Newton and Leibniz

1
Newton and Leibniz

• Worldviews and Achievements

2
Who discovered Calculus?

• Newton Leibniz are attributed with the
  discovery of Calculus, instead of Archemides,
  Oresme, Fermat or Isaac Barrows, etc., because
• they were the 1st to accomplish these 4 tasks

• 1. Developed general concepts relating the 2
  basic calculus problems, extrema area
• Newton called them fluxion and fluent
• Leibniz labeled them differential and integral

3
Who discovered Calculus?

• 2. Developed notation algorithms
• thus allowing easy use of these concepts
• 3. Understood applied inverse relationships of
  their two concepts
• 4. Used the 2 concepts in the solution of many
  difficult unsolved problems
• Yet neither established the Calculus with the
  rigor of classical Greek geometry. This awaited
  a precise definition of limits.

4
Sir Isaac Newton (1642-1727)

• Wrote three laws of motion (inertia wasnt his
  but from Philoponus)
• Solved problems such as the velocity of a
  projectile to escape earths gravity.
• Credited with amazing problem-solving ability and
  mental stamina
• In 1669 1671 he wrote, but didnt publish
• De analysi per aequantiones numero terminorum
  infinitas (On Analysis by Equations with
  Infinitely Many Terms) and
• Tractatus de methodis serierum et fluxionum (A
  treatise on the method of series fluxions)
• Yet they circulated to some extent in manuscript
  form among mathematicians of England.

5
Sir Isaac Newton (1642-1727)

• These manuscripts were the result of two years of
  self-study in the mid 1660s. He consolidated and
  generalized all the material on tangents and
  areas ever developed into the magnificent
  problem-solving tool exhibited in the 1000-page
  calculus textbooks of our own day. (See Katz pg
  505)
• His magnum opus, Principia (1687, 2nd 3rd
  editions in 1713 1726) , was the most important
  text of the Scientific Revolution.
• As opposed to the common belief that Newton
  developed calculus to explain physics, the
  evidence shows that in fact the calculus was
  developed well before the physics. But what he
  did do was use the ideas and methodology of the
  calculus to derive many physical results.

6
Newtons Theology

• Member of the Royal Society of London, a
  scientific club founded by English Puritans
• Had some trouble reconciling how Jesus was fully
  God and fully man
• Wrote several books of Biblical chronology and
  observations
• Based all his scientific motivations on God as
  first cause of all mechanical processes

7
Gottfried Leibniz (1646-1716)

• Constructed a calculating machine that multiplied
  and divided
• Worked in history, politics, law, theology, and
  economics
• Developed calculus method as far as Newton and in
  the same time period
• Published first, but about 10 years after
  Newtons manuscripts, so Newton is given the most
  credit. To clear up the matter, in 1714 he wrote
• Historia et origo calculi differentialis (History
  Origin of the Differential Calculus)

8
Leibnizs Theology

• Believed in preestablished harmony between
  thought and reality
• Gave himself to science to see the wonders of God
  more clearly
• Lived in Germany, the heart of the Protestant
  Reformation movement
• Believed in the Creator God as also the sustainer
  of all things

9
Four Puritan Factors in Science

• Absolute authority of Scripture (reason and
  science are tools of dominion).
• God is Creator and Lawgiver (ability to study).
• Vocation and calling (application of Biblical
  principles to secular activities).
• Optimistic eschatology (positive outlook
  concerning progress of society).

10
Christianity and Modern Science

• Scientific thought was hindered by the Roman
  Catholic view of God as a mystical embodiment of
  divinity.
• The Reformation brought about a view of God from
  His work.

• Those who used the understanding of God as a
  motivation to study included but were not limited
  to Copernicus, Galileo, Kepler, Newton, Leibniz,
  Pascal, and Maxwell.

11
What We Gather

• It is quite obvious that the concept and
  understanding of God presented both Newton and
  Leibniz with an unsurpassed motivation to
  mathematically model the world around them.
• The idea of God as the Law-Giver helped give
  weight to the theory that nature was created with
  a set of its own laws.
• This has shown to be true in all understood cases
  and may be applied to unknown territory in
  scientific study in order to better understand
  such subjects.

12
Sir Isaac Newton England - island
Gottfried Leibniz Germany - continent
It is most important to remember that in either
case, these great mathematicians would admit that
the driving force behind their work was their
Christian belief in God. Without this force, it
cannot be said that each mans greatest
innovations would have been achieved.
13
Finis

• Presentation Jordan Harp
• Questions, Comments...
• Email webmaster_at_reticence.net