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Hilbert's 21st problem, on the existence of linear DEs with prescribed monodromy group, was for a long time thought to have been solved by Plemelj in 1908. In fact, Plemelj died in 1967 still believing he had solved the problem. However, in 1989, Bolibruch discovered a counterexample. Details are in the book The Riemann-Hilbert Problem by Anosov and Bolibruch (Vieweg-Teubner 1994), and a nice popular recounting of the story is in Ben Yandell's The Honors Class (A K Peters 2002). |
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Hilbert's 21st problem, on the existence of linear DEs with prescribed monodromy group, was for a long time thought to have been solved by Plemelj in 1908. In fact, Plemelj died in 1967 still believing he had solved the problem. However, in 1989, Bolibruch discovered a counterexample. Details are in the book The Riemann-Hilbert Problem by Anosov and Bolibruch (Vieweg-Teubner 1994), and a nice popular recounting of the story is in Ben Yandell's The Honors Class (A K Peters 2002). |
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