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Scientists explain why modern man cannot do without mathematics
Pythagoras argued that numbers rule the world, and Alexander Suvorov called mathematics the "gymnastics of the mind".
Now interest in this science is gradually recovering. T&P has asked five famous mathematicians to understand why the formulas and equations needed in everyday life, why is math interesting and creative subject, and that loses the Humanities, waving away the science.
"He who does not know mathematics can not even detect their ignorance"
Sergei Lando, doctor of physico-mathematical Sciences, Dean of the faculty of mathematics, HSE
As my teacher Vladimir Igorevich Arnold, "the main goal of mathematics education should be the education of the mathematically ability to study phenomena of the real world." The essence of mathematics is the study of General regularities describing the qualitative nature of the world around us — the changing of the seasons, the planets, climate change, currency fluctuations or the cost of oil, the development of natural grammars, or principles of designing of artificial languages. Mathematicians have designed and developed a variety of methods — computational, algebraic, geometrical, method of evidential reasoning, logical inference. In some cases, these methods are developed so that allow you to achieve a deep understanding of existing laws in others, this understanding is still a distant future. Knowledge of patterns allows not only to explain past events but also to predict the future.
The man who never met with mathematical reasoning, has serious difficulties to distinguish the fact from its interpretation of true statements from the false, to understand what consequences flow from that statement. A person unable to estimate the order of numeric values that can easily be manipulated by unscrupulous politicians and economists. As he wrote in 1267 Roger bacon, "He who does not know mathematics can not learn any other science and can not even detect their ignorance, and therefore do not seek from him a cure."
Nowadays common this approach is — I don't understand mathematics, physics, chemistry, biology,... so I better learn something humanitarian. That is, people from the beginning of their independent life accepts its own inferiority, on the deliberate lack of a certain, and valuable of quality. The Humanities is not going to benefit. And I would like to humanists were people with a strong interest in what they want to do, to the study of man and his activities. In the natural Sciences and mathematics such interest is present, in my opinion, more often. People learn them and do them later due to internal needs, not denying others, including humanitarian interests. "The man who never met with mathematical reasoning, has serious difficulties to distinguish the fact from its interpretation and true statements from the false" have You ever tried to describe the beauty of paintings of the man who never saw it? It is not completely impossible — if your partner has sufficient experience of visiting art galleries, well-acquainted with many masterpieces of world art. If the listener has no such experience, there is no hope that he will get from the description of positive emotions. The ability to perceive the beauty of mathematics also requires constant or at least regular work. It is possible to develop in young children starting to talk to them about the math even before school. There are cases when this beauty opens with a schoolboy unexpectedly. Initially that result was sent to school mathematical Olympiad: the lens of the beautiful tasks and beautiful solutions show a small part of the spectrum of beautiful ideas, to generate interest and to encourage them to go further.
Not to be unfounded and to give a concrete idea of mathematical beauty, will report this fact: if Moscow's plan to impose another, lesser plan, Moscow will definitely be a place that two plans will be represented by two points lying one above the other — the needle lanced through at these points, will be set to the same place in the city. Do you understand why this is happening? This statement serves as the beginning of a large and extensive mathematical theory and is used in a huge number of applications. It remains true in much more General situations — for example, if the second plan of Moscow is distorted or crumpled. "The Humanities are entering an era of high precision"
Ivan Arzhantsev, doctor of physico-mathematical Sciences, Dean of the faculty of computer science, the HSE and Yandex Why math? The phrase Lomonosov that "mathematics should be taught only then that she mind in order", could not be better reflects the essence. Rumors about the eccentric scientists are greatly exaggerated. People who understand mathematics, are valued not only because they have special knowledge, but rather because they know how to think and analyze.
If physicists, chemists, biologists need a laboratory, installation, consumables, math — she is always with you. Go to the train, took a piece of paper and pen or just closed my eyes and working on a solution to some problem. Beauty in mathematics no less than in art. If the work is math heavy and complicated, most likely the author either took the "wrong" problem or on a solution still needs to work. The proof of the theorem — like Assembly of the puzzle. Twist this way and that the existing fragments of known facts and methods of proof, and when everything happened at once — that is a beauty!
