Is mathematics discovery or invention?
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1 Is mathematics discovery or invention? From the problems of everyday life to the mystery of existence Part One By Marco Dal Prà Venice - Italy May
2 Foreword This document is intended as a starting point for serious reflection on a problem: the existence of physics. The aim is to open a debate, because the topic is much more interesting and profound than you might think. Suggestions & feedback: dalpra.marco@gmail.com 2
3 Preface / 1 Was mathematics discovered or invented of humans? Apparently it seems a very banal question, but on the contrary the answer has surprising consequences. In fact, physics is based on mathematics, so if you find answers to existential problems of mathematics, you can find answers to questions about the existence of the humans and the universe. 3
4 Preface / 2 Similar questions have been asked by some scientists of the early '900, in particular by the discoverers of quantum physics, as Einstein, Schroedinger, Bohr. On the contrary, the philosophers do not seem to have ever asked this question, and even contemporary scientists. Perhaps that some men consider it "uncomfortable"? Now, we start our reflection trying to analyze the problem to 360 degrees. 4
5 Problems of definition Before you begin, it is necessary to make a clarification on terminology. That is, it is essential to clarify what it means discovery and what it means invention, otherwise you risk getting lost in a thousand opinions without concluding anything. 5
6 From Dictinoary Merriam-Webster To INVENT - to produce as something useful for the first time through the use of the imagination or of ingenious thinking and experiment. INVENTION a product of the imagination. 6
7 From Dictinoary Merriam-Webster To Discover to obtain sight or knowledge of for the first time Discovery disclosure, display, exploartion. From Italian vocabulary : To discover : Identify, find, acquire human experience facts, concepts, places previously unknown. Discovery : Locating a subject of considerable interest (scientific, social, economic, cultural). 7
8 A bit of history To begin our analysis, it is necessary to analyze briefly the history of mankind and mathematics. Let us briefly. 8
9 Where is the origin of mathematics? Mathematics is a tool developed in ancient times to solve everyday problems as trade, commerce, construction, measurements and many other human activities. 9
10 Where is the origin of mathematics? Pythagoras... Then from addition and subtraction has passed, to multiplication and divisions. And then squaring, square roots, etc.. etc... 10
11 Mathematics follow the evolution As with all scientific and technical disciplines, also mathematics was developed with the help of so many men. Archimedes, Euclid, Fourier, Lagrange, Laplace, Euler, Cantor, Hilbert and many others, each is contributing to the advancement of the discipline. 11
12 Meanwhile, someone look over... Eratosthenes, librarian of Alexandria in Egypt, is one of the first to use mathematics and geometry for "scientific purpose. In about 200 BC, he was able to calculate the circumference of the earth using the shadows of the sun inside the wells of two Egyptian cities. (with an error very small: about 1,5%!!!) 12
13 Then came Newton Isaac Newton, to solve the problems of the motion of objects, realized how essential it was mathematics to solve them. In practice, he could not approach the problem in a scientific manner without first was endowed of the appropriate mathematicians "tools". And since these tools for this problem did not exist, He had to "invent them. (eg. infinitesimal calculus) 13
14 Physics and mathematics At this point, without further historical quotations, it is quite clear that the physics to exist, needs mathematics! Instead, the opposite is not true : mathematics does not need the physics to exist. In fact... the mathematics doesn t need no other discipline to exist! 14
15 Physics and mathematics The dependence of physics from mathematics is not essential to solve our initial question. But will subsequently be used to analyze the consequences to which port the answer. 15
16 What do they say mathematicians? We now move in the early 1900s. In this age we find some mathematicians who express opinions about mathematics and its role, its foundations. 16
17 David Hilbert German mathematician ( ), father of the Formalist school. About mathematics, Hilbert said One of the supreme achievements of purely intellectual human activity. In other words, according to this discipline, mathematics is an activity of free thought. 17
18 Godfrey Harold Hardy English mathematician ( ), author of the fundamental contributions that we will see later. In his book A Mathematician's Apology is written: "I am interested in mathematics only as a creative art A A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. 18
19 Alan Touring English Mathematical and logical ( ), father of computer science. He about the mathematics said : Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity 19
20 The race ends... At this point, are the mathematicians to tells us that mathematics is an invention. Its formulas in fact stems from the human s mind, by his free thoughts. 20
21 A foregone conclusion! In fact, the mathematical formulas were not discovered such example was with vaccines, DNA, chemical elements, electricity. They are the result of reflections of the human intellect as were the inventions: the phone, the press, the light bulb, the steam engine, etc.. 21
22 But what happens? Everything seems to be resolved, but only apparently. The answer generates a new question, much more complicated than the first. If mathematics is a logical exercise of the human imagination, how can it explain the phenomena of the universe? 22
23 This creates a mathematical short-circuit If mathematics is born in the human's mind, how can we explain the existence of the physics? 23
24 Part One - End Continues in the second part: Consequences of the invention of mathematics Marco Dal Prà dalpra.marco@gmail.com 24
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