By Michael J. Bradley

Even though mathematical innovation stagnated in Europe after the autumn of the Roman Empire, students in southern Asia and the center East persevered to maintain the mathematical writings of the Greeks and contributed new principles to mathematics, algebra, geometry, and trigonometry, in addition to astronomy and physics. The 5 centuries from CE 1300 to 1800 marked the tip of a wealthy interval of cultural, mathematical, and clinical developments in China, India, and Arabic international locations, whereas witnessing new highbrow lifestyles in Europe and the Western Hemisphere. "The Age of Genius" acquaints center and highschool scholars with the lives and contributions of 10 interesting yet might be lesser-known mathematical pioneers of this time. integrated right here, for instance, is a portrait of 14th-century Iranian mathematician Ghiyath al-Din Jamshid Mas'ud al-Kashi, who constructed and superior tools for approximating numerical values, and brought geometrical tools for settling on components and volumes of architectural domes, arches, and vaults.

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Further Advances in Geometry, Trigonometry, and Algebra In his other mathematical works, Viète contributed new methods, ideas, and insights to several branches of mathematics. In 1592, he gave a series of public lectures refuting French mathematician 24 The Age of Genius J. J. Scaliger’s claim that he had found ruler-and-compass methods to square the circle, trisect an angle, and construct the two mean proportionals between two line segments. Viète’s presentation of his arguments was so effective that Scaliger left the country, with his reputation as a scholar severely tarnished.

In 1636, Fermat sent his two unpublished manuscripts to Marin Mersenne, a Jesuit priest and French mathematician living in Paris who served the mathematical community by communicating new discoveries to a network of mathematicians throughout France. At the same time, another French mathematician, René Descartes, was finalizing a manuscript titled Discours de la méthode pour bien conduire sa raison et chercher la vérité dans les sciences (Discourse on the method for rightly directing one’s reason and searching for truth in the sciences) and its mathematical appendix, La géométrie (The geometry).

Pierre de Fermat 4 (1601–1665) Pierre de Fermat investigated properties of prime numbers, divisibility, and powers of integers that established the discipline of modern number theory. (University of Rochester, courtesy of AIP Emilio Segrè Visual Archives) Father of Modern Number Theory Through the hundreds of letters that he sent to other mathematicians, Pierre de Fermat (pronounced fair-MAH or FER-mat) contributed influential ideas to four areas of mathematics. With René Descartes, he shares the credit for developing the basic ideas of analytic geometry.