Most math applications. They not only guarantee her right to exist, but are the medium, which generates a new purely mathematical problems. In addition to applications in the natural Sciences — physics, chemistry, biology — mathematics is increasingly used in Economics, social Sciences and Humanities. The special role of mathematical results play in the world of IT. Technological breakthroughs are often based on fundamentally new algorithms and theorems, often from very abstract areas of mathematics.
In March 2014 opened the faculty of computer science HSE and Yandex. We are the guys who are interested in mathematics and programming. They after a while will be able to apply the Arsenal of mathematical methods to the problems of information retrieval and computer vision, automated text processing and bioinformatics, development of software packages and Internet services. One of the areas of Computer Science is the "new math" to work with big data. What here it is possible to achieve, is on the verge of science fiction.
There is a feeling that right now the Humanities comes into the "era accuracy". It's not just about the opportunity to build a more accurate mathematical models of various processes and calculate these models on super computers. New technologies allow to capture and store accurate information about various real events. The only question is that with this information you can do the collected piles of data, people or even research team will not be able to perform for many years. The idea of modern data analysis what computer systems and implemented them to the algorithms themselves work with the obtained range information and give the user only the final result — he is interested in statistics and certain discovered regularities. This allows us not only with mathematical rigor to prove or disprove the hypothesis of the humanitarian sphere, but also to detect dependencies that were unknown to the specialists. Mathematically-savvy humanitarians there is required — they can put a task to explain what kind of data you intend to collect and what kind of characteristics we are interested in.
Recently Yandex has decided to hold a national checklist for everyone who loves math, or, perhaps, wanted to like, but somehow did not develop: students, moms, dads, grandparents. The tasks are easy, according to basic school curriculum — however, for a successful solution you need to be careful. The training missions are already open on the website — you can test your strength.
Control on March 14, the day of PI. To participate in the control, you can not only online in Moscow tasks it will be possible to work out in the Tower, who became a partner of the project. The project was supported by universities in many regions of Russia: Yekaterinburg, Novosibirsk, Kazan and other. Highly recommend to see the hours from Saturday and join in — especially those who are afraid of mathematics. After the test the faculty will disassemble tasks together with the project participants.
"Ignorance of mathematics threatens porridge in the head"
Alexei Savvateev, doctor of physical and mathematical Sciences, expert of the Department of theoretical and applied developments of the company Yandex, scientific Director of the Laboratory of social analysis at the University of Dmitry Pozharsky now there is a debate about politics. It would seem, at what here the math? But a detailed study of the situation it is clear that the Humanities are not familiar with the basics of mathematics, in the head not an opinion but a "mess." They don't have to focus, jump from one argument (the chaotic and often contradictory) on the other. And it is with each of the warring parties. Have someone who understands the math in my head in order, everything in its place. He is considering his position in the chaff it won't. So, ignorance of mathematics threatens to mess in my head.
Humanitarians need to learn beautiful mathematics — pictures, pictures and again pictures. They should immediately get to work on the head: to think, to compare, compare and draw conclusions. Not just to contemplate beautiful mathematical construction, and to be their active co-organizer, to see what purpose is one or the other, to understand the simple logical transitions.
Then, at the next stage, you can already move on to abstract concepts and terms — paradoxically, they are better humanitarians than hard-boiled and hard-nosed techies! It is possible to solve various Diophantine equations to talk about complex numbers, number systems (rings, boxes) and how they help in solving problems. Very affordable already at early stages of comprehension of the mathematics task analysis to the build, what you can and cannot build a compass and a ruler. In General, I would recommend any humanist to learn the book of Courant and Robbins "What is mathematics".
What is the beauty in mathematics? Find a geometric proof of the Pythagorean theorem and you'll understand!
