Ludwig Boltzmann & Bipolar Disorder: the Physicist Who Called Himself a Mixture

Ludwig Boltzmann worked out that the behaviour of gases, the direction of time and the nature of entropy could be explained statistically, by treating matter as made of enormous numbers of atoms. He was right about all of it, and he spent the last twenty years of his life being told by eminent colleagues that atoms did not exist.

His mood swings were noted by scientists across Europe, and he joked about them himself. He is one of the more credible historical cases on this website.

The Physics

Boltzmann's achievement is foundational. He gave a statistical explanation of the second law of thermodynamics, showing that entropy increases because disordered states are overwhelmingly more probable than ordered ones — which means the arrow of time itself is a statistical phenomenon.

His entropy equation, relating entropy to the logarithm of the number of possible microscopic arrangements, is carved on his gravestone in Vienna's Central Cemetery.

He held chairs at Graz, Vienna, Munich and Leipzig, moving frequently — a restlessness that is itself sometimes cited as evidence of his temperament.

Twenty Years of Being Told He Was Wrong

The intellectual context matters enormously to any assessment of his mental state.

In the late nineteenth century the existence of atoms was genuinely contested. An influential school — the energeticists, led by Wilhelm Ostwald, with philosophical support from Ernst Mach — held that science should confine itself to observable quantities and that unobservable atoms were an illegitimate hypothesis.

Boltzmann's entire life's work rested on atoms being real. He spent decades in public disputation defending it, and he described himself at one point as a man fighting alone against the current.

He was largely vindicated within a few years of his death: Einstein's 1905 paper on Brownian motion and Perrin's subsequent experiments settled the question definitively in favour of atoms.

The Mood Evidence

Contemporary accounts describe Boltzmann alternating between exuberant, sociable, extraordinarily productive periods and episodes of severe despondency, anxiety and inability to work. Colleagues and students noted it; so did his family.

He made a joke about it that has become the standard quotation in every account of him: that his rapid swings between happiness and sadness were explained by his having been born on the night between Shrove Tuesday and Ash Wednesday — the boundary between carnival and Lent. It is a good joke, and it is also a man describing his own cyclical mood with complete accuracy.

In his final years the depressive periods deepened. He suffered from severe headaches, asthma, worsening eyesight that threatened his ability to read, and anxiety about his teaching. He attempted suicide at least once before his death.

He died in September 1906 at Duino, near Trieste, while on holiday with his family; his death was by suicide. His wife and daughter had gone swimming.

If you're struggling, please reach out. A doctor, a mental health professional, or a crisis line in your country — and emergency services if you're in immediate danger.

So Was Boltzmann Bipolar?

Reasonably plausible, and better supported than most historical cases here.

In favour: multiple independent contemporary observers describing cyclical alternation between elevated, highly productive periods and incapacitating depression, sustained across decades rather than concentrated in one crisis; his own recognition of the pattern; and a family history that some accounts suggest included similar difficulties.

Against, or complicating: he had real physical illness in later life, real professional persecution, and real fear about losing his sight. Any of those would depress anyone. The romantic version of his story — that he died because the scientific establishment rejected his atoms — is almost certainly too neat, and rather insulting to a man with a documented long-standing illness.

Our reading is that Boltzmann probably had a cyclical mood disorder, that his final years combined it with severe physical illness and professional isolation, and that the standard tragic narrative flattens something more complicated.

Legacy

Boltzmann's statistical mechanics underpins modern physics and chemistry. The Boltzmann constant is one of the fundamental constants of nature, now used in the definition of the kelvin.

His gravestone carries his entropy formula, which is as good a monument as any scientist has received.

The lesson we would draw is the one his story usually obscures: he was not killed by his critics. He was a man with what appears to have been a serious recurrent illness, at a time when nothing whatever could be done for it, who also happened to be under enormous professional strain. Both things are true, and the illness deserves naming rather than being folded into the martyrdom.

Frequently Asked Questions