Adventures in formalism
type: Item
instance of: scholarly article
zbMATH Open document ID: 1254.00013
publication date: 2012-08-14T00:00:00Z
Mathematics Subject Classification ID: 00-01
Mathematics Subject Classification ID: 00-02
Mathematics Subject Classification ID: 00A35
Mathematics Subject Classification ID: 00A30
zbMATH DE Number: 6065489
zbMATH Keywords: formalism
zbMATH Keywords: axiomatization
author: Craig Smoryński
MaRDI profile type: Publication
title: Adventures in formalism
published in: Texts in Mathematics
review text: Adventures in formalism is a modern investigation into the role, form, development, effect, and appreciation of formalism in mathematics. The preface briefly explores various meanings of the word `formalism' and introduces three particular types of formalism that are explored via examples throughout the book. Type I formalism stands for the process of the manipulation of symbols fueled by `reasoning by analogy', where one is willingly blind to the meaninglessness of the manipulations (e.g., early appearance of imaginary numbers). Type II formalism stands for the transition from an intuitive notion to a precise concept (e.g., the formulation of limit). Type III formalism stands for the modern axiomatic approach whereby one describes what something is by what one can do with it rather than by how to build it.NEWLINENEWLINEThe adventures recounted span numerous areas of mathematics scattered across several millennia with the bulk of the journey taking place in the past four centuries. The exposition includes all of the mathematical details needed to fully understand each and every example considered with the exception of a handful of cases. An essential part of the exposition are the lively descriptions and analyses of the reactions of (both prominent and less prominent) mathematicians to various developments.NEWLINENEWLINEWhile portions of the book will be accessible to readers with no mathematical training, the book will be particularly appealing to those with some university level mathematical background. To the expert mathematician the book offers a very broad view of the development of modern ideas, as well as a wide selection of historical case studies, interesting in their own right, that can effectively be used as supplements when teaching analysis or algebra courses. To the advanced student/beginning researcher the book will demonstrate that the birth of some of the most fundamental aspects that we take for granted today was fraught with difficulties and was u…
reviewed by: Ittay Weiss
description: scientific article; zbMATH DE number 6065489