Cultural Foundations of Mathematics: The Nature of Mathematical Proof and the Transmission of the Calculus from India to Europe in the 16th C. CE

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Pearson Education India, 2007 - Calculus - 477 pages
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The Volume Examines, In Depth, The Implications Of Indian History And Philosophy For Contemporary Mathematics And Science. The Conclusions Challenge Current Formal Mathematics And Its Basis In The Western Dogma That Deduction Is Infallible (Or That It Is Less Fallible Than Induction). The Development Of The Calculus In India, Over A Thousand Years, Is Exhaustively Documented In This Volume, Along With Novel Insights, And Is Related To The Key Sources Of Wealth-Monsoon-Dependent Agriculture And Navigation Required For Overseas Trade - And The Corresponding Requirement Of Timekeeping. Refecting The Usual Double Standard Of Evidence Used To Construct Eurocentric History, A Single, New Standard Of Evidence For Transmissions Is Proposed. Using This, It Is Pointed Out That Jesuits In Cochin, Following The Toledo Model Of Translation, Had Long-Term Opportunity To Transmit Indian Calculus Texts To Europe. The European Navigational Problem Of Determining Latitude, Longitude, And Loxodromes, And The 1582 Gregorian Calendar-Reform, Provided Ample Motivation. The Mathematics In These Earlier Indian Texts Suddenly Starts Appearing In European Works From The Mid-16Th Century Onwards, Providing Compelling Circumstantial Evidence. While The Calculus In India Had Valid Pramana, This Differed From Western Notions Of Proof, And The Indian (Algorismus) Notion Of Number Differed From The European (Abacus) Notion. Hence, Like Their Earlier Difficulties With The Algorismus, Europeans Had Difficulties In Understanding The Calculus, Which, Like Computer Technology, Enhanced The Ability To Calculate, Albeit In A Way Regarded As Epistemologically Insecure. Present-Day Difficulties In Learning Mathematics Are Related, Via Phylogeny Is Ontogeny , To These Historical Difficulties In Assimilating Imported Mathematics. An Appendix Takes Up Further Contemporary Implications Of The New Philosophy Of Mathematics For The Extension Of The Calculus, Which Is Needed To Handle The Infinities Arising In The Study Of Shock Waves And The Renormalization Problem Of Quantum Field Theory.
 

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Decolonialized math should recognize that abstract rational number arithmetic was commonly in use for 3,600 years before base 10 decimal cultures, and colonial empires sometimes used Euclid as a geometry foundation. Gauss in 1801, Discussions on Arithmetic restated the traditional abstract number theory as congruences, a point of view that was restated as clock arithmetic in German schools after 1854, honoring the life work of Gauss. By 1910 an international conference concluded that Gaussian clock arithmetic in several remainder arithmetic forms should be an international standard. Had WW I not come along, and made all things Germans of ill repute , did Euclid reappear in U.K, French and USA schools
That us to conclude, omitting all references to abstract number theory that was in use prior to Mercantilism and colonies, Professor Rau has no meaningful understanding of western mathematical traditions, before , during or after colonial periods , hence unqualiied to the extreme to offer a replacement .
Milo Gardner
Math historian , reading Egyptian , Greej, Arab and medieval math texts based in abstract number theory ...not geometry .
 

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The author unknowingly summarised this book in his famous article on 𝑻𝒉𝒆 𝑪𝒐𝒏𝒗𝒆𝒓𝒔𝒂𝒕𝒊𝒐𝒏 ; 𝑻𝒐 𝒅𝒆𝒄𝒐𝒍𝒐𝒏𝒊𝒔𝒆 𝑴𝒂𝒕𝒉𝒔 , 𝑺𝒕𝒂𝒏𝒅 𝒖𝒑 𝒕𝒐 𝒊𝒕𝒔 𝑭𝒂𝒍𝒔𝒆 𝑯𝒊𝒔𝒕𝒐𝒓𝒚 𝒂𝒏𝒅 𝑩𝒂𝒅 𝑷𝒉𝒊𝒍𝒐𝒔𝒐𝒑𝒉𝒚 as
"Decolonised maths rejects the
redundant metaphysics of formal math as inferior knowledge. It reverts to a commonsense practical philosophy of mathematics as a technique of approximate calculation for practical purposes...It also leads to a better science, the simplest example being a better theory of gravitation arising from correcting Newton’s wrong metaphysical presumptions about calculus.
In short, maths can be decolonised. The simple way to do it is to have the courage to stand up to its false Western history and bad Western philosophy and focus solely on its practical value."
 

Contents

List of Boxes Tables and Figures
xv
Preface
xxvii
Introduction
xxxv
Euclid and Hilbert
3
Proof vs Pramāna
59
Boxes
64
Infinite Series and a
109
Time Latitude Longitude and the Globe
201
Models of Information Transmission
267
How and Why the Calculus Was Imported into Europe
321
Figures
372
Numbers in Calculus Algorismus and Computers
375
Math Wars and the Epistemic Divide in Mathematics
411
A Distributions Renormalization and Shocks
425
The Feynman diagrams for electron and photon selfenergy
441
Index
459

Tables
225
Kamāl or Rāpalagai
239

Common terms and phrases

Bibliographic information