number theory

Charles Hermite’s admiration for simple beauty in Mathematics

Charles Hermite’s admiration for simple beauty in Mathematics

On December 24, 1821, French mathematician Charles Hermite was born. He was the first to prove that e, the base of natural logarithms, is a transcendental number. Furthermore, he is famous for his work in the theory of functions including the application of elliptic functions and his provision of the first solution to the general equation of the fifth degree, the quintic equation. “There exists, if I am not mistaken, an entire…
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Carl Jacobi and the Elliptic Functions

On December 10, 1804, German mathematician Carl Gustav Jacob Jacobi was born. He made fundamental contributions to elliptic functions, dynamics, differential equations, and number theory. “Any progress in the theory of partial differential equations must also bring about a progress in Mechanics.” – Carl Jacobi, Vorlesungen über Dynamik [Lectures on Dynamics] (1842/3) Carl Jacobi – A Child Prodigy Carl Jacobi was the son of a banker and grew up in a rather…
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God made the integers, all the rest is the work of man – Leopold Kronecker

God made the integers, all the rest is the work of man – Leopold Kronecker

On December 7, 1823, German mathematician Leopold Kronecker was born, who worked on number theory and algebra. He criticized Cantor’s work on set theory, and his most cited quote says, “Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk” (traditionally rendered: “God made natural numbers; all else is the work of man“.) Leopold Kronecker – Early Life Leopold Kronecker was born in Liegnitz, Prussia (now Legnica, Poland) in a wealthy Jewish…
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Adrien-Marie Legendre – Providing the Essential Analytical Tools for Mathematical Physics

Adrien-Marie Legendre – Providing the Essential Analytical Tools for Mathematical Physics

On September 18, 1752, French mathematician Adrien-Marie Legendre was born. He is best known for his contributions in number theory, celestial mechanics and elliptic functions. It was in a paper on celestial mechanics concerning the motion of planets (1784) that he first introduced the Legendre Polynomials. Moreover, he served as director of the of the Bureau des Longitudes, standardizing French weights and measures. “All the truths of mathematics are linked to each…
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Marin Mersenne – Mathematics and Universal Harmony

Marin Mersenne – Mathematics and Universal Harmony

On September 8, 1588, French polymath Marin Mersenne was born. He is perhaps best known today among mathematicians for Mersenne prime numbers. He also developed Mersenne’s laws, which describe the harmonics of a vibrating string. “Philosophy would long ago have reached a high level if our predecessors and fathers had put this into practice; and we would not waste time on the primary difficulties, which appear now as severe as in the…
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Sophie Germain and the Chladni Experiment

Sophie Germain and the Chladni Experiment

On June 27, 1831, French mathematician, physicist, and philosopher Marie-Sophie Germain passed away. She is best known for her work in number theory and contributions to the applied mathematics of acoustics and elasticity. Her work on Fermat’s Last Theorem provided a foundation for mathematicians exploring the subject for hundreds of years after. Because of prejudice against her gender, she was unable to make a career out of mathematics, but she worked independently throughout her…
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Lejeune Dirichlet and the Mathematical Function

Lejeune Dirichlet and the Mathematical Function

On February 13, 1805, German mathematician Johann Peter Gustav Lejeune Dirichlet was born. Dirichlet is best known for his papers on conditions for the convergence of trigonometric series and the use of the series to represent arbitrary functions. He also proposed in 1837 the modern definition of a mathematical function. “In mathematics as in other fields, to find one self lost in wonder at some manifestation is frequently the half of a new discovery.”…
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Euclid of Alexandria – the Father of Geometry

Euclid of Alexandria – the Father of Geometry

At about 330 BC, Euclid of Alexandria was born, who often is referred to as the Father of Geometry. His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century. In the Elements, Euclid deduced the principles of what is now called Euclidean geometry from…
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Ernst Kummer and the Introduction of Ideal Numbers

Ernst Kummer and the Introduction of Ideal Numbers

On January 29, 1810, German mathematician Ernst Eduard Kummer was born. One of his major contributions is the introduction of ideal numbers, which are defined as a special subgroup of a ring, extended the fundamental theorem of arithmetic to complex number fields.He also discovered the fourth order surface based on the singular surface of the quadratic line complex. This Kummer surface has 16 isolated conical double points and 16 singular tangent planes.…
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Carl Friedrich Gauss – The Prince of Mathematicians

Carl Friedrich Gauss – The Prince of Mathematicians

On April 30, 1777, German mathematician and physical scientist Carl Friedrich Gauss was born. He contributed significantly to many fields, including number theory, algebra, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics. He is often referred to as Princeps mathematicorum (Latin, “the Prince of Mathematicians”) as well as “greatest mathematician since antiquity”. “Mathematics is the Queen of Science, and Arithmetic is the Queen of Mathematics” – handed down in Wolfgang Sartorius…
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