Progress in math is needed for progress in science

(written by lawrence krubner, however indented passages are often quotes). You can contact lawrence at: lawrence@krubner.com

Interesting:

The problem was that, in order to build a theory on this insight, Einstein needed to be able to create those descriptions in warped four-dimensional space-time. The Euclidean geometry used by Newton and everyone else was not up to this job; fundamentally different and much more challenging mathematics were required. Max Planck, the physicist who set off the revolution in quantum mechanics, thought this presented Einstein with an insurmountable problem. “I must advise you against it,” he wrote to Einstein in 1913, “for in the first place you will not succeed, and even if you succeed no one will believe you.”

Handily for Einstein, though, an old university chum, Marcel Grossmann, was an expert in Riemannian geometry, a piece of previously pure mathematics created to describe curved multi-dimensional surfaces. By the time of his lectures in 1915 Einstein had, by making use of this unorthodox geometry, boiled his grand idea down to the elegant but taxing equations through which it would become known.

Just before the fourth lecture was to be delivered on November 25th, he realised he might have a bit more to offer than thought experiments and equations. Astronomers had long known that the point in Mercury’s orbit closest to the sun changed over time in a way Newton’s gravity could not explain. In the 1840s oddities in the orbit of Uranus had been explained in terms of the gravity of a more distant planet; the subsequent discovery of that planet, Neptune, had been hailed as a great confirmation of Newton’s law. Attempts to explain Mercury’s misbehaviour in terms of an undiscovered planet, though, had come to naught.

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