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Ludwig Boltzmann was awarded a doctorate from Vienna in 1866. After this he became an assistant to his teacher Josef Stefan.
Boltzmann taught at Graz, moved to Heidelberg and then to Berlin. In these places he studied under Bunsen, Kirchhoff and Helmholtz.
In 1869 Boltzmann was appointed to a chair of theoretical physics at Graz. He held this post for four years then, in 1873, he accepted the chair of mathematics at Vienna. He did not stay very long in any place and after three years he was back in Graz, this time in the chair of experimental physics.
After another three years, in 1894, Boltzmann moved back to Vienna, this time to a chair of theoretical physics. In 1900 he moved to Leipzig but here he was a colleague of his strongest scientific opponent W Ostwald. Depressed by arguments with Ostwald which are described below he unsuccessfully attempted suicide during his time in Leipzig. In 1902 he returned to Vienna to his chair of theoretical physics which had not been filled.
Boltzmann obtained the Maxwell-Boltzmann distribution in 1871, namely the average energy of motion of a molecule is the same for each direction. He was one of the first to recognise the importance of Maxwell's electromagnetic theory.
In 1884 the work of Josef Stefan was developed by Boltzmann who showed how Josef Stefan's empirical T
law for black body radiation, formulated in 1879, could be derived from the principles of thermodynamics.
Boltzmann worked on statistical mechanics using probability to describe how the properties of atoms determine the properties of matter. In particular his work relates to the Second Law of Thermodynamics which he derived from the principles of mechanics in the 1890s.
The equations of Newtonian mechanics are reversible in time and Poincaré proved that if a mechanical system is in a given state it will return infinitely often to a state arbitrarily close to the given one. Zermelo deduced that the Second Law of Thermodynamics is impossible in a mechanical system. Boltzmann asserted that entropy increases almost always, rather than always. However he believed that Poincaré's result, although correct in theory, was in practice impossible to observe since the time before a system returns to near its original state was too long.
Boltzmann's ideas were not accepted by many scientists. In 1895, at a scientific meeting, W Ostwald presented a paper in which he stated:-
The actual irreversibility of natural phenomena thus proves the existence of processes that cannot be described by mechanical equations; and with this the verdict on scientific materialism is settled.Sommerfeld, who was at the meeting, described the resulting battle between Ostwald and Boltzmann. Sommerfeld wrote:-
... Boltzmann was seconded by Felix Klein. The battle between Boltzmann and Ostwald resembled the battle of the bull with the supple fighter. However, this time the bull was victorious ... . The arguments of Boltzmann carried the day. We, the young mathematicians of that time, were all on the side of Boltzmann ... .Ostwald led the opposition to Boltzmann's ideas which were opposed by many European scientists; they misunderstood them, not fully grasping the statistical nature of his reasoning. However some, including Mach, thought the arguments were too violent, and this certainly appeared to be the case when Boltzmann attempted suicide while a colleague of Ostwald.
In 1904 Boltzmann visited the World's Fair in St Louis, USA. He lectured on applied mathematics and then went on to visit Berkeley and Stanford. Unfortunately he failed to realise that the new discoveries concerning radiation that he learnt about on this visit were about to prove his theories correct. Depressed and in bad health, Boltzmann committed suicide just before experiment verified his work. However the cause of his suicide may have been wrongly attributed to the lack of acceptance of his ideas. We will never know the real cause.
References (8 books/articles)
References elsewhere in this archive:
Tell me about Boltzmann's work on quantum theory and his part in the history of mathematics
Ludwig Boltzmann was elected to the Royal Society of London in 1899. You can see a history of the Royal Society and a list of the members among the mathematicians in our archive.
There is a Crater Boltzmann on the moon. You can see a list of lunar features named after mathematicians.