From the Pythagorean theorem, through which every student begins to know Geometry, to Fermat's last theorem, to Newton's fundamental calculus, from the equation of Relativity, to the "elegant" theorem of Gauss and those of Gödel's incompleteness and Heisenberg's indeterminacy, the history and enterprise of knowledge can be recognized in some formulas, often simple, elegant and as concise to read as they are complex, mysterious and very rich in content, which reveal also personal events, intellectual challenges, dramatic turning points in the history of humanity and revolutions of thought. Six formulas capable of describing and synthesizing large portions of the world and its functioning.
The interlocutors of these Dialogues will be mathematicians, physicists, logicians, philosophers, psychologists, geneticists: Vincenzo Baron,Claudio Bartocci, Arnaldo Benini,Remo Bodei, Edoardo Boncinelli,Umberto Bottazzini, Massimo Bucciantini,Laura Catastini, Franco Ghione, Giulio Giorello,Paul Legrenzi, Gabriel Lolli, Piergiorgio Odifreddi, Guido Tonelli, and with the participation of Massimo popolizio. All meetings will be introduced and moderated by Pino Donghi.
THE PROGRAM
– 21 January 2018 at 11
a2 + b2 = c2
PYTHAGORAS, THE FATHER OF ALL THEOREMS
Remo Bodei and Umberto Bottazzini
Among the many legends that accompany the Pythagorean theorem, one tells of how the philosopher would have formulated his theorem while, sitting in a large hall of the palace of Polycrates in Samos, he observed the square tiles of the floor, perhaps seeing one of them "perfectly" broken on a diagonal… history or legend, whether it was Pythagoras who actually discovered it or whether it was already known among the Babylonians, in China and in India, the theorem of Euclidean geometry which establishes the relationship between the sides of a right triangle marks one of the starting points of civilization, cultural development, philosophy and aesthetics… as well as the first theorem we all study in school.
– 11 February 2018 at 11
E = mc2
EINSTEIN, RELATIVITY, SPACE AND TIME
Vincenzo Barone and Arnaldo Benini
Among the formulas that accompanied the "relativist" revolution of the early 900s, surpassing the great Newtonian synthesis, that of the relationship between mass and energy is also one of the most iconic in the history of thought. Simplicity and elegance combined with an explanatory power capable of subverting knowledge and opening countless horizons to scientific research and the investigation of meaning. With "special relativity" all otherwise conventional ideas about the world, starting from the notions of space and time, are called into question: Albert Einstein's equations become a vision of the world, the one in which we are living. And how can we understand the world without a sense of time?
– 18 March 2018 at 11
GAUSS, THE ELEGANT THEOREM
Laura Catastini, Franco Ghione, Guido Tonelli
In 1827 Gauss published a research destined to definitively change the history of mathematics and philosophical thought under the title Disquisitiones generales circasurfaces curvas. In this work Gauss indicates the way to coherently develop a geometry in a curved two-dimensional environment, with its segments, circles, triangles. In these spaces Gauss proves that the area of a triangle A,B,C does not depend on the length of its sides but on the size of its internal angles. Infinite other new geometries become possible, even those where the sum of the internal angles can be greater or less than 180°… and our image of the universe can develop freely by breaking the bars of the Euclidean cage.
– 8 April 2018 at 18pm
NEWTON, THE CALCULATION OF MODERN SCIENCE
Massimo Bucciantini and Giulio Giorello
“I have elaborated a general method which is applied, without having to resort to any complicated calculation, not only for drawing tangents and curves of any kind [...] but also for solving other more abstruse types of problems concerning curves and areas”. Thus wrote, in his own hand, Isaac Newton announcing the discovery of the fundamental theorem of calculus, whose basic relationship shows how "integration" and "differentiation" are the inverse of each other, this had an enormous impact on the study of trajectories and of the motions of moving bodies and their speed. At the center of a controversy that pitted the followers of Newton in England against those of Leibniz on the European continent, the fundamental theorem of calculus represents one of the most significant scientific results of that great revolution which, heralded by the astronomical theories of Copernicus, passing through Kepler and Galilei, arrives at the Newtonian synthesis, that is: the birth of modern science.
– 22 April 2018 at 11pm
an + bn =/ cn
FERMAT, THE DUEL OF THE SOLUTION
Paolo Legrenzi and Piergiorgio Odifreddi
The Egyptians already knew that 9 + 16 = 25, that is 32 + 42 = 52. And the Pythagoreans discovered infinite examples of triads of analogous integers. In 1637 Pierre de Fermat showed that it is not possible to find integers such that a4 + b4 = c4, and he imagined that it was not possible for any other exponent other than 2 either. He was right, but it took more than 350 years for Andrew Wiles proved it. This millennial story is a true saga, and in this meeting we will tell some anecdotes and some background.
– 13 May 2018 at 11
GÖDEL AND HEISENBERG, THE PRINCIPLES OF DOUBT
Claudio Bartocci, Edoardo Boncinelli, Gabriele Lolli and with the participation of Massimo Popolizio
Kurt Gödel's 1930 proof that, in a mathematical theory satisfying certain minimal conditions, it is possible to construct a syntactically correct proposition that can neither be proved nor disproved within the theory, with the consequence that the theory's coherence is not provable in the theory itself, together with the uncertainty principle enunciated by the German physicist Werner Heisenberg in 1927, which establishes limits for the knowledge of the position or speed of a sub-atomic particle, they represent two cornerstones of thought not only for the development of the respective disciplines , mathematics and physics, but for epistemological research and the philosophy of science of the twentieth century, and not only of that. Perhaps also to the extent of this relevance, there have been many misunderstandings and metaphorical escapes on which we can reflect today sedatis motibus. Without forgetting that the theoretical assumptions of the "Copenhagen interpretation" have inspired one of the most successful theatrical performances of the last twenty years.
For information www.mulino.it andwww.auditorium.com.