"This science teaches us that unsolvable with sight problems can be solved"
Dmitry Vetrov, candidate of physico-mathematical Sciences, head of big data and information retrieval faculty of computer science In the information age are increasingly voices that any serious knowledge of mathematics-specific and the average person doesn't really need. Many believe that skills in, say, a seven-digit number into four-digit or adding two fractions unnecessary — after all, it can be done on a smartphone. What can we say about the ability to solve logarithmic inequality, algebraic and differential equations, the problem of three-dimensional geometry (solid geometry) and other "higher mathematics"? There are two fundamental arguments against this position. First, the not-so-trivial mathematics is needed in everyday life. For example, to solve a simple problem ("one of the fastest growing African countries, the inflation stands at 32 million interest per year. Question: how many percent in this country rising prices in the day?" The answer many surprise you with its smallness [1]), we need the ability to write and solve equations with logarithms. It is impossible to calculate by what percentage you need to put 5 thousand dollars in the Bank account of a newborn son below 18 years, he was able to get 25 thousand, or is it better to invest our savings so that they will increase at 6% every six months, by 13% each year, or 27% every two years? Perhaps, even more vital (in March 2015) topic: which currency is better to keep their savings in rubles (banks promise high interest), in dollars or in euros? Intuition tells us the correct answer (in all currencies little by little), but in order to choose the right proportions, you should have a basic knowledge in the theory of risk. In meetings at work we often have to make a choice, which of the various points of view to support which group of supporters to join. To do it with the greatest advantage allows the theory of games. It also gives an answer to the question, what salary we can safely require, if you try to win over competitors without fear of a bad bargain or losing an advantageous offer. [1] on the day the inflation in the African country was "just" 4%. Despite seeming a little by the end of the year in the country out of paper for the printing of new banknotes. These are the insidious properties of exponents. Secondly, mathematics (even school) teaches to think logically. To understand what it implies and what is not (for example, from what we have in the fridge, there's herring, it follows that we are there and fish. But from what we have in the fridge, fish should not (although it can be), the herring). Almost the only school subject that teaches reasoning is geometry. But this is only the tip of the iceberg. In fact all around us there are more subtle patterns that go beyond ordinary logic, which operates with concepts of "truth" — false — "unknown". For example, research found that between the length of human hair and its growth there is a negative correlation (stochastic dependence), that is, if you take a random citizen of Russia and to inform us that he had short hair, we will be able with high probability to say that his height is above average. Now you know that I have short hair. Does that give you some additional information about my growth? The correct answer is no [2]. [2] know About me that I'm a man, but about a random citizen of the Russian Federation no. The correlation between height and hair length is currently unknown gender (women, on average, lower than men and have longer hair). Once gender is known, the relationship between length of hair and growth disappears. This phenomenon is known as conditional independence (conditional independence), underlies the whole theory of probabilistic graphical models are actively used in the analysis of texts, images, videos, social networking, etc., and there are many such examples (e.g. is there a relationship between the price of tomatoes in the supermarket and their quality or the relationship between the jeans of a certain brand and my attractiveness to girls; whether to take a paid diagnostic test gives the correct answer in 90% of cases to determine the disease, occurring in one out of ten thousand people [3]). To understand when relationships exist, and when it's false correlations generated by unaccounted factors, you need to have understanding of the basics of probability theory and Bayes ' theorem. Well-developed common sense and a solid b in geometry. [3] it is Not necessary. Even if the test will give a positive result, in 999 cases out of a thousand, it will be a false alarm. Of course, this does not apply to a situation when there are reasonable grounds to assume the existence of a rare disease such as its symptoms. Contemporary mathematics covers a much broader range of issues beyond the household. The largest search engine by which you may read this article, crammed with mathematical models that allow you to adjust the output of the result of our search query under a specific user. In other words, the same Google query I will give some links and you other just because we went to the browser under different gmail accounts. The complex mathematical models used by investment funds that manage our savings; online-shops that recommend us those or other goods; traffic signals that reduce the likelihood of congestion in the streets due to the constant adjustment of his regime; and many other technologies that surround us.
