MATHEMATICIANS

Johann Bernoulli (27 July 1667 – 1 January 1748) was a Swiss mathematician who studied reflection and refraction of light, orthogonal trajectories of families of curves, quadrature of areas by series and the brachystochrone. In 1691 Johann went to Geneva where he lectured on the differential calculus. From Geneva, Johann made his way to Paris and there he met de l'Hôpital and they engaged in deep mathematical conversations. Contrary to what is commonly said these days, de l'Hôpital was a fine mathematician, perhaps the best mathematician in Paris at that time, although he was not quite in the same class as Johann Bernoulli. De l'Hôpital was delighted to discover that Johann Bernoulli understood the new calculus methods that Leibniz had just published and he asked Johann to teach him these methods. Bernoulli received generous payment from de l'Hôpital for these lessons. After Bernoulli returned to Basel he still continued his calculus lessons by correspondence, and this did not come cheap for de l'Hôpital who paid Bernoulli half a professor's salary for the instruction. However it did assure de l'Hôpital of a place in the history of mathematics since he published the first calculus book Analyse des infiniment petits pour l'intelligence des lignes courbes (1696) which was based on the lessons that Johann Bernoulli sent to him. As one would expect, it upset Johann Bernoulli greatly that this work did not acknowledge the fact that it was based on his lectures. The well known de l'Hôpital's rule is contained in this calculus book and it is therefore a result of Johann Bernoulli.

Rene Descartes (March 31, 1596 - February 11, 1650), also known as Renatus Cartesius (latinized form), was a highly influential French philosopher, mathematician, scientist, and writer. He has been dubbed the "Father of Modern Philosophy" and the "Father of Modern Mathematics," and much of subsequent Western philosophy is a reaction to his writings, which have been closely studied from his time down to the present day. His influence in mathematics is also apparent, the Cartesian coordinate system that is used in plane geometry and algebra being named for him, and he was one of the key figures in the Scientific Revolution.
His system of coordinate geometry was described in La Geometrie, published at Leiden in 1637.

Maurits Cornelis Escher (17 June 1898 – 27 March 1972), usually referred to as M.C. Escher, was a Dutch graphic artist. He is known for his often mathematically inspired woodcuts, lithographs, and mezzotints. These feature impossible constructions, explorations of infinity, architecture, and tessellations.

Euclid fl. 300 BC, also known as Euclid of Alexandria and the "Father of Geometry", was a Greek mathematician of the Hellenistic period who was active in Alexandria, almost certainly during the reign of Ptolemy I (323 BC - 283 BC). Little is known about Euclid other than his writings. What little biographical information we do have comes largely from commentaries by Proclus and Pappus of Alexandria: Euclid was active at the great Library of Alexandria and may have studied at Plato's Academy in Greece. The date and place of Euclid's birth and the date and circumstances of his death are unknown.
His Elements is the most successful textbook in the history of mathematics. In it, the principles of what is now called Euclidean geometry are deduced from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, and rigor.

Pierre de Fermat (August 17, 1601 or 1607/8 - January 12, 1665) was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to modern calculus. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of the then unknown differential calculus, as well as his research into the theory of numbers. He also made notable contributions to analytic geometry, probability, and optics. Fermat was the first person known to have evaluated the integral of general power functions. Using an ingenious trick, he was able to reduce this evaluation to the sum of geometric series. The resulting formula was helpful to Newton, and then Leibniz, when they independently developed the fundamental theorem of calculus. In number theory, Fermat studied Pell's equation, Fermat numbers, perfect, and amicable numbers. It was while researching perfect numbers that he discovered the little theorem. He also invented a factorization method which has been named for him as well as the proof technique of infinite descent, which he used to prove Fermat's Last Theorem for the case n = 4. Fermat also developed the two-square theorem, and the polygonal number theorem, which states that each number is a sum of three triangular numbers, four square numbers, five pentagonal numbers, and so on.

Martin Gardner (born October 21, 1914, Tulsa, Oklahoma, died May 22, 2010) was an American mathematics and science writer specializing in recreational mathematics, but with interests encompassing micromagic, stage magic, pseudoscience, literature (especially the writings of Lewis Carroll), philosophy, scientific skepticism, and religion. He wrote the Mathematical Games column in Scientific American from 1956 to 1981, and he has published over 70 books. Gardner reportedly coined the term mathemagician.

