Gottfried Wilhelm Leibniz

The Scientific Revolution –
Ajay Kumar, Lyndon Shi,
Nicholas Voreas
Gerolamo Cardano
Father of Complex Numbers
Gerolamo Cardano - Biography
• Born 1501
• Unhappy childhood – illegitimate son
• Inventor, astrologer, philosopher, algebraist,
• Known as the “Gambling Scholar” for his
gambling skills
• Wrote more than 200 books on subjects that
interested him
• Committed suicide (September 21, 1576)
Complex Numbers
An Introduction
Complex Numbers
• Also known as imaginary numbers
• A variable (i) stands for the square root of a
negative number
• Always do the i part first when solving
Without Complex Numbers…
• No iPod
• No modern advancement
• No quantum theory
Francois Viete
French Mathematician
Lived 1540 to 1603
Father of modern symbolic algebra
Career as a lawyer, worked on mathematics in
spare time
• Involved in politics, worked for Kings Henry III
& IV
• Decoded messages sent to Philip II of Spain
• First works – Canon mathematicus, Universalium
Inspectionum Liber Singularis, (1579)
– Trigonometric tables calculated to 9 decimal places
– Collection of trigonometric formulas
• In artem analyticam isagoge (1591)
– Algebraic notation
– Use of letters for unknowns and constants
– Vowels are unknowns, letters are constants
• Math of
• Relationships
sides and
Symbolic Algebra
John Napier
Scottish noble/landowner
Lives 1550 to 1617
Attention to land (inventions)
Theologian/astronomer, worked on
mathematics in spare time
• Invented logarithms, Napier’s Bones, decimal
• The Plaine Discovery of the Whole Revelation
of St. John (1593)
– Against Papacy
• A Description of the Wonderful Canon of
Logarithms (1614)
– Explained inventions
– Logarithmic tables
– Led to base 10
• Exponential form
• How many of one number do we multiply to
get another
log2(8) = 3
Napiers Bones
• Multiplication tables
Blaise Pascal
Pascal’s Triangle
Blaise Pascal
• Born: June 19, 1623 (Clermont)
• Was kept away from mathematics at an early age
– led to curiosity on the subject
• Easily mastered properties of geometry by
experimenting himself
• Invented “arithmetic machine” – could
• Spent some time studying religion
• Died: August 19, 1662 (Paris)
Pascal’s Triangle
Isaac Newton
Born Dec. 25, 1642 in Woolsthorpe, England
Father died before he was born, mother moved away
Grew up with his uncle
Attended Trinity College at the University of Cambridge in
1661, received bachelor of arts in 1665
• In 1669, appointed professor of mathematics at Trinity
College, and elected to the Royal Society in 1672
• Elected to Parliament in 1691, warden of the mint in 1696
• Died March 20, 1727
Newton’s Development of Modern
• First version of Newton’s calculus published in 1665-6
• Seemed to be derived from ideas of motion
• Considered variables changing with time
• His calculus was geometrical, as opposed to analytical
• Used “infinitesimals”, infinitely small but not zero
• Later replaced by notions
• Applied his version of calculus to general physics
• Included the laws of differentiation and integration, second
and higher derivatives, and the notion of an approximating
polynomial series
• Calculus today is used in many ways, some including physical
sciences, engineering, computer science and statistics
Gottfried Wilhelm Leibniz
• Born in 1646
• Early years influenced by moral and religious views of
• Attended University of Leipzig at age 14 in 1661
• Studied philosophy, mathematics, rhetoric, Latin, Greek
and Hebrew
• Graduated with bachelor’s in 1663, got master’s degree in
philosophy the same year
• Death on November 14, 1716
Development of the Binary System
• Developed by Gottfried Wilhelm Leibniz
• Belief that all logic can be translated from a verbal
representation to an absolute mathematical condition
• Ideas were repelled, Leibniz dropped the idea for
about 10 years
• Hope revived when the Book of Change was
published, and he found confirmations of his ideas
within this book
• If such things as yes/no, on/off and male/female could
be reduced to straightforward propositions, why
couldn’t logic and thought?
• Went out to define his binary system
• Transposed numbers into seemingly infinite rows of
ones and zeroes
• At the end of his life he began to believe that his binary
number were quasi-religious mysticisms
• Claimed that it portrayed creation, with one being God,
and zero being void
• Hartshorne, Robin. "François Viète - Life." Mathematicians. 1998.
University of California Berkeley Math Department. 02 Dec. 2012
• Hartshorne, Robin. "Work." Mathematicians. 1998. University of California
Berkeley Math Department. 02 Dec. 2012
• O'Conner, J. J., and E. F. Robertson. "François Viète." Viete biography. Jan.
2000. School of Mathematics and Statistics University of St Andrews,
Scotland. 02 Dec. 2012 <>.
• O'Conner, J. J., and E. F. Robertson. "John Napier." Napier Biography.
School of Mathematics and Statistics University of St Andrews, Scotland,
Apr. 1998. Web. 02 Dec. 2012. <>.
• Russel, Deb. "John Napier Biography." John Napier Biography.,
2012. Web. 02 Dec. 2012.
• "1660-1670 Newton and Leibniz, Founders of Modern
Calculus." IT Support from MSP Provider in New Jersey RSS.
N.p., n.d. Web. 04 Dec. 2012.
• "Gottfried Wilhelm Leibniz - Biography." Gottfried Wilhelm
Leibniz. N.p., n.d. Web. 04 Dec. 2012.
• "Gottfried Wilhelm Leibniz (1646 - 1716)." Gottfried
Wilhelm Leibniz (1646 - 1716). N.p., n.d. Web. 04 Dec.
2012. <>.
• "The History of Calculus." The History of Calculus. N.p., n.d.
Web. 04 Dec. 2012.
"Google Images." Google Images. N.p., n.d. Web. 03 Dec. 2012.
"Articles with Keyword Pascal. - Answers in Genesis." Articles with
Keyword PascalEnter Website Address or Keywords to Cite. Answers in Genesis. N.p., n.d. Web. 03 Dec. 2012.
website address or keywords to cite.>.
"Blaise Pascal (1623 - 1662)." Blaise Pascal (1623 - 1662). N.p., n.d.
Web. 03 Dec. 2012.
"Gerolamo Cardano, Physician Extraordinaire." World Research
Foundation RSS. N.p., n.d. Web. 03 Dec. 2012.
"Pascal's Triangle." Pascal's Triangle. N.p., n.d. Web. 03 Dec. 2012.

similar documents