Active use of mathematical methods in modern natural Sciences and the Humanities. Processing of data from the Large hadron Collider has spawned an entire branch of mathematics, the so-called big data analysis (big data). Biologists use mathematical methods to recover the evolutionary tree as the remnants of genomes and organs of extinct species. Chemists are searching for promising future of polymer synthesis using algorithms of mathematical modeling. Critics define using the mathematics of authors, anonymous literary works and paintings. Finally, not to mention a revolution in the field of mathematical methods in machine learning that is happening before our eyes. With the advent and successful application of deep neural networks (deep neural networks) mankind began to rapidly approach the creation of artificial intelligence. Now a high school student who knows how to program, can build a new neural network model that can solve the next task (for example, the synthesis of music, understanding images, etc.) that were previously considered subject only to the human intellect.
Mathematics constantly teaches us that seemingly intractable problems can be solved if you move to a new level of thinking. We divide four by seven, subtract two from nine, operate with irrational numbers, faced with the fact that one equation can have many solutions, but each time has to overcome some break the pattern. The study of mathematics helps to understand that many of the truths we used to think the absolute, are actually relative, and much of what we thought has a different nature, in fact special cases of the same phenomenon just from a different angle of view. Such effects are observed not only in mathematics and its applications, but, for example, in politics. "Global removal of mathematics from society will lead to disaster"
Roman Mikhailov, doctor of physico-mathematical Sciences, leading researcher, SPbSU Adam named the animals. It starts with math. He deals with the classification, the established order. He faces a mobile world, he wants to find it in order to show compliance: "animal" — "name."
In the famous Soviet cartoon kid learns to count. He runs and finds new animal friends. Some are outraged, don't want to be seen. And he is happy with this abstract game. He does math.
Here are some of the areas of modern mathematics: the Classification of complex objects, phenomena, relations. There are objects, which are many, even infinitely many, they need to classify, to distinguish between: rough, thin, somehow.
— Identification of anomalous structures, which do not fit the General smooth classification. Are there animals in the forest who do not fit the common names or which cannot be counted?
— Working with infinity. A huge part of mathematics deals with the asymptotics, it often turns out that the work "far" easier than "close". There are even machines that are attached to an endless ceiling, there is a machine running "past infinity".
— Finding the language to talk with the deep nature. The establishment of various relationships, the creation of dictionaries, the establishment of equivalences of categories. "The largest search engine by which you may read this article, crammed with mathematical models" we Often hear questions about the benefits to society of abstract mathematics, people mention taxpayers, trying to understand what the immediate satisfaction society can bring to what we do. For example, the following.
Modernity gave us the opportunity to run through the text to explore the text in new ways. In a fraction of seconds you can count the number of words in the text, to determine their distribution, to see the standard patterns in the construction of phrases. Once we learn to look at a literary text as a topological space, explore it with the accuracy of deformation, explore its soft nature. Now apply the methods of textual statistics for their research but statistics only gives the rhythm, the pulse of the text, not more. It begins to seem that the languages that we develop over the years, one will find the same application. But not about physics or rocket science, and in psychiatry, psycholinguistics, qualitative studies of the architecture of the nonsense in the theory of consciousness, in the inner bonding patterns. And as before us lay a complex space, so before us will lie a complex and schizophrenia, and it will be clear that there are only a thousand of schizophrenia with these "homology". Try to write long crazy lyrics. Good analysis will show that it is an imitation. There suggestions would be marvelous, but the glue will either be absent altogether, or they will not be enough. The hash to check uninteresting. It is interesting to study the complicated nonsense and try to qualitatively distinguish it from nebreda. Yes, I think that textual criticism will someday apply our topological methods, speak with complex texts in the languages that we developed.
Of course, to study mathematics is optional. Almost none of my friends of his youth could not add fractions. Well? Some have become respected people. Unable to meet with the Professor of philosophy and quite clearly explain to him who he is and what he is and who is right. But the global removal of mathematics from society will cause a disaster soon nature will show some another his face, and the person does not own the language in which to talk to him, and will not know the method of constructing such a language.
About the beauty of mathematics do not really want to talk. Take the checkered notebook, draw your dreams, link similar images in these dreams surfaces, paint it different colors — it's beautiful, try to qualitatively distinguish the configuration of the ligaments in my dreams, who came to new moon. If the difference is sure to be beautiful, will envy you. It is a secret beauty. Text: Elena Kiseleva
P. S. And remember, just changing your mind — together we change the world! ©
Source: theoryandpractice.ru
Now interest in this science is gradually recovering. T&P has asked five famous mathematicians to understand why the formulas and equations needed in everyday life, why is math interesting and creative subject, and that loses the Humanities, waving away the science.
