraev said that no one has ever used dialectics, through deductive method, like Sherlock Holmes, did not come to God. Agree. But I can say that for people who have studied physics and science in general, this deductive method is very helpful in acquiring faith. He cuts off the unnecessary, various Eastern cults, sects - and the remainder leaves only Orthodoxy, that is, the Truth.
“But it’s true that many priests have turned out to be physicists,” I take the side of my neighbor-physiologist. - Why is that?
“Well, I would say so,” the priest rubbed his prominent forehead. – Physicists are accustomed to critically evaluate reality, to start from bare obvious fact. And who else but them should know: human works are weak, but Divine ones are immeasurably more powerful than what a person can create. You see the works of God in the universe, you see His greatness - and, accordingly, you are looking for a faith in which the Lord appears in this greatness and sets a high task for you. Well, where is there even more? high goals, if not in Christianity? Christ said: be perfect like the Heavenly Father. Much higher...
– Do you yourself regret that you left science?
“The parish also has a lot of physics,” Father Georgy laughs again, “the roof is leaking, it needs to be patched.” This and that. In general, in the village of Pervo Maya I have a wonderful St. Nicholas Church, and the community is wonderful. But this is a separate conversation.
The conference continued, but I decided to wrap it up - I found out everything I wanted. As a farewell gift, I gave Father George our newspaper (he was very surprised to learn that I was from it - he subscribed to “Vera”) and asked for a blessing for the journey. The priest, in a booming whisper, trying not to attract too much attention, made the sign of the cross in the name of the Father and the Son and the Holy Spirit.
Having lingered in the corridor labyrinths of Moscow State University, I did not immediately get out into the street. I approach the locker room and see the huge figure of Father George in the street door. He is already dressed, a briefcase under his arm, concern on his face. After all, I never sat at the conference among my fellow physicists! He is in a hurry somewhere, apparently on his parish business. Once in a while you get to Moscow, but you need to buy something for the temple, and order something, and bookstores walk. Isn't there enough to do?
M. VYGIN
Sayings of scientists. Mathematics is the queen of sciences, and arithmetic is the queen of mathematics. K. Gaus
Aristotle. Mathematics... reveals order, symmetry and certainty, and this is most important species beautiful. Aristotle (384 BC BC), ancient Greek philosopher.
A Strong Science Mathematics is a complex but interesting science. Mathematics is the language in which the book of nature is written. G. Galileo Galilei Galileo ()
A physicist without mathematics is blind. (M.V. Lomonosov) A mathematician who is not to some extent a poet will never be a real mathematician. (K. Weierstrass) Mathematics is the language spoken by all the exact sciences. (N.I. Lobachevsky) Mathematics is the best and even the only introduction to the study of nature. (D.I. Pisarev) Astronomy (as a science) began to exist since it was combined with mathematics. (A.I. Herzen)
Mathematics is the queen. If you don’t know mathematics, it’s difficult for you to live in this world. Without mathematics, of course, you won’t be able to: divide, multiply and add. Physics and chemistry are friends with it, geometry is always with it, mathematics, of course, is the power and queen in its field.
Tasks: 1. Guess the riddle To dress your sons warmly, Two socks are missing. How many sons are there in a family, If there are six socks in the house?... 2. Think! The three little pigs built three houses out of straw, twigs, and stones. Each of them received one house: Nif-Nif - not made of stones or twigs; Nuf-Nuf is not made of stones. Which house did Naf-Naf get? /
3. Solve the problem. The canteen received 200 kg of fruit. There were 150 kg of apples and oranges, and kg of oranges and pears. How many individual apples, oranges and pears were brought to the dining room? 4.Using the number key given in each example, try to find the numbers. All numbers are different =12 =10 =11
5. Determine your age. Masha is 4 years older than Nastya. Nastya is now 15 years old. How old will Masha be in 5 years? 6. Solve puzzles. PO100 O 7 I S3ZH 100lb 7. Place between the numbers 1,2,3,4,5,6 and 7 for a total of 3 mathematical sign(+ and -) so that the result is 2.
8. Arrange the brackets so that the equality is true: 4 = 5 9. The area of the rectangle is 91 square meters. cm. The length of one of its sides is 13 cm. What is the sum of all sides of the rectangle? 10. Think! The passenger was traveling by taxi to the village. On the way he met 5 trucks and 3 cars. How many cars in total went to the village? Good luck!
Even in ancient times, people were confident that numbers were a secret code with which one could understand the structure of our world. Thousands of years have passed since then, and modern scientists not only share the opinion of our ancestors, but also never cease to prove that mathematics is the queen of sciences. In music, in a plate, in the elements... Numbers can express everything that exists in our world. But what do we ourselves know about this mysterious and at the same time the most accurate science?
Mathematics is the queen of sciences. Who said this phrase? We know exactly what the numbers are called and in what order they follow each other. But how often do we think about where the numbers come from, why they look this way and not otherwise? Why exactly did they become the main instrument of mathematics?
