Please explain why the Dirac delta function was named after Dirac, who lived in the 20th century, and what was so special about it.

I ask this because it is used in Green's function which pre-dated Dirac by 200 years. I find Green's function more insightful and so wonder why it is not called Green's delta. Fourier and Cauchy are also cited on the Wikipedia page for the Dirac delta as having used the impulse concept.

I am therefore hoping to find out what Dirac's special contribution was since the maths was already two centuries old. I don't see this contribution on the Wikipedia page even though its implicitly referred to as Dirac's invention.

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    $\begingroup$ Maybe he popularized it. Very many things in mathematics are not named after the inventor but are instead named after the one who made the thing popular. $\endgroup$ – user1271772 Aug 14 '20 at 20:54
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    $\begingroup$ "The Arnold Principle. If a notion bears a personal name, then this name is not the name of the discoverer. The Berry Principle. The Arnold Principle is applicable to itself" (source) $\endgroup$ – Rodrigo de Azevedo Aug 14 '20 at 20:56
  • $\begingroup$ Thanks. I thought I'd missed something that Dirac had come up with. I think his use of it in quantum mechanics raised its profile and so his name stuck with it. $\endgroup$ – rupert Aug 14 '20 at 21:10
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    $\begingroup$ Green only predated Dirac by a century and nothing like delta function was used in Green's function, everything was phrased in terms of classical functions. Its relation to delta is only an after the fact reinterpretation produced after the delta function was introduced. The same goes for Fourier's, Cauchy's, etc., formulas. Delta's conceptualization as a new self-standing object was Dirac's contribution, and it turned out to be very useful in mathematics. Who came close to it before Dirac was not Green but Heaviside. $\endgroup$ – Conifold Aug 14 '20 at 22:12
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    $\begingroup$ @RodrigodeAzevedo See also here. $\endgroup$ – J.G. Aug 16 '20 at 5:18

It's because of Diracs use of it in QM. After QM was a revolutionary new theory of physics and so had immense visibility because of this.

This is very similar to how Einstein popularised the study of non-Euclidean geometry by his use of such in his revolutionary theory of space and time. After all, non-Euclidean geometry had been known since Gauss's time but it simply didn't have the glamour or cachet that it began to have once Einstein arrived on the scene.


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