"He who does not know mathematics can not even detect their ignorance"
Sergei Lando, doctor of physico-mathematical Sciences, Dean of the faculty of mathematics, HSE
As my teacher Vladimir Igorevich Arnold, "the main goal of mathematics education should be the education of the mathematically ability to study phenomena of the real world." The essence of mathematics is the study of General regularities describing the qualitative nature of the world around us — the changing of the seasons, the planets, climate change, currency fluctuations or the cost of oil, the development of natural grammars, or principles of designing of artificial languages. Mathematicians have designed and developed a variety of methods — computational, algebraic, geometrical, method of evidential reasoning, logical inference. In some cases, these methods are developed so that allow you to achieve a deep understanding of existing laws in others, this understanding is still a distant future. Knowledge of patterns allows not only to explain past events but also to predict the future.
The man who never met with mathematical reasoning, has serious difficulties to distinguish the fact from its interpretation of true statements from the false, to understand what consequences flow from that statement. A person unable to estimate the order of numeric values that can easily be manipulated by unscrupulous politicians and economists. As he wrote in 1267 Roger bacon, "He who does not know mathematics can not learn any other science and can not even detect their ignorance, and therefore do not seek from him a cure."
Nowadays common this approach is — I don't understand mathematics, physics, chemistry, biology,... so I better learn something humanitarian. That is, people from the beginning of their independent life accepts its own inferiority, on the deliberate lack of a certain, and valuable of quality. The Humanities is not going to benefit. And I would like to humanists were people with a strong interest in what they want to do, to the study of man and his activities. In the natural Sciences and mathematics such interest is present, in my opinion, more often. People learn them and do them later due to internal needs, not denying others, including humanitarian interests. "The man who never met with mathematical reasoning, has serious difficulties to distinguish the fact from its interpretation and true statements from the false" have You ever tried to describe the beauty of paintings of the man who never saw it? It is not completely impossible — if your partner has sufficient experience of visiting art galleries, well-acquainted with many masterpieces of world art. If the listener has no such experience, there is no hope that he will get from the description of positive emotions. The ability to perceive the beauty of mathematics also requires constant or at least regular work. It is possible to develop in young children starting to talk to them about the math even before school. There are cases when this beauty opens with a schoolboy unexpectedly. Initially that result was sent to school mathematical Olympiad: the lens of the beautiful tasks and beautiful solutions show a small part of the spectrum of beautiful ideas, to generate interest and to encourage them to go further.
Not to be unfounded and to give a concrete idea of mathematical beauty, will report this fact: if Moscow's plan to impose another, lesser plan, Moscow will definitely be a place that two plans will be represented by two points lying one above the other — the needle lanced through at these points, will be set to the same place in the city. Do you understand why this is happening? This statement serves as the beginning of a large and extensive mathematical theory and is used in a huge number of applications. It remains true in much more General situations — for example, if the second plan of Moscow is distorted or crumpled. "The Humanities are entering an era of high precision"
Ivan Arzhantsev, doctor of physico-mathematical Sciences, Dean of the faculty of computer science, the HSE and Yandex Why math? The phrase Lomonosov that "mathematics should be taught only then that she mind in order", could not be better reflects the essence. Rumors about the eccentric scientists are greatly exaggerated. People who understand mathematics, are valued not only because they have special knowledge, but rather because they know how to think and analyze.
If physicists, chemists, biologists need a laboratory, installation, consumables, math — she is always with you. Go to the train, took a piece of paper and pen or just closed my eyes and working on a solution to some problem. Beauty in mathematics no less than in art. If the work is math heavy and complicated, most likely the author either took the "wrong" problem or on a solution still needs to work. The proof of the theorem — like Assembly of the puzzle. Twist this way and that the existing fragments of known facts and methods of proof, and when everything happened at once — that is a beauty!
