2.  Born July 1, 1646 in Leipzig, Germany  Son of a professor of moral philosophy  Went to university at 15 and graduated at 17 in theology, law, and math.  Instead of going into academia, he professionally served noblemen in areas such as official historian and legal advisor.  Died in 1716 http://en.wikipedia.org/wiki/Gottfried_Leibniz

3.  Worked on what is now called topology, the study of the properties of geometric figures that remain unchanged when under distortion. ◦ A good example is that a circle is topologically equivalent to an ellipse

4.  Leibniz is given credit along with Newton for discovering infinitesimal calculus (variable having zero as limit).  Made a calculus machine (an early version of a calculator)  Summed infinite series including Sum 1/ n(n+1), Sum 1/ n(n+1)(n+2) etc. using the idea of difference equations (maths.uwa)  Rewrote Pascal's proof of sin' x = cos x in terms of increment in y /increment in x  Discovered the algorithms for the sum, product and quotient rule.

5.  “I shall now show that the general problem of quadratures can be reduced to the finding of a line that has a given law of tangency, that is, for which the sides of the characteristic triangle have a given mutual relation. Then I shall show how this line can be described by a motion that I have invented. For this purpose I assume for every curve C(C') a double characteristic triangle, one, TBC, that is assignable, and one, GLC, that is inassignable, and these two are similar.” http://www.maths.uwa.edu.au/~schultz/3M3/L19Leibniz.html

7. The Relational Theory  there is no absolute location in either space or time  Space and time are not in themselves real (they are not substances)  Space and time are ‘thus the hypostatizations of ideal relations.’ In English this means they are not real

8. http://www.iep.utm.edu/l/leib-met.htm#H1 http://mathworld.wolfram.com/Topology.html http://ww.ugrad.math.ubc.ca/coursedoc/math100/labs/lab1/lab1.html http://www.worldbookonline.com/student/article?id=ar318720&st=leibniz http://dictionary.reference.com/browse/infinitesimal http://www.maths.uwa.edu.au/~schultz/3M3/L19Leibniz.html http://en.wikipedia.org/wiki/Gottfried_Leibniz