SPHERICAL GEOMETRY and SPHERICAL TRIGONOMETRY and their applications to geography and astronomy and

SPHERICAL GEOMETRY and SPHERICAL TRIGONOMETRY and their applications to geography and astronomy and

developed original concepts that were later used in CALCULUS .

Bing, R. H. (1914–86) American topologist and native of Texas who studied TOPOLOGY and two- and three-dimensional

MANIFOLDS . The BING LINK is named after him. Birkhoff, George David (1884–1944) American mathematician who

did important work in ergodic theory, DYNAMICAL SYSTEMS , and quantum theory. By solving a three-body problem posed by Poincaré, he became the first American mathematician to have international fame.

Birman, Joan (b. 1927) American mathematician who is a leading expert in the theory of KNOTS and BRAIDS . She began her study of mathematics after raising three children and is now a

Joan Birman (Joe Pineiro)

professor at Barnard College.

BIOGRAPHIES

Betti – Birman Betti – Birman

al-Bir ¯uni, Ab¯u al-Rayhan (973–1048) Islamic mathematician, astronomer, and astrologer of central Asia who was also a skilled diplomat and traveled widely. He wrote about many subjects, including TRIGONOMETRY and SPHERICAL TRIGONOMETRY .

Bolyai, János (1802–60) Hungarian mathematician who independently discovered HYPERBOLIC GEOMETRY . He also developed ABSOLUTE GEOMETRY , which is based only on Euclid’s first four postulates.

Bombieri, Enrico (b. 1940) Italian mathematician who studies NUMBER THEORY and MINIMAL SURFACES . He was awarded the Fields Medal in 1974 for work in number theory and is currently interested in applying number theory to the study of QUASICRYSTALS . He is a member of the Institute for Advanced Study in Princeton, New Jersey.

Bonnet, Pierre Ossian (1819–92) French engineer who later chose to become a teacher of mathematics. He worked in DIFFERENTIAL GEOMETRY and introduced the concept of GEODESIC CURVATURE , proving the general case of the Gauss-Bonnet theorem.

Borcherds, Richard E. Richard Borcherds (b. 1959) British mathematician who was

awarded the Fields Medal in 1998 for a dazzling theorem that (UC Berkeley, 1998) connects symmetries in higher-dimensional space to modular

functions and STRING THEORY . He now teaches at the University of California at Berkeley.

Bordoni, Antonio Maria (1789–1860) Italian mathematician who was interested primarily in DIFFERENTIAL GEOMETRY . He was a professor of mathematics at Pavia University.

Borel, Armand (1923–2003) Swiss-born American mathematician who made contributions to NUMBER THEORY , TRANSFORMATION GROUPS , and ALGEBRAIC TOPOLOGY . He was a member of the NICHOLAS BOURBAKI group and was professor emeritus at the Institute for Advanced Study in Princeton.

Bott, Raoul (b. 1923) Hungarian-born American mathematician who won numerous prizes for his work in TOPOLOGY and ALGEBRAIC TOPOLOGY . His most important contribution is

Armand Borel (IAS)

al-Bir ¯uni – Bott BIOGRAPHIES

BIOGRAPHIES

“Bourbaki” – Brianchon

the Bott periodicity theorem about the HOMOTOPY GROUPS of higher-dimensional spaces. He was a professor of mathematics at Harvard University for 40 years before retiring.

“Bourbaki, Nicolas”

A group of French mathematicians started in 1935 who adopted the pseudonym “Nicholas Bourbaki” to publish their textbooks, which were to cover all of mathematics. Nicholas Bourbaki emphasized the importance of the abstract axiomatic approach to the study of mathematics. The Bourbaki approach influenced the theoretical development of mathematics during the 20th century.

Bouvelles, Charles de (c. 1471–c. 1553) French philosopher and geometer who introduced the HYPOTROCHOID as a way to solve

Raoul Bott (Kris Snibbe/

the problem of SQUARING THE CIRCLE .

Harvard News Office)

Boys, Charles Vernon (1855–1944) British physicist and inventor who studied the mathematical properties of soap bubbles.

Brahmagupta (598–c. 665) Indian astronomer and mathematician who wrote about arithmetic, algebra, TRIGONOMETRY , and mensurational geometry. He developed methods for approximating the sine function and discovered a formula for the area of a quadrilateral inscribed in a circle.

Branner, Bodil (b. 1943) Danish mathematician who has studied DYNAMICAL SYSTEMS defined by cubic polynomials and their associated FRACTALS . She is a professor of mathematics at the Technical University in Copenhagen.

Bravais, Auguste (1811–63) French scientist who independently discovered the 32 CRYSTAL CLASSES and the 14 three- dimensional LATTICES that are named for him.

Brianchon, Charles Julien (c. 1783–1864) French mathematician who served in Napoleon’s army before beginning a teaching career in mathematics. While a student at the École Polytechnique, Brianchon proved Brianchon’s theorem, the dual of Pascal’s MYSTIC HEXAGRAM THEOREM . In 1820, Brianchon and Poncelet gave the first proof of the properties of the NINE - POINT CIRCLE .

BIOGRAPHIES

“Bourbaki” – Brianchon