Gottfried Wilhelm Leibniz

BY ERIK NEWHOUSE

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

His Life Story (in a nutshell)

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Mathematical Contributions

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

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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.

Math (cont.)

“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.”

Leibniz at work…http

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According to Leibniz, “a conception of truth has important consequences for a conception of reality and how it is to be understood at its most profound level.” (iep.utm)

Leibniz was known to question statements such as that “the sky is gray,” with the thinking that the statement is true only if the thing we call the “sky” is really gray. This raises the question, is the sky gray? Does it have color? AUGHHHHHH!

Philosophy

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

Physics

Sources 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