Johann Carl Friedrich Gauss (30 April 1777-23 Feb 1855) was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, electrostatics, astronomy, and optics. Sometimes known as the princeps mathematicorum (Latin, usually translated as "the Prince of Mathematicians", although Latin princeps also can simply mean "the foremost") and "greatest mathematician since antiquity", Gauss had a remarkable influence in many fields of mathematics and science and is ranked as one of history's most influential mathematicians.
Gauss was a child prodigy. There are many anecdotes pertaining to his astounding precocity while a mere toddler, and made his first ground-breaking mathematical discoveries while still a teenager. He completed Disquisitiones Arithmeticae, his magnum opus, in 1798 at the age of 21, though it would not be published until 1801. This work was fundamental in consolidating number theory as a discipline and has shaped the field to the present day.

The Mandelbrot set fractal is named after Benoit Mandelbrot who discovered it in 1976 and is largely responsible for the present interest in fractal geometry. He showed how fractals can occur in many different places in both mathematics and elsewhere in nature.

He was born in Poland in 1924 into a family with a very academic tradition. His father, however, made his living buying and selling clothes while his mother was a doctor. As a young boy, Mandelbrot was introduced to mathematics by his two uncles.

For more on the Mandelbrot set read Chaos by James Gleick, or The Armchair Universe by A.K.Dewdney.

Sir Isaac Newton (4 January 1643 - 31 March 1727) was the greatest English mathematician of his generation. He laid the foundation for differential and integral calculus. His work on optics and gravitation make him one of the greatest scientists the world has known.
Newton's laws of motion are three physical laws which provide relationships between the forces acting on a body and the motion of the body, first compiled by Sir Isaac Newton. Newton's laws were first published together in his work Philosophiae Naturalis Principia Mathematica (1687). The Principia is recognised as the greatest scientific book ever written. Newton analysed the motion of bodies in resisting and non-resisting media under the action of centripetal forces. The results were applied to orbiting bodies, projectiles, pendulums, and free-fall near the Earth. He further demonstrated that the planets were attracted toward the Sun by a force varying as the inverse square of the distance and generalised that all heavenly bodies mutually attract one another.

The laws form the basis for classical mechanics.

1. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.
2. The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. Acceleration and force are vectors (as indicated by their symbols being displayed in slant bold font); in this law the direction of the force vector is the same as the direction of the acceleration vector.
3. For every action there is an equal and opposite reaction.

Blaise Pascal (June 19, 1623 – August 19, 1662), mathematician and philosopher, was educated at home by his father, himself a considerable mathematician. The origins of probability are usually found in the correspondence between Pascal and Fermat where they treated several problems associated with games of chance. The letters were not published but their contents were known in Parisian scientific circles. Pascal's only probability publication was the posthumously published Traite du triangle arithmetique (1654); this treated Pascal's triangle with probability applications. Pascal introduced the concept of expectation and discussed the problem of gambler's ruin.

Pythagoras (about 569 BC - 475 BC) was a Greek philosopher who made important developments in mathematics, astronomy, and the theory of music. Pythagoras of Samos is often described as the first pure mathematician. He is an extremely important figure in the development of mathematics yet we know relatively little about his mathematical achievements. Unlike many later Greek mathematicians, where at least we have some of the books which they wrote, we have nothing of Pythagoras's writings. The society which he led, half religious and half scientific, followed a code of secrecy which certainly means that today Pythagoras is a mysterious figure.
The theorem now known as Pythagoras's theorem was known to the Babylonians 1000 years earlier but he may have been the first to prove it.

John Venn (4 Aug 1834 - 4 April 1923) was awarded a mathematics scholarship in his second year of study at Caius College Cambridge. He was elected a Fellow of Gonville and Caius College shortly after graduating, and two years later was ordained a priest. In fact the year after his graduation, in 1858, he had been ordained a deacon at Ely, then after his ordination as a priest he had served as a curate first at Cheshunt, Hertfordshire, and then for a year as a curate at Mortlake, Surrey.
In 1862 he returned to Cambridge University as a lecturer in Moral Science, studying and teaching logic and probability theory. He had already become interested logic, philosophy and metaphysics, reading the treatises of De Morgan, Boole, John Austin, and John Stuart Mill.

Venn extended Boole's mathematical logic and is best known to mathematicians and logicians for his diagrammatic way of representing sets, and their unions and intersections. He considered three discs R, S, and T as typical subsets of a set U. The intersections of these discs and their complements divide U into 8 non-overlapping regions, the unions of which give 256 different Boolean combinations of the original sets R, S, T.