Most math applications. They not only guarantee her right to exist, but are the medium, which generates a new purely mathematical problems. In addition to applications in the natural Sciences — physics, chemistry, biology — mathematics is increasingly used in Economics, social Sciences and Humanities. The special role of mathematical results play in the world of IT. Technological breakthroughs are often based on fundamentally new algorithms and theorems, often from very abstract areas of mathematics.
In March 2014 opened the faculty of computer science HSE and Yandex. We are the guys who are interested in mathematics and programming. They after a while will be able to apply the Arsenal of mathematical methods to the problems of information retrieval and computer vision, automated text processing and bioinformatics, development of software packages and Internet services. One of the areas of Computer Science is the "new math" to work with big data. What here it is possible to achieve, is on the verge of science fiction.
There is a feeling that right now the Humanities comes into the "era accuracy". It's not just about the opportunity to build a more accurate mathematical models of various processes and calculate these models on super computers. New technologies allow to capture and store accurate information about various real events. The only question is that with this information you can do the collected piles of data, people or even research team will not be able to perform for many years. The idea of modern data analysis what computer systems and implemented them to the algorithms themselves work with the obtained range information and give the user only the final result — he is interested in statistics and certain discovered regularities. This allows us not only with mathematical rigor to prove or disprove the hypothesis of the humanitarian sphere, but also to detect dependencies that were unknown to the specialists. Mathematically-savvy humanitarians there is required — they can put a task to explain what kind of data you intend to collect and what kind of characteristics we are interested in.
Recently Yandex has decided to hold a national checklist for everyone who loves math, or, perhaps, wanted to like, but somehow did not develop: students, moms, dads, grandparents. The tasks are easy, according to basic school curriculum — however, for a successful solution you need to be careful. The training missions are already open on the website — you can test your strength.
Control on March 14, the day of PI. To participate in the control, you can not only online in Moscow tasks it will be possible to work out in the Tower, who became a partner of the project. The project was supported by universities in many regions of Russia: Yekaterinburg, Novosibirsk, Kazan and other. Highly recommend to see the hours from Saturday and join in — especially those who are afraid of mathematics. After the test the faculty will disassemble tasks together with the project participants.
"Ignorance of mathematics threatens porridge in the head"
Alexei Savvateev, doctor of physical and mathematical Sciences, expert of the Department of theoretical and applied developments of the company Yandex, scientific Director of the Laboratory of social analysis at the University of Dmitry Pozharsky now there is a debate about politics. It would seem, at what here the math? But a detailed study of the situation it is clear that the Humanities are not familiar with the basics of mathematics, in the head not an opinion but a "mess." They don't have to focus, jump from one argument (the chaotic and often contradictory) on the other. And it is with each of the warring parties. Have someone who understands the math in my head in order, everything in its place. He is considering his position in the chaff it won't. So, ignorance of mathematics threatens to mess in my head.
Humanitarians need to learn beautiful mathematics — pictures, pictures and again pictures. They should immediately get to work on the head: to think, to compare, compare and draw conclusions. Not just to contemplate beautiful mathematical construction, and to be their active co-organizer, to see what purpose is one or the other, to understand the simple logical transitions.
Then, at the next stage, you can already move on to abstract concepts and terms — paradoxically, they are better humanitarians than hard-boiled and hard-nosed techies! It is possible to solve various Diophantine equations to talk about complex numbers, number systems (rings, boxes) and how they help in solving problems. Very affordable already at early stages of comprehension of the mathematics task analysis to the build, what you can and cannot build a compass and a ruler. In General, I would recommend any humanist to learn the book of Courant and Robbins "What is mathematics".
What is the beauty in mathematics? Find a geometric proof of the Pythagorean theorem and you'll understand!