Ancient numbers
“Mathematics is the queen of sciences, and arithmetic is the queen of mathematics” - these are the words of the famous German mathematician Carl Gauss.
The history of mathematics begins approximately from the moment our ancestors realized that the number of pots and hunting equipment required accounting. This is how the prototypes of numbers and the very first mathematical operation- addition.
The need for mathematical calculations grew every day. It was necessary to be able to accurately count not only the number of people in one’s community, but also the number of livestock and the area of pastures. WITH rapid development trade and construction ownership elementary mathematics became a guarantee of well-being. To survive and feed their families, people had to be able to count.
Indeed, mathematics is the queen of sciences, and arithmetic is what this science began with and without which it cannot exist.
Egyptian system
It is not surprising that very soon we will wear a large number of stones and sticks for counting became very inconvenient. The ancient Egyptians solved this problem. Around the 3rd millennium BC. e. they introduced the first generally accepted system of writing numbers. Thus, the unit was represented by a short vertical stick, the number 10 was indicated by a hieroglyph in the form of a horseshoe, and the number 100 by a measuring rope. And the most big number- 10 million - depicted as the god Amon Ra in the form of the rising sun.
Record any big composite number took a lot of time, and any mathematical work required time and knowledge, so mathematics was studied only by priests or other people associated with the cult.
There was no separate science of mathematics; there was, according to Aristotle, metaphysics, which united all sciences. She was an element secret knowledge, which was owned by the priests.
The only mathematics that man has encountered is counting money. And in general, from the moment the formula “commodity-money-commodity” appeared, calculations have great value for a person.
Arabic numerals
Familiar to us Arabic numbers appeared only several thousand years later. By the way, the history of the birth of these numbers is still very confusing. Until now, no one knows how and under what circumstances they were invented. It is certain that they are not Arabs.
This happened at the end of the 1st millennium AD. e. The numbers belong to the Hindus, but at first they had a completely different meaning.
It is surprising that such an exact science was formed under the influence of esoteric and religious beliefs. Representatives of ancient civilizations often chose sacred signs to depict numbers.
Mathematics is the queen of sciences, and numbers are its unique tool. If you look around, it becomes obvious that they surround us everywhere.
Mathematics in music
Each of us likes harmonious music. It evokes pleasant emotions, helps you relax, and can lift your spirits. But is it only thanks to the skill of the musician? It turns out that there is mathematics behind the harmonious combination of sounds. The Queen of Sciences decreed that two notes separated by a musical interval such as an octave sound beautifully together. This is the most perfect combination in music. An octave is the ratio of frequencies between sounds, which can be written mathematically as 1/2. A perfect fifth is 3/2, a major third is 5/4. However, any combination of notes is written using the usual mathematical proportion. The connection between music and mathematics was guessed back in ancient times, and Pythagoras was the first to think of this.
“Music is the secret arithmetic of the soul, which does not know what it is calculating,” the famous philosopher and mathematician Leibniz once noted.
The universality of mathematics never ceases to amaze. It seems that the power of this science is generally limitless. Even natural disasters can be calculated mathematically.
Mathematics in the elements
A group of Russian mathematicians has found a way to simulate and calculate natural disasters of the future. Using mathematical pattern recognition, scientists calculated zones for predicting the most strong earthquakes. An algorithm was also developed that helps prevent accidents at enterprises.
Children begin to study this subject as early as preschool age, and in schools the wall newspaper “Mathematics - the Queen of Sciences” has already become traditional, which students draw during the week of this subject in the walls educational institution. They depict various mathematical problems, crosswords and interesting stories.
Fairy tale story
Why is mathematics the queen of sciences? In one fairy-tale dimension there existed a Kingdom. The head of it was Natural Science, Mathematics, his wife was the queen, and Literature, their daughter, was the princess. The family lived in complete harmony, and they had many servants - auxiliary sciences.
But one day Mathematics, the queen of sciences, had a fight with her husband, and, offended, simply left the Kingdom.
Very quickly, real confusion began in the fairy-tale state. The Princess of Literature could not number pages in books and chapters in novels. Natural science could not count either the planets, or the stars, or the days of the week, or the months of the year. History could not determine the exact dates of events, and geography could not calculate the length of rivers and the distances between seas. Chaos ensued because the cook could not weigh the food and the builders could not build the tower. Not a single resident fairyland I couldn't do without Mathematics.
Then the Tsar gave orders to all ambassadors and messengers to find the princess and return her back to the kingdom. And when Mathematics, the queen of sciences, returned, order and harmony came again in the Kingdom of Sciences.
Ivanova Ekaterina, student of MBOU "Secondary School No. 43", Nizhnevartovsk
The purpose of this work is to prove the statement that “Mathematics is the queen of all sciences” and for all times. To achieve the goal, statements about the importance of mathematics from people living in different time, the connection between mathematics and other sciences is traced through quotes, aphorisms and statements of people, a survey is conducted among students in grades 5-6 “What does mathematics mean to me?”
