How smart do you have to be to convince Albert Einstein to change his mind?

Pretty smart. He never invoked 'the science is settled' or ridiculed the political party of physicists who insisted the universe was expanding. It was static until someone proved otherwise.

Eventually they did, but it was not the urban legend that claimed in 1931 American astronomer Edwin Hubble showed Einstein his observations of redshift in the light emitted by far away nebulae - what we call galaxies now. The tipping point was instead a tortuous thought process following many encounters with some of the most influential astrophysicists of his generation.

Writing in European Physical Journal H, Harry Nussbaumer from the Institute of Astronomy at ETH Zurich, Switzerland outlines how, in 1917, Einstein applied his theory of general relativity in the universe, and suggested a model of a homogenous, static, spatially curved universe. This interpretation had one major problem: If gravitation was the only active force, his universe would collapse – an issue Einstein addressed by introducing the cosmological constant.

Contemporaries suggested that the universe was expanding but he remained unconvinced. In 1922, Russian physicist Alexander Friedman showed that Einstein's equations were viable for dynamical worlds and, in 1927, Georges Lemaître, a Belgian astrophysicist from the Catholic University of Louvain, concluded that the universe was expanding by combining general relativity with astronomical observations.

Gradually, he came around. In an April 1931 report to the Prussian Academy of Sciences, Einstein adopted a model of an expanding universe and in 1932 he teamed up with the Dutch theoretical physicist and astronomer Willem de Sitter to propose an eternally expanding universe which became the cosmological model generally accepted until the middle of the 1990s.

So ended the cosmological constant.  But he wasn't convinced by pictures or observational data, he had to be convinced his model was unstable. We should all keep that in mind the next time we see papers claiming to draw conclusions from weak observational data, fMRI images, or surveys of college students.

Citation: H. Nussbaumer (2013), Einstein’s conversion from his static to an expanding universe, European Physical Journal H, DOI 10.1140/epjh/e2013-40037-6