**:**

The Last "Universal Genius"

The Last "Universal Genius"

**Biography**

Leibniz v. Newton

Leibniz's Calculus

Childhood

born in Leipzig on July 1, 1646

family was Lutheran & elite

parents:

father (Friedrich) was a jurist and professor of Moral Philosophy at the University of Leipzig

mother (Catharina) was the daughter of a professor of Law

Education & Life

University of Leipzig (baccalaureate)

University of Altdorf (Doc. of Law)

spent 4 years in Paris & met many influential people (intellectuals, mathematicians, etc.)

tutored by Christiaan Huygens in physics, philosophy, and math

developed many of his ideas after exposure to Pascal's manuscripts

Mathematical Discoveries & Later Life

Origin of the Dispute

Newton wrote

Method of Fluxions

in 1671 but refused to publish (or even publicly discuss) his works.

Leibniz published his papers on differential and integral calculus in 1684 and 1686, respectively

Newton's works were finally published in 1736, almost ten years after his death

By this time, Leibniz's works were already very well-read

Differences

Results

In 1715, the Royal Society credited Newton with the discovery of calculus & Leibniz was guilty of plagiarism

Leibniz died unhonored & poor

After the death of Leibniz, the accusations of plagiarism were proved false & both men now are accredited for the discovery.

Newton had an impressive, stately funeral, but it was too late for Leibniz.

Much of Leibniz's discoveries are used commonly in calculus today, while Newton's are not.

General Leibniz Rule (the Product Rule)

Leibniz is generally credited with finding and providing the proof for the product rule, in which (fg)'= f'g+fg'.

So thanks for that.

Determinants

http://www.amazon.com/Bahlsen-Leibniz-Butter-Biscuits-7-Ounce/dp/B000FBQ4YU

http://www.gwleibniz.com/

http://www.phillwebb.net/history/modern/leibniz/leibniz.htm

http://maps.google.com/

http://harpers.org/blog/2009/12/pascals-principle-of-convergence/http://remus.shidler.hawaii.edu/genes/Bavaria/Altdorf/home.htm

http://en.wikipedia.org/wiki/Leipzig_University

http://en.wikipedia.org/wiki/Eiffel_Tower

http://www.ssplprints.com/image/95580/leibniz-calculating-machine-1694

Mathnotes.org

goparallel.sourceforge.net

http://www1.umn.edu/ships/9-1/calculus.htm

http://blog.stephenwolfram.com/2013/05/dropping-in-on-gottfried-leibniz/

The Argument

Had Leibniz discovered calculus independently or had he just invented another notation for Newton's ideas?

Debate lasted from 1709 until Leibniz's death in 1716 and involved Newton's disciple John Keill, as well as many other mathematicians

No one doubted that Newton had already developed his method when Leibniz began work, but there was no proof of this.

He only explained his method a full 20 years later, when Leibniz's articles were already well-read.

His manuscripts came to light only in 1736, well after his death and Leibniz's.

Leibniz's Arguments

Leibniz

published a description of his method years before Newton printed anything;

always alluded to the discovery as being his own invention, a statement which went unchallenged for years;

demonstrated in his private papers his development of calculus independently of Newton's path.

Newton's Arguments

Leibniz

saw some of Newton's papers on the subject around 1676.

may have obtained the fundamental ideas of the calculus from those papers.

The fact that Leibniz's claim went unchallenged is immaterial, and no attempt was made to rebut the private demonstrations.

Leibniz's Disadvantages

Leibniz had less education than Newton and was generally regarded as not having as much mathematical skill.

Leibniz saw mathematics as a link to his other interests, especially philosophy, & didn't pursue it as intensely.

Newton was already well-known for other achievements

A method for finding the determinant was

rediscovered and applied by Leibniz.

http://en.wikipedia.org/wiki/Leibniz_formula_for_determinants

http://en.wikipedia.org/wiki/Determinant

Example: Find the Determinant

Leibniz's Integral Rule

The Derivative is equal to...

Used when a function is defined as an

integral. Can be used to analyze a mathematical model or to evaluate very challenging integrals.

Example:

Find the derivative, f'(x)

What do organic mathematicians throw into their fireplaces?

Natural Logs!

F(x,t)=

(cos(tx))/t (dt)

2

discovered differential calculus, integrals, & infinite series

designed a calculating machine capable of performing addition, subtraction, multiplication, and division

vast network of correspondents

sent letters to over 1100 people

died November 14th, 1716

http://www.pinterest.com/ssupermom/inked/

http://en.wikipedia.org/wiki/Leibniz_integral_rule

yay calculus

A math professor in an unheated room is cold and calculating.

Around 1673, Leibniz found a series that was able to converge to the value of pi by using James Gregor's arctangent expansion.

It converges very slowly: 5 billion terms are needed to get 10 correct digits of pi.(Pattanayak)

Finding Pi

Deaf mathematicians communicate through sine language.

When the stats teacher wrote a cookbook, she called it 'Pi A La Mode.'

**with puns!**

Now try it yourself!

Find the derivative, f'(t)

1

f(x,t)=

Bibliography

Conrad, Keith. “Differentiating Under the Integral

Sign.” PDF file. Web. 3 June 2014.

“Generalized Product Rule: Leibniz’s formula”.

Physics pages. Wordpress, March 2011. Web. 27 May 2014.

Hand, Paul. “Problem on computing the

determinant of a 3x3 matrix.” Leading Lesson. 2014. Web. 3 June 2014

Look, Brandon. “Gottfried Wilhelm Leibniz.” The

Stanford Encyclopedia of Philosophy (Fall 2014 Edition). Stanford University, 22 Dec. 2007. Web. 20 May 2014.

Bibliography

O’Connor, John J., and Edmund F. Robertson.

“Gottfried Wilhelm von Leibniz.” The MacTutor History of Mathematics Archive. University of St. Andrews, April 2o14. Web. 20 May 2014.

Pattanayak, Ari. The Mathematical Leibniz.

Rutgers Department of Mathematics, May 2002. Web. 27 May 2014.

Thiel, Christopher. “Determinants.” Internet

Archive. Internet Archive, March 2013. Web. 1 June 2014.

Tisdale, Chris. “Differentiate under integral

signs: Leibniz rule.” Online Video Clip. Youtube. Youtube, 9 November 2011. Web. 2 June 2014.