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Niels Henrik Abel (1802-1829)
  • Born in Norway.
  • He demonstrated that the general quintic equation could not be solved algebraically.
  • He transformed the theory of elliptic integrals by introducing elliptic functions.
  • He provided the first stringent proof of the bionomial theorem.

Maria Gaetana Agnesi (1718-1799)
  • Born in Italy.
  • In her book Analytical Institutions, she formed a complete and integrated treatment of algebra and analysis and new ideas and techniques of calculus.

Albuzjani (940-998)
  • Born in Iran.
  • He introduced some trigonometrical functions.
  • He constructed tables of tangents and cotangents.

Omar Alkayami (fl. early 11th century)
  • Born in ??.
  • Through geometric tratment of cubic equations, he obtained a root as the abcissa of a point of intersection of a conic and a circle.
  • He is said to have stated that a formula showing that the sum of two cubes equals a third cube is impossile to solve.

Anaximander (611 BCE - 545 BCE)
  • Born in Greece.
  • It is stated that he wrote a treatise on geometry, in which he paid attention to the properties of spheres and to the concept of infinity in space and time.

Apollonius of Perga (ca. 262-240 BCE to ca. 190-170 BCE)
  • Born in Greece.
  • He was one of the founding fathers of mathematical astronomy.
  • He described in his writings a new idea on how to subdivide the cone to produce circles.
  • He catalogued new kinds of closed curves that he named ellipses, parabolas, and hyperbolas.
  • He presented a method of figuring at what points a planetary orbit takes on apparent retrograde motion.

Archimedes (fl. ca. 225 BCE)
  • Born in Italy.
  • He proved the modern formula for the area of a circle involving pi.
  • He provided a means of finding the area of a parabola by summing a certain infinite geometric series.
  • He found how to determine surfaces areas of spheres and related bodies.
  • He was the first to apply geometry successfully to statics and hydrostatics.
  • He proved a number of theorems about the area swept by a spiral.

Archytas (fl. ca. 400 BCE)
  • Born in Italy.
  • He produced a solution for finding the side of a cube whose volume is double that of a given cube.

Jean Robert Argand (1768-1822)
  • Born in Switzerland.
  • He gave a geometrical representation of a complex number, and applied it to show that every algebraic equation has a root.