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  B E N O I T   M A N D E L B R O T
              Biography
        edited by Dave Moorman


    Benoit Mandelbrot is largely
responsible for the present interest
in fractal geometry. He showed how
fractals can occur in many different
places in both mathematics and
elsewhere in nature.

    Mandelbrot was born in Poland in
1924 into a family with a very
academic tradition. His father,
however, made his living buying and
selling clothes while his mother was a
doctor. As a young boy, Mandelbrot was
introduced to mathematics by his two
uncles.

    Mandelbrot's family emigrated to
France in 1936 and his uncle Szolem
Mandelbrojt, who was Professor of
Mathematics at the College de France,
took responsibility for Benoit's
education.

    Mandelbrot attended the Lycie
Rolin in Paris up to the start of
World War II, when his family moved to
Tulle in central France. This was a
time of extraordinary difficulty for
Mandelbrot who feared for his life on
many occasions.

  "The war, the constant threat of
  poverty and the need to survive kept
  him away from school and college and
  despite what he recognizes as
  'marvellous' secondary school
  teachers, he was largely self
  taught."

    Mandelbrot attributed much of his
success to this unconventional
education. It allowed him to think in
ways that might be hard for someone
who, through a conventional education,
is strongly encouraged to think in
standard ways. It also allowed him to
develop a highly geometrical approach
to mathematics, and his remarkable
geometric intuition and vision began
to give him unique insights into
mathematical problems.

    Mandelbrot is responsible for most
of the creation of fractal geometry
and chaos theory -- two concepts that
promise to change the way mathematics
are viewed from now on.


[The Concept of Fractals]

    A fractal is a shape that is self
similar: i.e. the image is made up of
an infinite number of copies of
itself. The shape of the fractal is
repeated in the fractal. Fractals are
the first nonlinear shapes to be
produced. They cannot be represented
with lines, thus not displayable with
calculus, geometry, and algebra.

    In fact, all shapes in reality are
fractal, which is why none of them can
be reduced to a mere line, Therefore
the linear logic of calculus, geometry
and algebra are stuck with describing
theoretical planes, and cannot be
applied to everyday matter.


[The Fractal Geometry of Nature]

    The intricate, nonlinear forms of
fractals are not just pretty pictures,
though they do have many applications
in reality. Take the fern: it is a
living fractal. Each individual branch
is a reflection of the whole -- each
leaf, a reflection of the branch. The
same similarity can be found in oak
trees, clouds, and even mountain
ranges; the fractal symmetry of nature
is everywhere.

    After studying at Lyon, Mandelbrot
entered the Ecole Normale. He left
after just one day (which must be come
kind of record!). He began his
studies at the Ecole Polytechnique in
1944.

    After completing his courses at
the Ecole Polytechnique, Mandelbrot
went to the United States where he
visited the California Institute of
Technology. After a Ph.D. granted by
the University of Paris, he went to
the Institute for Advanced Study in
Princeton where he was sponsored by
John von Neumann.

    Mandelbrot returned to France in
1955 and worked at the Centre National
de la Recherche Scientific. He married
Aliette Kagan while there and in
Geneva, Switzerland.

  "Still deeply concerned with the
  more exotic forms of statistical
  mechanics and mathematical
  linguistics and full of non-standard
  creative ideas, Mandelbrot found the
  huge dominance of the French
  foundational school of Bourbaki not
  to his scientific tastes. In 1958 he
  moved to the United States
  permanently and began his long
  standing and most fruitful
  collaboration with IBM as an IBM
  Fellow at their world renowned
  laboratories in Yorktown Heights,
  New York."

    IBM presented Mandelbrot with an
environment which allowed him to
explore a wide variety of different
ideas. He has spoken of how this
freedom at IBM to choose the
directions that he wanted to take in
his research presented him with an
opportunity which no university post
could have given him. After retiring
from IBM, he found similar
opportunities at Yale University.

    In 1945 Mandelbrot's uncle had
introduced him to Julia's important
1918 paper, claiming that it was a
masterpiece and a potential source of
interesting problems. But Mandelbrot
did not like it.

    Indeed, he reacted rather badly
against suggestions posed by his
uncle, since he felt that his own
whole attitude to mathematics was so
different. Instead Mandelbrot chose
his own course which, however, brought
him back to Julia's paper in the 1970s
after a path through many different
sciences.

    With the aid of computer graphics,
Mandelbrot, then working at IBM's
Watson Research Center, was able to
show how Julia's work is a source of
some of the most beautiful fractals
known. To do this he had to
develop not only new mathematical
ideas, but also developed some of the
first computer graphics programs.

    His famous "Set" was first
elaborated in his book [Les objets]
[fractals, forn, hasard et dimension]
(1975) and more fully in [The fractal]
[geometry of nature] in 1982.

On June 23, 1999 Mandelbrot received
the Honorary Degree of Doctor of
Science from the University of St.
Andrews.

  "We should not get the impression
  that he was a mathematician alone.
  The first of his great insights was
  the discovery that extraordinarily
  complex, almost pathological
  structures, which had been long
  ignored, exhibited certain universal
  characteristics requiring a new
  theory of dimension to treat them
  adequately. The second great insight
  was that the fractal property was
  present almost universally in
  Nature.


  "The overwhelming smoothness
  paradigm with which mathematical
  physics had attempted to describe
  Nature proved to be radically flawed
  and incomplete. Fractals and
  pre-fractals -- once noticed -- are
  everywhere."

    Mandelbrot has received numerous
honors and prizes in recognition of
his remarkable achievements.



From an article by: J J O'Connor and
E F Robertson

 DMM