"This science teaches us that unsolvable with sight problems can be solved"
Dmitry Vetrov, candidate of physico-mathematical Sciences, head of big data and information retrieval faculty of computer science In the information age are increasingly voices that any serious knowledge of mathematics-specific and the average person doesn't really need. Many believe that skills in, say, a seven-digit number into four-digit or adding two fractions unnecessary — after all, it can be done on a smartphone. What can we say about the ability to solve logarithmic inequality, algebraic and differential equations, the problem of three-dimensional geometry (solid geometry) and other "higher mathematics"? There are two fundamental arguments against this position. First, the not-so-trivial mathematics is needed in everyday life. For example, to solve a simple problem ("one of the fastest growing African countries, the inflation stands at 32 million interest per year. Question: how many percent in this country rising prices in the day?" The answer many surprise you with its smallness [1]), we need the ability to write and solve equations with logarithms. It is impossible to calculate by what percentage you need to put 5 thousand dollars in the Bank account of a newborn son below 18 years, he was able to get 25 thousand, or is it better to invest our savings so that they will increase at 6% every six months, by 13% each year, or 27% every two years? Perhaps, even more vital (in March 2015) topic: which currency is better to keep their savings in rubles (banks promise high interest), in dollars or in euros? Intuition tells us the correct answer (in all currencies little by little), but in order to choose the right proportions, you should have a basic knowledge in the theory of risk. In meetings at work we often have to make a choice, which of the various points of view to support which group of supporters to join. To do it with the greatest advantage allows the theory of games. It also gives an answer to the question, what salary we can safely require, if you try to win over competitors without fear of a bad bargain or losing an advantageous offer. [1] on the day the inflation in the African country was "just" 4%. Despite seeming a little by the end of the year in the country out of paper for the printing of new banknotes. These are the insidious properties of exponents. Secondly, mathematics (even school) teaches to think logically. To understand what it implies and what is not (for example, from what we have in the fridge, there's herring, it follows that we are there and fish. But from what we have in the fridge, fish should not (although it can be), the herring). Almost the only school subject that teaches reasoning is geometry. But this is only the tip of the iceberg. In fact all around us there are more subtle patterns that go beyond ordinary logic, which operates with concepts of "truth" — false — "unknown". For example, research found that between the length of human hair and its growth there is a negative correlation (stochastic dependence), that is, if you take a random citizen of Russia and to inform us that he had short hair, we will be able with high probability to say that his height is above average. Now you know that I have short hair. Does that give you some additional information about my growth? The correct answer is no [2]. [2] know About me that I'm a man, but about a random citizen of the Russian Federation no. The correlation between height and hair length is currently unknown gender (women, on average, lower than men and have longer hair). Once gender is known, the relationship between length of hair and growth disappears. This phenomenon is known as conditional independence (conditional independence), underlies the whole theory of probabilistic graphical models are actively used in the analysis of texts, images, videos, social networking, etc., and there are many such examples (e.g. is there a relationship between the price of tomatoes in the supermarket and their quality or the relationship between the jeans of a certain brand and my attractiveness to girls; whether to take a paid diagnostic test gives the correct answer in 90% of cases to determine the disease, occurring in one out of ten thousand people [3]). To understand when relationships exist, and when it's false correlations generated by unaccounted factors, you need to have understanding of the basics of probability theory and Bayes ' theorem. Well-developed common sense and a solid b in geometry. [3] it is Not necessary. Even if the test will give a positive result, in 999 cases out of a thousand, it will be a false alarm. Of course, this does not apply to a situation when there are reasonable grounds to assume the existence of a rare disease such as its symptoms. Contemporary mathematics covers a much broader range of issues beyond the household. The largest search engine by which you may read this article, crammed with mathematical models that allow you to adjust the output of the result of our search query under a specific user. In other words, the same Google query I will give some links and you other just because we went to the browser under different gmail accounts. The complex mathematical models used by investment funds that manage our savings; online-shops that recommend us those or other goods; traffic signals that reduce the likelihood of congestion in the streets due to the constant adjustment of his regime; and many other technologies that surround us.
Active use of mathematical methods in modern natural Sciences and the Humanities. Processing of data from the Large hadron Collider has spawned an entire branch of mathematics, the so-called big data analysis (big data). Biologists use mathematical methods to recover the evolutionary tree as the remnants of genomes and organs of extinct species. Chemists are searching for promising future of polymer synthesis using algorithms of mathematical modeling. Critics define using the mathematics of authors, anonymous literary works and paintings. Finally, not to mention a revolution in the field of mathematical methods in machine learning that is happening before our eyes. With the advent and successful application of deep neural networks (deep neural networks) mankind began to rapidly approach the creation of artificial intelligence. Now a high school student who knows how to program, can build a new neural network model that can solve the next task (for example, the synthesis of music, understanding images, etc.) that were previously considered subject only to the human intellect.
