Calculus

Karl Weierstrass – the Father of Modern Analysis

Karl Weierstrass – the Father of Modern Analysis

On February 19, 1897, German mathematician Karl Theodor Wilhelm Weierstrass passed away. Weierstrass often is cited as the “father of modern analysis“. He formalized the definition of the continuity of a function, proved the intermediate value theorem and the Bolzano–Weierstrass theorem, and used the latter to study the properties of continuous functions on closed bounded intervals. “… it is true that a mathematician who is not somewhat of a poet, will never be a…
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Standing on the Shoulders of Giants – Sir Isaac Newton

Standing on the Shoulders of Giants – Sir Isaac Newton

Sir Isaac Newton (1643-1727), Portrait by Sir Godfrey Kneller (1689) On January 4, 1643 [N.S.] (25 December 1642 [O.S.]), Sir Isaac Newton, famous physicist, mathematician, astronomer, natural philosopher, alchemist and theologian, was born. With his Principia Newton laid the foundation of modern classical mechanics. Besides he constructed the very first reflecting telescope and independent of Gottfried Wilhelm Leibniz developed differential and integral calculus [10]. “We are to admit no more causes of natural…
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Read Euler, he is the Master of us all…

Read Euler, he is the Master of us all…

On September 18, 1783, Swiss mathematician and physicist Leonhard Euler passed away. Euler is considered to be the pre-eminent mathematician of the 18th century and one of the greatest mathematicians to have ever lived. He is also one of the most prolific mathematicians. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis,…
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Henri Léon Lebesgue and the Theory of Integration

Henri Léon Lebesgue and the Theory of Integration

On June 28, 1875, French mathematician Henri Léon Lebesgue was born. He is best known for his theory of integration, which was a generalization of the 17th century concept of integration, i.e. summing the area between an axis and the curve of a function defined for that axis. By extending the work of Camille Jordan and Émile Borel on the Riemann integral, Lebesgue provided a generalization that solved many of the difficulties…
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Cavalieri’s Principle

Cavalieri’s Principle

On November 30, 1648, Italian mathematician Bonaventura Cavalieri passed away. He is known for his work on the problems of optics and motion, work on the precursors of infinitesimal calculus, and the introduction of logarithms to Italy. Cavalieri’s principle in geometry partially anticipated integral calculus. “Rigor is the concern of philosophy not of geometry.” (Bonaventura Cavalieri) Born at Milan, Cavalieri was given the name Francesco when he was born. His father’s name was…
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Brook Taylor – Forerunner of Differential Calculus

Brook Taylor – Forerunner of Differential Calculus

Brook Taylor (1685–1731) On August 18, 1685, English mathematician Brook Taylor was born. He is best known for Taylor’s theorem and the Taylor series, a method for expanding functions into infinite series. Brook Taylor was born in Edmonton to John Taylor of Bifrons House, Kent, and Olivia Tempest in 1685. It was the year when King Charles II passed away and his Roman Catholic brother succeeded him as King James II of England, the…
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Augustin-Louis Cauchy and the Rigor of Analysis

Augustin-Louis Cauchy and the Rigor of Analysis

On August 21, 1789, French mathematician Augustin-Louis Cauchy was born. He is considered one of the greatest mathematicians during the nineteenth century. There are 16 concepts and theorems named for Cauchy, more than for any other mathematician. Cauchy was one of the most prolific mathematicians of all times. Cauchy wrote 789 papers, a quantity exceeded only by Euler and Cayley, which brought precision and rigor to mathematics. Actually, Cauchy was one of…
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Let Us Calculate – the Last Universal Academic Gottfried Wilhelm Leibniz

Let Us Calculate – the Last Universal Academic Gottfried Wilhelm Leibniz

Gottfried Wilhelm Leibniz (1646 – 1716) On July 1, 1646, one of the last universally interdisciplinary academics, active in the fields of mathematics, physics, history, politics, philosophy, and librarianship was born. Gottfried Wilhelm Leibniz counts as one of the most influential scientists of the late 17th and early 18th century and impersonates a meaningful representative of the Age of Enlightenment. Leibniz made up his interests concerning philosophy and law studies in his…
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