During the work, 125 statements about mathematics were considered famous figures science, art, culture, political figures from the time of Aeschylus to the present day.
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Ivanova Ekaterina Dmitrievna
MBOU "Secondary School No. 43", 5th grade
Research Plan
"Mathematics is the queen of all sciences." This is the saying written above school board in the mathematics classroom, asserts the superiority of all kinds of formulas and numbers. Has it always been like this? Or did it happen after a certain period? I set myself
target prove the statement that “Mathematics is the queen of all sciences” and for all times.” To achieve my goal I need to decide the following tasks :- Find quotes and aphorisms about mathematics;
- Study the statements of great people about the importance of mathematics living at different times;
- Trace the connection of mathematics with other sciences through quotes, aphorisms and statements.
- Conduct a survey among students in grades 5-6 “What does mathematics mean to me?”
This project is relevant because it forms in students an idea of mathematics as a science useful for studying other subjects, improves development intellectual abilities, broadens the horizons of students.
Practical significanceThe project lies in the fact that its materials can be used both in mathematics lessons and in other lessons, as additional material, when preparing students for olympiads and competitions.
Scientificity work is determined by the fact that I consider several hypotheses:
- Mathematics is the first of all sciences, both useful and necessary for them. (R. Bacon)
- Mathematics is the language in which the book of nature is written. (G. Galileo)
- Mathematics is one of the art forms. (N. Wiener)
- Mathematics is the shortest way to independent thinking. (V. Kaverin)
To successfully solve the problems of my project, I found out the definitions and meanings of the words:
Quote - a verbatim excerpt from a text.Quoting the text verbatim is accepted in scientific literature to convey the author's thoughts without distortion. Part of the quotation may be omitted, which is indicated by an ellipsis in place of the missing text.In Russian, the word “quote” has been used since the 1820s. The word “quote” has been noted in dictionaries since 1861.
Aphorism (Greek “definition”) - an original complete thought, expressed or written down in a laconic, memorable text form and subsequently repeatedly reproduced by other people.
Statement - a speech work created during a specific speech act. Considered in the context of this speech act as part of the text.
In the course of my work, I examined 125 statements about mathematics by famous figures in science, culture, art, politicians starting from the 4th century BC. from the time of Aeschylus to the present day. All data was recorded in tables. For example:
In the process of analyzing the collected material, the hypotheses were proven.
Preview:
1. Introduction 2
2. Proof of the hypotheses put forward
2.1 Mathematics is the first of all sciences, both useful and necessary for them. 2
2.2 . 3
2.3 4
2.4 5
3. Sociological survey 7
4.Conclusion 8
5. List of references and Internet resources 9
Mathematics is the queen of all sciences
Ivanova Ekaterina Dmitrievna
MBOU "Secondary School No. 43", 5th grade
Research Article
- Introduction
The importance of mathematics is now continuously increasing. New ideas and methods are born in mathematics. All this expands the scope of its application. Nowadays it is no longer possible to name an area of human activity where mathematics does not play a significant role. It has become an indispensable tool in all natural sciences, technology, and social science. Even lawyers and historians are using mathematical methods.
Any science uses mathematical methods. The task of mathematics is to develop those models and methods that will allow solving a wide variety of problems. The most common applications of mathematics are used in mechanics and physics. It is there that you can see the application of mathematics achievements more clearly. For example, recognition by a missile for the “friend or foe” task is based on mathematical calculations. Mathematical accuracy is needed in many areas of our lives: for example, when designing modern aircraft, during the construction of any objects.
If a signal is encoded, it can be both decoded and re-encoded. This means there is a security problem. Databases and banking transactions will require additional protection. All these problems can be successfully solved with the participation of mathematics. Mechanic and shipbuilder Alexei Nikolaevich Krylov noted that “Sooner or later, every correct mathematical idea finds application in one thing or another.”
In my work, I turned to the statements of famous scientists, writers, and political figures from the time of Aeschylus to the present day.
- Proof of the hypotheses put forward
2.1 Mathematics is the first of all sciences, both useful and necessary for them.(Roger Bacon)
The first statement about mathematics as a science is known, which was said by the ancient Greek playwright Aeschylus, who lived in the 4th century BC:
“The wisdom of numbers, the most important of the sciences,I invented it for people.”
In the 3rd century BC, the founder of the philosophical school, Plato, in a conversation with his interlocutor, continues the thought: “Have you not noticed that he who is capable of mathematics is sophisticated in all the sciences in nature?”
