Short answers, pulled from the story.
Max Planck presented the formula on the 14th of December 1900 before the German Physical Society. This presentation introduced energy emission in discrete packets known as Planck's constant.
The Bohr-Sommerfeld model emerged from Niels Bohr's 1913 atomic model and Arnold Sommerfeld's extension allowing elliptical trajectories. It incorporated space quantization through the z-component of angular momentum to explain fine structure in spectral lines.
William Wilson and Arnold Sommerfeld required that the integral of momentum over one period equals an integer times Planck's constant. This condition applied only to systems where motion could be separated into periodic coordinates.
The Bothe-Geiger coincidence experiment rejected the BKS theory because experimental evidence showed that energy and momentum were conserved only in individual interactions. This failure forced physicists to abandon semi-classical compromises entirely.
Werner Heisenberg published his Umdeutung paper in 1925 reformulating all quantum theory using Kramers' Fourier components. Max Born and Pascual Jordan collaborated with him to develop matrix mechanics based on this work.