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to
evolve, contracting or expanding depending on whether matter or the cosmological constant played the dominant role.
    In 1922, Friedmann published his seminal paper, “On the Curvature of Space,” in which he showed that not only Einstein’s but also de Sitter’s universes were merely very special cases of a much wider range of possible behaviors for the universe. In fact, the most general solutions were for universes that either contracted or expanded in time. A certain class of models could even expand and grow and then contract again, leading to a never-ending succession of cycles. Friedmann’s results also released Einstein’s cosmological constant from its duty of keeping the universe static. There was nothing to pin the cosmological constant to any particular value, unlike in Einstein’s original model. In the conclusions of his paper, Friedmann wrote dismissively,“The cosmological constant . . . is undetermined . . . since it is an arbitrary constant.” By giving up Einstein’s requirement that the universe be static, Friedmann had shown that Einstein’s cosmological constant was, to all effects, irrelevant. If the universe evolved, there was no need to complicate the theory with an arbitrary fix as Einstein had done.
    Here was a paper that came out of nowhere. Friedmann had not taken part in the discussions with Einstein, had not sat through the succession of lectures that Einstein had given to the Prussian Academy of Sciences. He was an outsider who had become enthused by the wave of euphoria that had followed Eddington’s eclipse expedition. A mathematical physicist first and foremost, all Friedmann had done was deploy the same skills and techniques he had used for studying bombs and the weather, and he had uncovered a result that went against Einstein’s gut feeling.
    For Einstein, the possibility that the universe was evolving was absurd. When Einstein first read Friedmann’s paper, he refused to accept that his theory would serve up such a possibility. Friedmann
must
be wrong, and Einstein set about trying to prove it. He carefully worked through Friedmann’s paper and found what he took to be a fundamental mistake. Once that mistake was corrected, Friedmann’s calculation delivered up a static universe just as Einstein had predicted. Einstein rapidly published a note in which he asserted that“the significance” of Friedmann’s work was to prove that the universe’s behavior was constant and immutable.
    Friedmann was mortified by Einstein’s note. He was sure he hadn’t made a mistake and that Einstein himself had miscalculated. Friedmann wrote a letter to Einstein showing where Einstein had gone wrong and added at the end: “If you find the calculations presented in my letter correct, please be so kind as to inform the editors of the
Zeitschrift für Physik
about it.” He sent off his letter to Berlin, hoping Einstein would act swiftly.
    Einstein would never receive the letter. His fame had propelled him into an endless succession of seminars and conferences, forcing him to travel around the world, from Holland and Switzerland to Palestine and Japan, and keeping him away from Berlin where Friedmann’s letter sat gathering dust. It was only by chance that Einstein ran into one of Friedmann’s colleagues while passing through the Leiden Observatory and learned about Friedmann’s response. And so it was that, almost six months later, Einstein published a correction to
his
correction of Friedmann’s paper, rightfully acknowledging Friedmann’s main result and admitting “there are time varying solutions” to the universe. The universe could indeed evolve in his general theory of relativity. But still, all Friedmann had done was show that there were solutions to Einstein’s theory that led to an evolving universe. That was just mathematics, according to Einstein, not