The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, followed closely by Ancient Egypt and the Levantine state of Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the patterns in nature, the field of astronomy and to record time and formulate calendars.
Johannes Kepler was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws of planetary motion, and his books Astronomia nova, Harmonice Mundi, and Epitome Astronomiae Copernicanae. These works also provided one of the foundations for Newton's theory of universal gravitation.
Menelaus of Alexandria was a Greek mathematician and astronomer, the first to recognize geodesics on a curved surface as natural analogs of straight lines.
The year 1643 in science and technology involved some significant events.
The Kepler conjecture, named after the 17th-century mathematician and astronomer Johannes Kepler, is a mathematical theorem about sphere packing in three-dimensional Euclidean space. It states that no arrangement of equally sized spheres filling space has a greater average density than that of the cubic close packing and hexagonal close packing arrangements. The density of these arrangements is around 74.05%.
Bonaventura Francesco Cavalieri was an Italian mathematician and a Jesuate. He is known for his work on the problems of optics and motion, work on indivisibles, the precursors of infinitesimal calculus, and the introduction of logarithms to Italy. Cavalieri's principle in geometry partially anticipated integral calculus.
Pappus of Alexandria was one of the last great Greek mathematicians of antiquity, known for his Synagoge (Συναγωγή) or Collection, and for Pappus's hexagon theorem in projective geometry. Nothing is known of his life, other than what can be found in his own writings: that he had a son named Hermodorus, and was a teacher in Alexandria.
In mathematics, Pappus's centroid theorem is either of two related theorems dealing with the surface areas and volumes of surfaces and solids of revolution.
Antoine de Laloubère, a Jesuit, born in Languedoc, is chiefly known for an incorrect solution of Pascal's problems on the cycloid, which he gave in 1660, but he has a better claim to distinction in having been the first mathematician to study the properties of the helix.
Jost Bürgi, active primarily at the courts in Kassel and Prague, was a Swiss clockmaker, a maker of astronomical instruments and a mathematician.
Niccolò Zucchi was an Italian Jesuit, astronomer, and physicist.
Thomas Callister Hales is an American mathematician working in the areas of representation theory, discrete geometry, and formal verification. In representation theory he is known for his work on the Langlands program and the proof of the fundamental lemma over the group Sp(4). In discrete geometry, he settled the Kepler conjecture on the density of sphere packings and the honeycomb conjecture. In 2014, he announced the completion of the Flyspeck Project, which formally verified the correctness of his proof of the Kepler conjecture.
Federico Commandino was an Italian humanist and mathematician.
The University of Graz Library, in Graz, Austria is the largest scientific and public library in Styria and the third largest in Austria. It holds the right of legal deposit. It is part of the University of Graz and consists of the main library, two faculty libraries and several branch libraries and is open to the public.
Paolo Casati was an Italian Jesuit mathematician. Born in Piacenza to a Milanese family, he joined the Jesuits in 1634. After completing his mathematical and theological studies, he moved to Rome, where he assumed the position of professor at the Collegio Romano. He was given the chair in mathematics after teaching philosophy and theology.
During the Renaissance, great advances occurred in geography, astronomy, chemistry, physics, mathematics, manufacturing, anatomy and engineering. The collection of ancient scientific texts began in earnest at the start of the 15th century and continued up to the Fall of Constantinople in 1453, and the invention of printing democratized learning and allowed a faster propagation of new ideas. Nevertheless, some have seen the Renaissance, at least in its initial period, as one of scientific backwardness. Historians like George Sarton and Lynn Thorndike criticized how the Renaissance affected science, arguing that progress was slowed for some amount of time. Humanists favored human-centered subjects like politics and history over study of natural philosophy or applied mathematics. More recently, however, scholars have acknowledged the positive influence of the Renaissance on mathematics and science, pointing to factors like the rediscovery of lost or obscure texts and the increased emphasis on the study of language and the correct reading of texts.
This is a timeline of ancient Greek mathematicians.
A timeline of algebra and geometry
Johannes Kepler is a 1974 East German historical drama film directed by Frank Vogel and starring Reimar J. Baur, Trude Bechmann and Kurt Böwe. It is a biopic of the German astronomer and mathematician Johannes Kepler.