Mathematics constantly teaches us that seemingly intractable problems can be solved if you move to a new level of thinking. We divide four by seven, subtract two from nine, operate with irrational numbers, faced with the fact that one equation can have many solutions, but each time has to overcome some break the pattern. The study of mathematics helps to understand that many of the truths we used to think the absolute, are actually relative, and much of what we thought has a different nature, in fact special cases of the same phenomenon just from a different angle of view. Such effects are observed not only in mathematics and its applications, but, for example, in politics. "Global removal of mathematics from society will lead to disaster"
Roman Mikhailov, doctor of physico-mathematical Sciences, leading researcher, SPbSU Adam named the animals. It starts with math. He deals with the classification, the established order. He faces a mobile world, he wants to find it in order to show compliance: "animal" — "name."
In the famous Soviet cartoon kid learns to count. He runs and finds new animal friends. Some are outraged, don't want to be seen. And he is happy with this abstract game. He does math.
Here are some of the areas of modern mathematics: the Classification of complex objects, phenomena, relations. There are objects, which are many, even infinitely many, they need to classify, to distinguish between: rough, thin, somehow.
— Identification of anomalous structures, which do not fit the General smooth classification. Are there animals in the forest who do not fit the common names or which cannot be counted?
— Working with infinity. A huge part of mathematics deals with the asymptotics, it often turns out that the work "far" easier than "close". There are even machines that are attached to an endless ceiling, there is a machine running "past infinity".
— Finding the language to talk with the deep nature. The establishment of various relationships, the creation of dictionaries, the establishment of equivalences of categories. "The largest search engine by which you may read this article, crammed with mathematical models" we Often hear questions about the benefits to society of abstract mathematics, people mention taxpayers, trying to understand what the immediate satisfaction society can bring to what we do. For example, the following.
Modernity gave us the opportunity to run through the text to explore the text in new ways. In a fraction of seconds you can count the number of words in the text, to determine their distribution, to see the standard patterns in the construction of phrases. Once we learn to look at a literary text as a topological space, explore it with the accuracy of deformation, explore its soft nature. Now apply the methods of textual statistics for their research but statistics only gives the rhythm, the pulse of the text, not more. It begins to seem that the languages that we develop over the years, one will find the same application. But not about physics or rocket science, and in psychiatry, psycholinguistics, qualitative studies of the architecture of the nonsense in the theory of consciousness, in the inner bonding patterns. And as before us lay a complex space, so before us will lie a complex and schizophrenia, and it will be clear that there are only a thousand of schizophrenia with these "homology". Try to write long crazy lyrics. Good analysis will show that it is an imitation. There suggestions would be marvelous, but the glue will either be absent altogether, or they will not be enough. The hash to check uninteresting. It is interesting to study the complicated nonsense and try to qualitatively distinguish it from nebreda. Yes, I think that textual criticism will someday apply our topological methods, speak with complex texts in the languages that we developed.
Of course, to study mathematics is optional. Almost none of my friends of his youth could not add fractions. Well? Some have become respected people. Unable to meet with the Professor of philosophy and quite clearly explain to him who he is and what he is and who is right. But the global removal of mathematics from society will cause a disaster soon nature will show some another his face, and the person does not own the language in which to talk to him, and will not know the method of constructing such a language.
About the beauty of mathematics do not really want to talk. Take the checkered notebook, draw your dreams, link similar images in these dreams surfaces, paint it different colors — it's beautiful, try to qualitatively distinguish the configuration of the ligaments in my dreams, who came to new moon. If the difference is sure to be beautiful, will envy you. It is a secret beauty. Text: Elena Kiseleva
P. S. And remember, just changing your mind — together we change the world! ©
Source: theoryandpractice.ru
