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It is commonly known that Feynman's path integral was inspired by Dirac's observation that the kernel is proportional to $\exp{\dfrac{i}{\hbar} S}$. It was Feynman, however, who had the idea of expressing the kernel as the integral of such an expression over all possible paths.

Is it known what led Feynman to try out this idea of an integral over all paths? He provides motivation from a probabilistic understanding of quantum mechanics in "Non-relativistic Quantum Mechanics" and Quantum Mechanics and Path Integrals, but is this motivation what actually led him to try out the idea of the path integral and discover that up to suitable normalization, it recovered the correct expression for the kernel and the Schrodinger equation?

Moreover, why was Dirac's observation of the proportionality of the final answer to $\exp{\dfrac{i}{\hbar} S}$ insufficient as the basis for an alternative formulation of quantum mechanics?

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    $\begingroup$ Possible duplicate of Dirac's remark that inspired Feynman when formulating path integral $\endgroup$
    – Anyon
    Commented Apr 13, 2019 at 16:26
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    $\begingroup$ If you are more interested in the actual historical process than the physics themselves, then this question would be more at home on History of Science and Mathematics $\endgroup$
    – ACuriousMind ♦
    Commented Apr 13, 2019 at 16:34
  • $\begingroup$ Feynman's doctoral thesis is widely available in print, and it is likely to contain, at least, relevant information. $\endgroup$
    – Emilio Pisanty
    Commented Apr 13, 2019 at 19:08
  • $\begingroup$ Presumably, Feynman was trying to solve the Schrodinger equation, realised that there will be an easy answer for small time steps, and then tried to glue the time steps together to construct a solution for finite time differences, which leads directly to a wavefunction which is the path integral. $\endgroup$
    – Wakabaloola
    Commented Apr 14, 2019 at 10:54

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