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.