Stefan Banach: Quick Facts

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Facts

Born	March 30, 1892 • Kraków • Austria-Hungary
Died	August 31, 1945 (aged 53)
Subjects Of Study	Banach space

David Hilbert

German mathematician

Jacques-Salomon Hadamard

French mathematician

Laurent Schwartz

French mathematician

Vaughan Jones

New Zealand mathematician

Jean Bourgain

Belgian mathematician

Jean Dieudonné

French mathematician

Frigyes Riesz

Hungarian mathematician

Timothy Gowers

British mathematician

Stanisław Leśniewski

Polish logician and mathematician

Stanislaw Ulam

American scientist

$Mandelbrot setDuring the late 20th century, Polish mathematician Benoit Mandelbrot helped popularize the fractal that bears his name. The fundamental set contains all complex numbers C such that the iterative equation Zn + 1 = Zn2 + C stays finite for all n starting with Z0 = 0. As shown here, the set of points that remain finite through all iterations is white, with darker colours showing how quickly other values diverge to infinity. The fractal edge between points that remain finite and those that diverge to infinity is extremely complicated, with self-repeating features that can be seen at all scales.$

Benoit Mandelbrot

Polish-born French American mathematician

$Sierpiński gasketPolish mathematician Wacław Sierpiński described the fractal that bears his name in 1915, although the design as an art motif dates at least to 13th-century Italy. Begin with a solid equilateral triangle, and remove the triangle formed by connecting the midpoints of each side. The midpoints of the sides of the resulting three internal triangles are connected to form three new triangles that are then removed to form nine smaller internal triangles. The process of cutting away triangular pieces continues indefinitely, producing a region with a Hausdorf dimension of a bit more than 1.5 (indicating that it is more than a one-dimensional figure but less than a two-dimensional figure).$