I put the statements of other great people into a table, while observing the time frame and indicating the main area of their activity:
Name of famous figure | Field of activity | Years of life | |
Aeschylus | ancient Greek playwright | 525 BC 456 BC | The wisdom of numbers, the most important of the sciences, I invented it for people. |
Plato | Philosopher, founder of a philosophical school | 427 BC-347 | Have you not noticed that he who is capable of mathematics is sophisticated in all sciences in nature? |
Roger Bacon | Scientist, doctor | 1214-1292 | We draw wisdom from history, wit from poetry, and insight from mathematics. |
Mikhail Vasilievich Lomonosov | Scientist chemist, physicist | 1711-1765 | ...chemistry is the right hand of physics, mathematics is its eyes. Mathematics must then be taught so that it puts the mind in order. Anyone who wants to study chemistry further must also be proficient in mathematics. A physicist without mathematics is blind. |
Immanuel Kant | representative of German philosophy | 1724–1804 | In each natural science there is as much truth contained in it as there is mathematics in it. |
Johann Wolfgang Goethe | the greatest poet and genius of German literature | 1749–1832 | Mathematicians are like the French: when you talk to them, they translate your words into their language and immediately you get something completely different |
Nikolai Ivanovich Lobachevsky | Mathematician, geometer | 1792–1856 | Mathematics is the language that all exact sciences speak. |
Niels Henrik Abel | Norwegian mathematician. | 1802-1829 | Mathematics is to a scientist what a scalpel is to an anatomist. |
Alexander Ivanovich Herzen | Russian revolutionary, writer, philosopher. | 1812-1870 | Astronomy (as a science) has existed since it was combined with mathematics. |
Panfutiy Lvovich Chebyshev | Mathematician, mechanic | 1821-1894 | Since ancient times, the mathematical sciences have attracted special attention; nowadays they have received even more interest due to their influence on art and industry. |
Pyotr Fedorovich Kapterev | Russian teacher and psychologist | 1849-1922 | Mathematics is needed to study many sciences, but it itself does not need any science. |
George Santayana | Writer, publicist, philosopher, USA | 1863-1952 | Just as all arts tend toward music, all sciences tend towards mathematics. |
Yuri Markovich Nagibin | Russian prose writer, journalist and screenwriter. | 1920- 1994 | For modern physicist mathematics is like perfect pitch for a composer. |
- Mathematics is the language in which the book of nature is written. (Galileo Galilei)
Numbers in nature are present everywhere and control many processes. You might think that sunflowers are geniuses in many ways, because their countless seeds are arranged in such a way as to make the most of the area given to them without wasting a millimeter. The branches and leaves of plants are arranged in such an order to receive maximum light, thanks to this, they do not interfere with each other.
The connection between mathematics and nature and its phenomena was also noticed by people from different areas activities and at different times.
Name of famous figure | Field of activity | Years of life | Sayings, quotes, aphorisms |
Galileo Galilei | Philosopher, astronomer, physicist, inventor | 1564-1642 | Mathematics is the language in which the book of nature is written. |
Jean Baptiste Joseph Fourier | French mathematician and physicist. | 1768-1830 | A close, deep study of nature is the source of the most fruitful discoveries in mathematics." |
Dmitry Ivanovich Pisarev | Critic, democrat, translator | 1840-1868 | Mathematics is the best and even the only introduction to the study of nature. |
Veniamin Fedorovich Kagan | Russian and Soviet mathematician | 1869-1953 | It would be easier to stop the Sun, it would be easier to move the Earth, than to reduce the sum of the angles in a triangle, reduce the parallels to convergence and move the perpendiculars to the straight line to diverge. |
Hermann Klaus Hugo Weil | German mathematician. | 1885 -1955 | In nature there is an inherent hidden harmony, reflected in our minds in the form of simple mathematical laws. This explains why natural phenomena can be predicted using a combination of observations and mathematical analysis. |
Andrey Nikolaevich Kolmogorov | Soviet mathematician, one of the greatest mathematicians of the twentieth century. | 1903-1987 | “Without knowledge of mathematics it is impossible to understand the basics modern technology, nor how scientists study natural and social phenomena" Mathematics is what people use to control nature and themselves. |
- Mathematics is one of the art forms.(N. Wiener)
In the first half of the 4th century BC, the ancient Greek painter Pamphilus lived in Amphipolis, from whom young people of noble rank studied painting. He believed that no painter could paint well without knowing geometry. “Our outlines, which set out the entire art of painting in all absolute perfection, will be easily understood by any geometer, but an ignoramus in geometry will not understand either these or any other rules of painting.”
Leon Battista Alberti, an Italian scientist, humanist, writer, one of the founders of new European architecture and a leading theorist of Renaissance art, argues that a painter simply needs to study geometry in order to achieve something in painting.
In the table below I have presented sayings, quotes and aphorisms that also talk about mathematics as an art.
