newton and leibniz worldviews and achievements who discovered calculus? newton & leibniz are...
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Newton and Leibniz
Worldviews and Achievements
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
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.
Sir Isaac Newton (1642-1727)• Wrote three laws of motion (inertia wasn’t his but from
Philoponus)
• Solved problems such as the velocity of a projectile to escape earth’s gravity.
• Credited with amazing problem-solving ability and mental stamina
• In 1669 & 1671 he wrote, but didn’t 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.
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.
Newton’s 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
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 Newton’s
manuscripts, so Newton is given the most credit. To clear up the matter, in 1714 he wroteHistoria et origo calculi differentialis (History & Origin
of the Differential Calculus)
Leibniz’s 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
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).
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.
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.
Sir Isaac Newton England - island
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 man’s greatest innovations would have been achieved.
Gottfried Leibniz Germany - continent
