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Miller and Modigliani derived the theorem and wrote their groundbreaking article when they were both professors at the Graduate School of Industrial Administration (GSIA) of Carnegie Mellon University. It is said that Miller and Modigliani were set to teach corporate finance for business students despite the fact that they had no prior experience in corporate finance. When they read the material that existed they found it inconsistent so they sat down together to try to figure it out. The result of this was the article in the American Economic Review and what has later been known as the M&M theorem.
The theorem was originally proven under the assumption of no taxes. It is made up of two propositions which can also be extended to a situation with taxes. Consider two firms which are identical except for their financial structures. The first (Firm A) is unlevered: that is, it is financed by equity only. The other (Firm B) is levered: it is financed partly by equity, and partly by debt. The Modigliani-Miller theorem states that the value of the two firms is the same.
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