I am knee-deep in Grattan-Guinness' latest book: "The Norton History
of the Mathematical Sciences: The Rainbow of Mathematics" (First US
edition 1998).
1 Pre-viewing the rainbow
2 Invisible origins and ancient traditions
3 A quiet millennium: from the early Middle Ages into the European
Renaissance
4 The age of trigonometry: Europe, 1540-1660
5 The calculus and its consequences, 1660-1750
6 Analysis and mechanics at centre stage, 1750-1800
7 Institutions and the profession after the French Revolution
8 Mathematical analysis and geometries, 1800-1860
9 The expanding world of algebras, 1800-1860
10 Mechanics and mathematical physics, 1800-1860
11 International mathematics, but the rise of Germany
12 The rise of set theory: mathematical analysis, 1860-1900
13 Algebras and geometries: their relations and axioms, 1860-1900
14 An era of stability: mechanics, 1860-1900
15 An era of media: mathematical physics, 1860-1900
16 The new century, to the Great War and beyond
17 Re-viewing the rainbow
According to Ivor G-G, the present book differs significantly from many
others histories of mathematics in several respects. One of these is the
following:
"I take _the word 'history'_ to relate to the question
'What happened in the past?';
by contrast, mathematicians (and scientists in general, and
even a distressing number of historians) take history to mean
'How did we get here?'
The difference between these two questions is worth pondering.
Answers to the second one draw _only_ on those parts of the
past that have led to our present situation; while a perfectly
respectable form of research, they can give quite mistaken
impressions about the aims and purposes of historical figures,
and the priorities they saw in their own work."
Now... the difference between the two questions mentioned above is worth
pondering, but should these questions be placed in disjoint baskets? ...
Greetings to all,
Julio GC