Archimedes, Aristarchus, and Eratosthenes were scientists and mathematicians from 300 B.C. in Greece. They invented mechanisms that are still with us today: the compound pulley, pump, the discovery of Pi along with the realization of centers of gravity of planar regions. They dedicated their lives to their work and in some cases lost their lives while engrossed in their work. Archimedes was killed in just that way in Syracuse by a Roman invasion.
Those scientists did not know through empirical evidence that the earth was 4 billion years old or about the “big bang” theory, but their studies and contributions lead their successors to prove those scientific facts.
The next distinguishable contributions in Calculus were by John Napier and Johannes Kepler from 1550-1617. Napier discovered the concept of the logarithm. After that, Pierre de Fermat (1601-1665) invented the concept of maxi ma and mini-ma of the tangent of a graph. He is famous for founding the probability theory, and for Fermat’s last theorem, which was not solved until 1994 by Andrew Wiles at Princeton University.
In England, Sir Isaac Newton was one of two people to invent Calculus. At an early age (25), he was the lead Professor of Mathematics at Cambridge. He originally went there to study law, but authored the law of gravitation from his intense studies of physics and astronomy. After a nervous illness, he became the warden of the Government Mint, became wealthy and was honored to be a life long member of the Royal Society.
His rival, Von Leibniz (1646-1716), conflicted with Newton because of his beliefs about the dy/dx derivative and the integral. Von Leibniz wanted to create a new algebra encompassing all reasoning. He, like many of his predecessors, was a prodigy at age 14 and attended the University of Leipzig in Germany.
The next significant figure in Calculus is Leonhard Euler (1707-1783). He graduated from the universityand became a professor of Math and Physics in Basel, Switzerland. He won the Grand Prize in Paris for his discovery of “e” or irrational numbers with his formula. Despite his great contributions, he suffered bouts of ill health and eye problems that eventually lead to blindness.
Joseph-Louis Lagrange (1736-1813) was the Director of Mathematics in Berlin and attended the Academy of Sciences in Paris. He invented the Lagrange multiplier method in Calculus with the variation of finding paths that optimize certain physical quantities of energy particles moving along them. Napoleon awarded him the Legion of Honor award.
In 1854, Bernhard Riemann (1826-1866) was responsible for the theory of integral Riemann sums. He used analytic tools with Geometry which was the framework for the Theory of Relativity.
Francis Galton (1822-1911) was the cousin of Charles Darwin and attended Trinity College at Cambridge where he made advances as a meteorologist studying the relationships between wind, speed, direction and barometric pressure.
The American scientist William Libby invented formulas known as the Product Rule and the Quotient Rule and these were used to measure the decay of radioactive carbon. Carbon dating (C-14) and (C-12) and formulas (40) and (39) are responsible for decoding art forgeries during World War II. The Master painter Jan Vermeer (1632-1675) used paint containing white lead which has a radioactive substance called Lead-210. After the war, a man named Meegeren collaborated with the Nazi’s in Holland to copy paintings and sell them on the black market as originals. Because of Libby's discoveries, investigators were able to tell the time of manufacture of the paintings based on the half life rate of decay of white lead in the paint and prove that the paintings were forgeries based on the decay constant in L-210.
There are many other practical uses for calculus from figuring out mortgages based on the number of months and monthly payment compounded with monthly interest to analyzing graphs to formulate conjectures, solve problems, and support written work with scientific evidence. The fundamental Theorem of Calculus is to make connections between integration and differentiation and how to evaluate a definite integral.
The information compiled for this list is taken from “A Brief Version of Calculus: Ideas and Applications” by Alex Himonas and Alan Howard.
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