Irregularities are merely regularities in need of an explanation

It was a small anomaly, but, as Kepler had demonstrated and as several generations of natural philosophers had learned, irregularities are merely regularities in need of an explanation. And so astronomers looked for one. Perhaps previously unseen planetary matter was the culprit – a planet between Mercury and the sun (which Le Verrier in advance christened Vulcan) or a belt of asteroids near the sun or a moon of Mercury. For more than half a century, astronomers strained to find just such a “material cause,” as Le Verrier called it; a few even claimed to have seen the mystery planet, but follow-up observations were never able to confirm these sightings. In the end, some astronomers reluctantly began to consider the one other, far less agreeable, recourse: an inadequacy in Newton’s law of gravitation.
It was just such an inadequacy that Einstein thought he’d detected in his calculation. If space did indeed curve in the presence of mass, then by this estimation that curvature would be detectable in the rapid orbit of the comparatively minuscule planet Mercury, spinning deep within the great gravitational maw of the sun. And because astronomers had already performed the necessary observations of Mercury, all Einstein presumably had to do in using that planet to test his theory was to plug the numbers from the existing data into his new formula to see how well the math matched Newcomb’s 43 arc seconds per century.
The result wasn’t even close: 30 arc minutes. Einstein soon realized that he’d made a mistake and recalculated, and the answer this time – 18 arc seconds – was indeed much closer that what he’d hoped. But it was no more satisfying, at least nog in a universe operating on a Keplerian scale of precision.
So maybe Mercury wasn’t a test. Maybe there was another, simpler explanation for the advance in the planet’s perihelion, one that had nothing to do with Einstein’s math. In any event, as Einstein continued revising his theory he no longer bothered to worry about Mercury. In September 1913, he proclaimed to a friend, “The gravitational affair has been clarified to my complete satisfaction.” Not quite, as it turned out. He continued refining, and the following year presented his results to a meeting of the Prussian Academy in Vienna, declaring the theory to be near to its final form. His fellow physicists weren’t so sure; some thought they detected a mathematical error. Einstein didn’t see it. A year later, he did. By then, however it was too late: He’d already booked himself into four further addresses at the Prussian Academy.
On November 4, 1915, he appeared before the academy to confess that he had “completely lost confidence” in his theory. He was, however, working on a revision, which he broadly outlined. The following week, he returned to the academy to elaborate on the revision and to introduce some new equations. Later, at home, he made another adjustment, and then, recalling the earlier test, he sat down to see if just possibly his new version could withstand comparison with Mercury’s motions. He plugged numbers in, ran the calculations, arrived at a result: 43 arc seconds per century, precisely.
Something burst inside him.

A leap of faith [fragment]
uit: The invisible century : Einstein, Freud, and the search for hidden universes - Richard Panek