Name of famous figure | Field of activity | Years of life | Sayings, quotes, aphorisms |
Aristotle | ancient Greek philosopher. Disciple of Plato from 343 BC. e. - teacher of Alexander the Great. | 384 BC uh 322 BC uh | Mathematics reveals order, symmetry and certainty, and these are the most important types of beauty. We enjoy learning about mathematics... It delights us like a lotus flower. |
Leon Battista Alberti | Italian scientist, humanist, writer | 1404-1472 | A painter needs to learn geometry. |
Leonardo da Vinci | Painter, sculptor, architect, engineer, scientist | 1452-1519 | All problems of Perspective can be clarified using the five terms of Mathematics: point, line, angle, surface and solid. |
Johannes Kepler | German astronomer, physicist, astrologer, | 1571-1630 | Mathematics is a prototype of the beauty of the world. |
Francois Jacques Blondel | architect | 1618-1686 | The satisfaction we feel when looking at wonderful work art, stems from the fact that rules and measure are observed in it, for only proportions cause pleasure in us. |
Alexander Sergeevich Pushkin | Russian poet, playwright and prose writer. | 1799-1837 | “Everything that exceeds geometry exceeds us,” said Pascal. And as a result, he wrote his philosophical thoughts Inspiration is needed in geometry, as in poetry. |
Karl Weierstrass | German mathematician | 1815-1897 | A mathematician who is not also a bit of a poet will never be a complete mathematician You can't be a real mathematician without being a little poet. |
Nikolai Egorovich Zhukovsky | Russian scientist, creator of aerodynamics as a science. | 1847-1921 | Mathematics has its own beauty, just like painting and poetry. |
Jules Henri Poincaré | French mathematician, physicist, astronomer, philosopher | 1854-1912 | Mathematics is the art of calling different things by the same name. |
Bertrand Russell | English philosopher, logician, mathematician, sociologist | 1872-1970 | Mathematics, properly understood, has not only truth, but also greatest beauty, which the art of sculpting possesses. |
Hermann Klaus Hugo Weil | German mathematician. | 1885-1955 | Beauty is closely related to symmetry. Symmetry...is the idea through which man has tried for centuries to comprehend and create order, beauty and perfection. |
Alexander Viktorovich Voloshinov | Doctor philosophical sciences, Professor of the Department of Cultural Studies. | mathematics is a symbol of the wisdom of science, a model of scientific rigor and simplicity, a standard of excellence and beauty in science. Mathematics found a meaningful and systematic application to art, of course, in music, in the works of the ancient Greek mathematician Pythagoras, his many students and followers. |
- Mathematics is the shortest path to independent thinking.(V. Kaverin)
A remarkable property of thinking is its creative nature. Thinking is capable of generating new ideas, new knowledge based on experience, experiment, hypothesis testing, analysis, reasoning, etc.
Today creative potential thinking is supported by the great experimental and instrumental capabilities of science and technology, modern information technology, high-speed methods of testing hypotheses, ideas and conclusions using computer technology.
The development of memory and thinking was important many years ago. Thus, Galilius noted that “geometry is the most powerful means for refining mental abilities,” but nothing is given so easily - you need to work a lot on yourself. Even earlier, the ancient Greek mathematician Euclid warned that “There is no royal path to geometry.” However, the Russian writer Lev Nikolaevich Tolstoy reassured “The majority life tasks are decided how algebraic equations: bringing them to the simplest form."The Polish scientist Hugo Dionysius Steinhaus, one of the founders of the Lviv mathematical school, continues: “No science so strengthens faith in the power of human mind, like mathematics."
Statements by famous figures about the influence of mathematics on mental capacity and human thinking are shown in the table:
Name of famous figure | Field of activity | Years of life | Sayings, quotes, aphorisms |
Euclid | ancient Greek mathematician. | around 300 BC e.) | There is no royal path to geometry. |
Galileo Galilei | Astronomer, physicist, inventor | 1564-1642 | Geometry is the most powerful tool for sharpening our mental abilities |
Johann Heinrich Pestalozzi | Swiss teacher | 1746- 1827 | Counting and calculations are the basis of order in the head. |
Lazare Carnot | French statesman and military leader, engineer and scientist | 1753- 1823 | The first condition that must be fulfilled in mathematics is to be precise, the second is to be clear and, as far as possible, simple. |
Nikolai Ivanovich Lobachevsky | Mathematician, geometer | 1792–1856 | Mathematics should be taught in school for the purpose that the knowledge acquired here would be sufficient for ordinary needs in life. |
Mikhail Vasilievich Ostrogradsky | Russian mathematician and mechanic | 1801 -1862 | Much of mathematics does not remain in memory, but when you understand it, then it is easy to remember what you have forgotten on occasion. |
Edgar Allan Poe | American writer, poet, literary critic | 1809 -1849 | The highest harmony of the imaginative intellect is always endowed with a predominantly mathematical character. |
Lev Nikolaevich Tolstoy | Russian writer, thinker | 1828- 1910 | Most life problems are solved as algebraic equations: by reducing them to their simplest form |
George Bernard. Show | British writer, novelist, playwright, | 1856 - 1950 | The ability to think mathematically is one of the noblest human abilities. |
