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Bolyai Prize6spectral theory13honorary doctorate of Technion24Henri Poincaré Prize31statistical mechanics32Steele Prize for Lifetime Achievement34honorary doctor of the University of Munich70Dannie Heineman Prize for Mathematical Physics88quantum mechanics117functional analysis193mathematical physics258Fellow of the Society for Industrial and Applied Mathematics419Fellow of the American Mathematical Society1,245Fellow of the American Physical Society1,747physics2,244mathematics3,760Guggenheim Fellowship12,265194615,5171940143,130English435,916United States442,023201,347,152male1,587,100