Louis de Branges de Bourcia (born August 21, 1932) is a French-American mathematician. He was the Edward C. Elliott Distinguished Professor of Mathematics at Purdue University in West Lafayette, Indiana, retiring in 2023. He is best known for proving the long-standing Bieberbach conjecture in 1984, now called de Branges's theorem. He claims to have proved several important conjectures in mathematics, including the generalized Riemann hypothesis. Born to American parents who lived in Paris, de Branges moved to the US in 1941 with his mother and sisters. His native language is French. He did his undergraduate studies at the Massachusetts Institute of Technology (1949–53), and received a PhD in mathematics from Cornell University (1953–57). His advisors were Wolfgang Fuchs and then-future Purdue colleague Harry Pollard. He spent two years (1959–60) at the Institute for Advanced Study and another two (1961–62) at the Courant Institute of Mathematical Sciences. He was appointed to Purdue in 1962. An analyst, de Branges has made incursions into real, functional, complex, harmonic (Fourier) and Diophantine analyses. As far as particular techniques and approaches are concerned, he is an expert in spectral and operator theories.
Works De Branges' proof of the Bieberbach conjecture was not initially accepted by the mathematical community. Rumors of his proof began to circulate in March 1984, but many mathematicians were skeptical because de Branges had earlier announced some false (or inaccurate) results, including a claimed proof of the invariant subspace conjecture in 1964 (incidentally, in December 2008 he published a new claimed proof for this conjecture on his website). It took verification by a team of mathematicians at Steklov Institute of Mathematics in Leningrad to validate de Branges' proof, a process that took several months and led later to significant simplification of the main argument. The original proof uses hypergeometric functions and innovative tools from the theory of Hilbert spaces of entire functions, largely developed by de Branges. Actually, the correctness of the Bieberbach conjecture was not the only important consequence of de Branges' proof, which covers a more general problem, the Milin conjecture.
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