Arthur Conan Doyle | Scottish and English writer | 1859- 1930 | ...it is simply impossible to deceive a person who knows how to observe and analyze. His conclusions will be as infallible as Euclid's theorems. |
Mikhail Ivanovich Kalinin | State and party leader | 1875-1946 | If you would like to participate in great life, then fill your head with mathematics while you have the opportunity. She will then provide you with great assistance in all your work. |
Hermann Hesse | German-Swiss writer and artist | 1877- 1962 | Any well resolved math problem provides mental pleasure. |
Albert Einstein | great physicist; | 1879 -1955 | Mathematics is the only perfect method that allows you to fool yourself by the nose. |
Hugo Dionysius Steinhaus | Polish scientist, founder of the Lviv mathematical school | 1887-1972 | No science strengthens faith in the power of the human mind like mathematics. From the house of reality it is easy to wander into the forest of mathematics, but only a few are able to return back. |
Heinrich Gustavovich Neuhaus | Russian pianist and teacher | 1888-1964 | Mathematics and music are at the extreme poles of the human spirit, that all creative spiritual activity of man is limited and determined by these two antipodes, and that between them lies everything that humanity has created in the field of science and art. |
Alexey Ivanovich Markushevich | Doctor of Physical and Mathematical Sciences, Professor | 1908-1979 | Anyone who studies mathematics from childhood develops attention, trains their brain, their will, and develops perseverance and perseverance in achieving goals. |
Alexander Danilovich Alexandrov | Soviet and Russian mathematician, geometer | 1912-1999 | The good thing about math is that it is difficult. Nowhere, as in mathematics, does the clarity and accuracy of the conclusion allow a person to wriggle out of an answer by talking around the question. Mathematics teaches the accuracy of thought, submission to the logic of proof, the concept of strictly substantiated truth, and all this shapes the personality, perhaps more than music. |
Vasily Alexandrovich Sukhomlinsky | Russian teacher | 1918 - 1970 | Mental work in mathematics lessons is a touchstone of thinking. |
Naum Yakovlevich Vilenkin | famous mathematician | 1920-1991 | Solving a difficult problem mathematical problem can be compared to taking a fortress. |
V. Schrader | Mathematician, artist | 1943 | The task is not to teach mathematics, but to discipline the mind through mathematics. |
sociological survey
I conducted a small study among students in grades 5-6 at our school. I compiled a questionnaire in which I asked them to answer two questions:
- What is the subject of mathematics for you?
- Name a quote, aphorism or saying famous people about mathematics.
127 students from grades 5a, 5b, 5d and 6c, 6d took part in the survey. The results are presented in the diagrams: “Diagram 1” and “Diagram 2”
From the survey results it became clear that most of students study mathematics with interest, but only 7 people were able to name more than three quotes, aphorisms and sayings of great people about mathematics. In this regard, I decided to present my project not only in my class (as previously planned), but also in other classes. Some of the aphorisms, quotes and sayings will be formatted as a brochure and posted in mathematics classrooms and on our school website.
Conclusion
Mathematics is needed by all people on earth. Mathematics is needed in history, physics, chemistry, biology, geography and even in the Russian language. Mathematics is needed in everyday life: for example, when sewing, cooking or when solving money issues. Mathematics allows a person to think, think logically, and draw conclusions. The famous Polish mathematician Hugo Steinhaus jokingly claims that there is a law that is formulated as follows: a mathematician will do it better. That is, if you entrust two people, one of whom is a mathematician, to perform any work unfamiliar to them, the result will always be the following: the mathematician will do it better. A mathematician sees a problem in any undertaking. And “The ability to solve problems is the same practical art like the ability to swim or ski. It can only be learned through imitation or exercise.If you want to learn to swim, then boldly enter the water, and if you want to learn how to solve problems, then solve them” (D Poya).
The German philosopher I. Kant wrote the following words: “In every science there is exactly as much truth as there is mathematics in it.” Yes, mathematics can indeed rightfully be considered the queen of all sciences, but she herself faithfully serves all sciences. After conducting research, I found confirmation of my hypotheses. And now I can say with firm confidence: “Mathematics is the queen of all sciences.” So it was, so it is and so it will be.
List of references and online resources
- Liman M.M. Schoolchildren about mathematics and mathematicians: a manual for students in grades 4-8 / M.M. Liman. – M.: Education, 1981. – 180 p.
- Encyclopedic Dictionary of Young Mathematicians / Ed. B.V. Gnedenko. Moscow, 1989 - 313s.
525 BC e - 456 BC uh.
Wisdom
numbers, the most important of the sciences,
I invented for people.
Nikolai Ivanovich Lobachevsky
Mathematician, geometer
1792–1856
Mathematics -
this is the language spoken by all exact sciences
Alexander Viktorovich Voloshinov
Doctor of Philosophy, Professor of the Department of Cultural Studies
Mathematics is a symbol of the wisdom of science, a model of scientific rigor and simplicity, a standard of excellence and beauty in science.
Mathematics found a meaningful and systematic application to art, of course, in music, in the works of the ancient Greek mathematician Pythagoras, his many students and followers.
