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We rarely acknowledge the immense body of work that is the base of present-day technology and our understanding of it. Most of the time, we take things for what they are, and we don’t realize the substantial progress that the scientists have made possible through continuous study and analysis.

One of the unsung heroes in the scientific field is Gaston Maurice Julia who was a French mathematician and the creator of the formula for the Julia set. His contribution was almost forgotten until another mathematician and polymath, Benoit Mandelbrot discussed him and his studies in several of his works.

Gaston Julia

A Brief Biography of Gaston Julia

Gaston Maurice Julia was born in the Algerian town of Sidi Bel Abbes in 1893. At that time, Algeria was under French occupation. Throughout his childhood and early youth, he had a deep interest in music and mathematics.

Gaston’s studies were abruptly interrupted by the beginning of the First World War. He was conscripted to the French army and sent on the battlefield.

Gaston Julia’s military career was marred by a severe injury in which he lost his nose. Unfortunately, the medical technology of the early 20th century was not advanced enough to reconstruct his original appearance, so he had to settle for a leather strap until the end of his life in 1978.

After the war, Julia started a career in teaching as a professor at the École Polytechnique in Paris. There, he conducted an important seminar on mathematics and continued his research in geometry and complex function theory. Gaston Julia is also the father of Marc Julia, the French organic chemist who discovered the Julia olefination.

Gaston Julia’s Contribution to Mathematics

Gaston Julia’s first contact with the scientific field came in the aftermath of his release from the military service. In 1918, he wrote a memoir on the iteration of polynomial functions (functions whose terms are all multiples of the variable raised to a whole number; e.g., 8×5 − Square root of √5×2 + 7). His study did not go unnoticed, and the French Academy of Sciences rewarded Julia with the Grand Prix in 1918.

Gaston Julia’s study went on to establish the foundations of what later became the Julia Set Theory together with an analogous memoir by French mathematician Pierre Fatou.

Julia showed that there is an essential distinction between points that tend to a limiting position as the iteration continues and the points that never settle down. Today, the academic rule distinguishes between Fatou’s set of points (the ones that tend to a position) and Julia’s set of points (the ones settling down).

The main conclusion that Julia reached is that his set of points is infinite even if it is closely related to Fatou’s set of points, which tend to return to themselves after a certain number of iterations.

Another result of his studies shows that his set of points tend to plane together with a point at infinity in some cases. In other situations, they connect within a curve or stand apart as entirely separate points.

For most of his career in mathematics, Gaston Julia did not have the opportunity to witness a visual representation of his theory. It wasn’t until the late 1970s and the advent of computer technology that the scientists were able to reproduce a graphic image of the Julia Set.

Nowadays, Gaston Julia’s contribution to mathematics is widely acknowledged and mathematicians everywhere consider that it has fundamental importance for the modern theory of fractals.

Gaston Julia – Selected Works

  • Étude sur les formes binaires non quadratiques à indéterminées réelles ou complexes, ou à indéterminées conjuguées, Gauthier-Villars 1917
  • Eléments de géométrie infinitésimale, Gauthier-Villars 1927
  • Leçons sur la représentation conforme des aires multiplement connexes, Gauthier-Villars 1934
  • Introduction Mathématique aux Théories Quantiques, 2 vols., Gauthier-Villars 1936
  • Exercices de géométrie, 2 vols., Gauthier-Villars 1944
  • Cours de géométrie infinitésimale, Gauthier-Villars 1953
  • Oeuvres, 6 vols., Paris, Gauthier-Villars 1968-1970