Summary Of "Brief History Of Mathematics" By Mónica Cerruti: UNIVERSITY SUMMARIES

By MAURICIO ENRIQUE FAU

THE CRISIS OF MODERN RATIONALITY has multiple manifestations and one of them in the history of mathematics, in the middle of the 19th century. At the beginning of modernity, mathematics was the scientific model par excellence. It was already considered a perfect science whose truths were exact and definitive, and when with Galileo physics was mathematized, mathematics also became a description of the order of the world, the precise representation of the essence of things. We have summarized the essentials of "A Brief History of Mathematics", by Monica Cerrutti

• Language: English
• Publisher: BOOKS AND SUMMARIES BY MAURICIO FAU
• Release date: Oct 7, 2021
• ISBN: 9798201909017

MAURICIO ENRIQUE FAU

Mauricio Enrique Fau nació en Buenos Aires en 1965. Se recibió de Licenciado en Ciencia Política en la Universidad de Buenos Aires. Cursó también Derecho en la UBA y Periodismo en la Universidad de Morón. Realizó estudios en FLACSO Argentina. Docente de la UBA y AUTOR DE MÁS DE 3.000 RESÚMENES de Psicología, Sociología, Ciencia Política, Antropología, Derecho, Historia, Epistemología, Lógica, Filosofía, Economía, Semiología, Educación y demás disciplinas de las Ciencias Sociales. Desde 2005 dirige La Bisagra Editorial, especializada en técnicas de estudio y materiales que facilitan la transición desde la escuela secundaria a la universidad. Por intermedio de La Bisagra publicó 38 libros. Participa en diversas ferias del libro, entre ellas la Feria Internacional del Libro de Buenos Aires y la FIL Guadalajara.

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Summary Of Brief History Of Mathematics By Mónica Cerruti

UNIVERSITY SUMMARIES

MAURICIO ENRIQUE FAU

Published by BOOKS AND SUMMARIES BY MAURICIO FAU, 2021.

While every precaution has been taken in the preparation of this book, the publisher assumes no responsibility for errors or omissions, or for damages resulting from the use of the information contained herein.

SUMMARY OF BRIEF HISTORY OF MATHEMATICS BY MÓNICA CERRUTI

First edition. October 7, 2021.

Copyright © 2021 MAURICIO ENRIQUE FAU.

ISBN: 979-8201909017

Written by MAURICIO ENRIQUE FAU.

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Summary Of Brief History Of Mathematics By Mónica Cerruti (UNIVERSITY SUMMARIES)

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Cerrutti, Mónica BRIEF HISTORY OF MATHEMATICS

THE CRISIS OF MODERN RATIONALITY has multiple manifestations, one of them in the history of mathematics, in the middle of the 19th century.

At the beginning of modernity, mathematics was the scientific model par excellence. It was already considered a perfect science whose truths were exact and definitive, and when with Galileo physics was mathematized, mathematics also became a description of the order of the world, the precise representation of the essence of things.

Moreover, Mathematics (with a capital letter) was considered a UNIT of knowledge: it was a coherent system of truths that were deduced from a few principles (axioms) that were considered evident (indubitably true). Mathematical truths are deduced from these axioms, that is, they are inferred by means of valid reasoning. The crisis will result in no longer speaking of Mathematics but of mathematics (with lower case and plural), i.e., the idea of unity is lost. This is due to the emergence of rival mathematical paradigms.

In the second decade of the 19th century it was thought that mathematics constituted a unitary system of knowledge, but mathematicians also knew that this unity was only an intuition and needed to be strictly demonstrated. It was then that the project of A LOGICAL FOUNDATION OF MATHEMATICS arose in some mathematicians. For this purpose demonstrations, clear definitions and axioms were constructed.

THE LOGICIST PROJECT WANTED TO SHOW THAT MATHEMATICS WAS ULTIMATELY REDUCIBLE TO LOGIC, THAT ITS TRUTHS WERE LOGICAL AND THEREFORE UNQUESTIONABLE.

The logicist project failed because it came to show that both logic and mathematics ultimately depend on set theory (in the sense that both presuppose it).

In parallel, in the field of geometry, NON-EUCLIDIAN GEOMETRY was born.

A NON-EUCLIDEAN GEOMETRY IS A GEOMETRIC THEORY THAT REJECTS ONE OF EUCLID'S AXIOMS AND REPLACES IT BY ANOTHER OR OTHERS.

Non-Euclidean geometries are incompatible with Euclidean geometry, in the sense that they cannot all be true because they contradict each other. The question then arises as to WHAT IS THE TRUE GEOMETRY OF THE PHYSICAL WORLD. It is no longer evident that Euclidean geometry is.

There is a very important mathematical result which is the so-called PROOF OF RELATIVE CONSISTENCY: it is difficult to prove that a theory is consistent, for logical reasons that are not worth developing here. But it is much easier to show that if a theory A is consistent, then another theory B is also consistent. This is called relative consistency and is not a minor result as long as there are good reasons to think that theory A