Johann Wolfgang Goethe
the greatest poet and universal genius of German literature
1749–1832
Mathematicians –
like the French: when you talk to them, they translate your words into their language and immediately you get something completely different
The Tale of the Kingdom of Sciences
Once upon a time there was a kingdom of sciences. The king there was Natural Science, the queen was mathematics, and the princess was literature. And many servants served the royal family.
One day the Queen quarreled with her husband. “Oh, well,” she exclaimed, “try to do without me. She slammed the door in anger and rushed off to another country.
At first everyone breathed a sigh of relief. But soon the real commotion began. It turned out that literature cannot number chapters, parts and pages in novels and poems. Natural science has lost count of the planets in the Galaxy, the days, months and weeks of the year. History cannot establish the exact dates of events, geography cannot calculate the distance between cities, builders cannot build new castle, and the cook doesn’t know how to weigh food to prepare dinner. No one could do without Mathematics.
Then they sent messengers all over the world, found Mathematics and asked her to return back to the kingdom of sciences. Queen Mathematics returned to her country, and since then order has reigned in the sciences.
Preview:
DIAGRAM 1
What is a math lesson like for you?
DIAGRAM 2
Number of named statements
24.11.08
Queen of Sciences
“In the current century, mathematicians are faced with the task of coming up with a single “calculator” that would calculate all of nature,” says one of the most cited Russian scientists in the world, Academician-Secretary of the Mathematical Department of the Russian Academy of Sciences Ludwig Faddeev
Olga Orlova, science columnist for Radio Liberty
Each time has its own flagship science, pushing forward the entire fleet of fields of knowledge. At the beginning of the 20th century, physics played this role, at the end of the century - biology. Now mathematics is claiming leadership. In any case, without it it is impossible to develop practically any area. And Russian mathematicians can play a significant role here. The best confirmation to that - Shaw Prize, " Nobel Prize East", which was awarded to Russian scientists this year. One of its laureates, director of the International Mathematical Institute named after L. Euler, academician-secretary of the mathematical department of the Russian Academy of Sciences Ludwig Faddeev told Itogi how he sees the development of this exact science in the 21st century.
- Ludwig Dmitrievich, may I know your forecast: what areas will be the most relevant for mathematics in the current century?
If we talk about mathematical physics, which is closer to me, here among main directions First of all, two stand out - quantum field theory and astrophysics. It is these areas of physics that “call the tune” for mathematicians. True, there is a significant difference here. Astrophysics itself does not require particularly sophisticated mathematics. To solve a problem posed by an astrophysicist, a mathematician can use already developed methods. But quantum field theory, being the basis of the theory elementary particles, not only uses the most modern mathematical apparatus, but also influences its development.
- Well, what can you say about the prospects for mathematics in a broader context?
Still relevant math program, announced back in the 1970s by the famous mathematician and 2007 Shaw Prize winner Robert Langlands: it should combine algebra, geometry and number theory. Specialists all over the world are involved in the implementation of this program, and not only the further advancement of mathematics, but also how clearly it will help physics largely depends on its implementation. Roughly speaking, in the current century, mathematicians are faced with the task of coming up with a single “calculator” that would calculate all of nature.
- Among latest achievements The most famous among Russian mathematicians is the proof of the Poincaré conjecture performed by Grigory Perelman. How will it affect the development of this area?
This is an absolutely amazing result. Perelman showed an unexpected direction - the use differential equations in topology. That is, he applied the traditional technique of using differential equations when describing them as smooth smooth physical processes, and “prickly”, “rough” mathematical objects, such as, for example, a topological three-dimensional sphere. Actually, it’s about her we're talking about in the famous Poincaré conjecture. This opens the way for a whole group of mathematicians who are looking for ways to describe complex objects. But that is not all. It turned out that the same equations that Perelman uses are also used in physics, in string theory.
- The same theory that people have already jokingly called “the theory of everything”?
Well, some people say that seriously. This physical theory attempts to classify all the particles that exist in the Universe, of which, as we now know, there are an incredible number. For physicists, the most promising thing about it is that it allows us to reconcile things that were previously in conflict. In particular, it will be possible to include the theory of gravity, which, within the framework quantum theory The field does not have a good wording. So physicists are faced with the task of coming up with their own “species theory”. But the problem is that, unlike biology, the physical “theory of species” does not correlate well with experimental data. We predict many particles, but there is no answer yet whether they actually exist.
- Do mathematicians have a more pragmatic interest in this theory?
In general, yes. For them, it is attractive primarily because it requires a huge number of modern mathematical methods, such as comprehensive analysis and algebraic geometry. For example, it predicts new properties mathematical structures which are called " mirror symmetry". Previously in mathematics there was whole line ideas - attractive, but it is not clear what they are applicable to. And it turned out that it was these mathematical ideas that were needed to describe string theory. However, it often happens that mathematicians seem to go into abstract jungle, and then it turns out that these jungle are not at all useless.
- So, the future belongs to string theory?
