Apparently there was some negative reception of Boltzmann's idea of an "atom". I assume the mathematics used by Einstein in his publication did not use any of Boltzmann's statistical mathematics otherwise Boltzmann would have know about it.
Einstein calculated the size of the atom as well as it's existence in his publication of Brownian motion.
Boltzmann apparently passed away a year after he had been vindicated by Albert Einstein. Was Boltzmann aware of this at the time that he passed away?
I’m afraid he no longer cared. According to Boltzmann biographer E. Broda (1981):
(p. 9): One might have thought Boltzmann would, after 1900, in lectures and writings refer to Planck’s work on radiation, made possible by adoption of his own, Boltzmann’s, statistical methods. This was not the case, however. While Boltzmann continued to lecture and publish till his tragic death in 1906, we find no word about Planck or about his work. Nor did Boltzmann refer to Planck in his classes, as told by his student Lise Meitner49). By the way, Boltzmann did not refer to Einstein either49), although Einstein’s explanation, in 1905, of Brownian movement as a fluctuation phenomenon, to which we shall return later, had been another triumph of Boltzmann’s ideas. It looks as if Boltzmann had quite systematically shut himself up in his own world (...)
(p. 15): Independently of Einstein, Smoluchowski developed the quantitative theory of Brownian movement on the basis of fluctuations. A curious fact that does not seem to have been discussed so far: Smoluchowski, who had done his thesis under Stefan, but called himself a student of Boltzmann, had been interested in Brownian movement, to be explained through fluctuations, since 1900. That was 6 years before Boltzmann’s death. Is it possible that Boltzmann was not aware of Smoluchowski’s promising investigations?
49) L. Meitner, Looking back, Bull. Atom. Scient. 20, No. 9, 2 (1964).
