<!DOCTYPE html><HTML lang="en"> <head><meta charset="utf-8"> <title>Gillies (Donald) - Revolutions in Mathematics: Introduction (Theo Todman's Book Collection - Paper Abstracts) </title> <link href="../../TheosStyle.css" rel="stylesheet" type="text/css"><link rel="shortcut icon" href="../../TT_ICO.png" /></head> <BODY> <CENTER> <div id="header"><HR><h1>Theo Todman's Web Page - Paper Abstracts</h1><HR></div><A name="Top"></A> <TABLE class = "Bridge" WIDTH=950> <tr><th><A HREF = "../../PaperSummaries/PaperSummary_10/PaperSummary_10568.htm">Revolutions in Mathematics: Introduction</A></th></tr> <tr><th><A HREF = "../../Authors/G/Author_Gillies (Donald).htm">Gillies (Donald)</a></th></tr> <tr><th>Source: Gillies - Revolutions in Mathematics</th></tr> <tr><th>Paper - Abstract</th></tr> </TABLE> </CENTER> <P><CENTER><TABLE class = "Bridge" WIDTH=400><tr><td><A HREF = "../../PaperSummaries/PaperSummary_10/PaperSummary_10568.htm">Paper Summary</A></td><td><A HREF = "../../PaperSummaries/PaperSummary_10/PapersToNotes_10568.htm">Notes Citing this Paper</A></td></tr></TABLE></CENTER></P> <hr><P><FONT COLOR = "0000FF"><U>Notes</U> <ol type="1"><li>Gillies starts with a brief account of three political revolutions which are important models for subsequent discussion of the possibility of revolutions in mathematics:- <ul type="disc"><li>The English 17th-century revolution (deposition of Charles I followed by a dictatorship and subsequently, after the restoration of Charles II, by the  Glorious Revolution , the replacement of James II by William and Mary) </li><li>The French revolution  similar deposition and execution of the King, followed by a dictatorship and subsequent restoration of the monarchy with attenuated powers (and with a similar epilogue, where a less suitable monarch  Charles X  is replaced by a more suitable one  Louis Philippe)</li><li>The Russian revolution where, while there is deposition and execution of the Czar, there is no subsequent restoration of the monarch. </li></ul></li><li>Kuhn s <I>The Structure of Scientific Revolutions</I> has been substantially accepted, with modifications since 1962. Kuhn s theory is that science continues in stasis in between revolutions where the dominant paradigm is replaced by a new one. Again, three examples are given :- <ol type="i"><li>Copernican: convoluted path from Aristotle-Ptolemy to Newton</li><li>Chemical: explanation of combustion as loss of phlogiston replaced by an explanation involving addition of oxygen</li><li>Einsteinian: replacement of Newtonian mechanics by the theory of relativity </ol> </li></ol> </FONT><FONT COLOR = "0000FF"><HR></P><a name="ColourConventions"></a><p><b>Text Colour Conventions (see <A HREF="../../Notes/Notes_10/Notes_1025.htm">disclaimer</a>)</b></p><OL TYPE="1"><LI><FONT COLOR = "0000FF">Blue</FONT>: Text by me; &copy; Theo Todman, 2018</li></OL> <BR><HR><BR><CENTER> <TABLE class = "Bridge" WIDTH=950> <TR><TD WIDTH="30%">&copy; Theo Todman, June 2007 - August 2018.</TD> <TD WIDTH="40%">Please address any comments on this page to <A HREF="mailto:theo@theotodman.com">theo@theotodman.com</A>.</TD> <TD WIDTH="30%">File output: <time datetime="2018-08-02T07:25" pubdate>02/08/2018 07:25:18</time> <br><A HREF="../../Notes/Notes_10/Notes_1010.htm">Website Maintenance Dashboard</A></TD></TR> <TD WIDTH="30%"><A HREF="#Top">Return to Top of this Page</A></TD> <TD WIDTH="40%"><A HREF="../../Notes/Notes_11/Notes_1140.htm">Return to Theo Todman's Philosophy Page</A></TD> <TD WIDTH="30%"><A HREF="../../index.htm">Return to Theo Todman's Home Page</A></TD> </TR></TABLE></CENTER><HR> </BODY> </HTML>