You know, in America it has come to the point that if a mathematical physicist does not study string theory, then it is already difficult for him to find a job at the university. Although, of course, we need to look at things more broadly. For example, there is a problem: both within the framework of the Yang and Mills theory, which is the basis standard model elementary particles, explain the phenomenon of the appearance of mass in them. I was pleasantly surprised at one time when American physicist Edward Witten, an active proponent of string theory, noted and formulated this problem as a properly mathematical one. And my other colleague, Nobel laureate David Gross, on the other hand, insists on string theory and doesn't want to hear anything else. But in Europe now this theory is viewed more carefully. A new symbiosis has appeared there - string theory and integrable models. That is, an attempt is made to combine the “theory of species” for elementary particles and the “theory of species” for the equations of quantum field theory. In this way, it will be possible to reconcile the two physical theories.
- How do you think the ratio of “applied specialists” and “fundamentalists” in mathematics should change?
Basic sciences are much cheaper, but they are extremely important for the country's competitiveness. You cannot buy all developments abroad. Eat military security, there are trade secrets. In the 1930s, Ioffe was going to close at the Leningrad Phystech nuclear physics and transfer Kurchatov and Artsimovich to another, more relevant, as it seemed to him, direction. If this had happened, what would we have been doing in the 1940s? How would things turn out? A state that takes itself seriously must have scientists working on fundamental problems. Another thing is that there should be few of them.
-Can you tell me how much?
In former times, out of 250 people who studied at the Mathematical Department (in St. Petersburg terminology) or the Mechanics and Mathematics Department (in Moscow), two people were taken to the Academy of Sciences, three to a university or higher education institutions, and the rest were employed in application areas. When I was the director of the St. Petersburg branch of the Steklov Mathematical Institute of the Russian Academy of Sciences, I hired two or three people a year. If a university can produce two strong specialists a year, that is already enough for fundamental science. That's not the problem. The tragedy of Russian mathematics is that more than a half Of those few who chose fundamental mathematics, they left the country. About forty of the best scientists from our institute went abroad - this is a big loss. And as a result, at the last mathematical congress in Madrid, more than 20 speakers were representatives of the Russian mathematical school, but most of them work abroad. And only two are at home.
- Do you think it will change the situation? new program interaction with the scientific diaspora?
The other day I received a letter from my student, a professor who now works in the USA: he wrote that he wanted to return. I certainly welcome this. After all, if people, as planned, will be attracted through a competition and paid a million rubles a year (as they promise), then this is normal. I don’t think that many people will go, but it is important to give the opportunity to come to those who want to come.
- Is it possible to raise new famous mathematicians in today's Russia? How do you feel about the fact that the rules for holding Olympiads for schoolchildren have changed?
Previously, the Olympics were a matter of enthusiasts. Any winner then dealt anyway entrance exams. I remember well how I went to the Olympiad for 5th grade. To regional and school tours I didn’t go, I went straight to the city one. By the way, the tasks for the children were prepared by world-class scientists. But then there was no such excitement. The children went for the sake of curiosity and interest, and not for a place in the elevator that would take them straight to the institute. I’m afraid it will turn out that the new rules of the Olympiads are more likely to help produce successful applicants than real mathematicians.
- Many people pin their hopes on special schools and physics and mathematics boarding schools.
Their role has always been huge. For example, many employees of our institute graduated from the 239th math school Leningrad. Now, I know, there is a tendency to eradicate elite education. And it must be preserved, even in small quantities. Certainly, fundamental science You don't need many geniuses. It takes as much as is necessary for its development. And in order to have somewhere to look for geniuses, it is necessary to maintain a good average background from which the elite feeds.
Dossier
Hall of Fame
Ludwig Faddeev is one of the most prominent mathematicians and physicists of the second half of the twentieth - beginning of this century. His works largely determined current state mathematical physics. The scientist contributed decisive contribution in solving the three body problem in quantum mechanics(Faddeev equations), inverse problem scattering theory for the Schrödinger equation in the three-dimensional case, in the creation of the quantum theory of solitons and the quantum inverse problem method, in the development of the theory of quantum groups, etc. Author of more than 200 scientific works and five monographs.
Ludwig Faddeev - Academician-Secretary of the Department of Mathematical Sciences of the Russian Academy of Sciences, professor. Laureate of USSR State Prizes (1971) and Russian Federation(1995, 2005). His works are constantly cited and used in scientific literature. He heads National Committee mathematicians of Russia, International Mathematical Institute named after. L. Euler in St. Petersburg.
Faddeev became a foreign member of the academies of the leading countries of the world (USA, France, Sweden, Finland, Poland, Brazil). Professor Emeritus foreign universities, member of one of the world's oldest academies - French Academy Sciences, laureate of the D. Heinemann Prize of the American Physical Society, international award named after A.P. Karpinsky, awarded the Max Planck gold medal of the German Physical Society, medal named after P. Dirac International Institute theoretical physics.
In 1986-1990, Faddeev was the first - and so far the only one among Soviet and Russian scientists - president of the International Mathematical Union.