The problem of a blast wave from an essentially pointlike source arose during the Second World War, when the possibility of nuclear weapons became well-known in the physics community. Taylor first treated the problem in 1941, with a numerical solution for an explosion in air. Taylor's initially-classified paper on the subject was published in 1949 as ``The formation of a blast wave by a very intense explosion; I. Theoretical discussion.'' The theoretical discussion of 1941 included some fairly crude experimental comparisons, based on the blasts of conventional weapons, and Taylor also added some better conventional weapons data for the 1949 publication.
As a better experimental test, Taylor produced a companion article, ``The formation of a blast wave by a very intense explosion; II. The atomic explosion of 1945.'' Using a time series of then-recently-declassified photographs of the Trinity explosion near Alamogordo, New Mexico, Taylor tested his scaling hypothesis and calculated the energy of the blast. The frequently-quoted strength of the explosion--18.6 kilotons (the equivalent of 18.6 thousand tons of trinitrotoluene)--is quite close to Taylor's calculated value of 16.8 kiltons.
While Taylor's scaling law was correct, and his numerical solution worked remarkably well for the case of air, a more general solution was needed, to study a blast wave propagating into a cold gas with a more general equation of state. This is important, for example, in the study of supernova explosions. This need had already been answered by the time Taylor published his paper in 1949. Sedov and von Neumann independently found an analytic solution to the problem, for the same set of approximations that Taylor used. For this reason, the solution to the blast problem is conventionally known as the ``Sedov solution.''
It is important to note one further fact. A nuclear explosion has several
unique properties; Taylor's paper is a description of only one. The first (and
ultimately, most deadly) part of the explosion is the blinding flash, the
burst of electromagnetic radiation released by the nuclear processes (be they
fission or fusion). The second stage is the ``fireball,'' the
beautifully-spherical shock front that the Sedov solution describes. Finally,
there is the infamous mushroom cloud, which comes about through the
interaction of the fireball interior with the ground and the stratification of
the atmosphere. There are also other, more subtle, effects that are of little
importance in calculating the damaging power of a bomb, but are physically
interesting nonetheless. For example, 
-rays may ionize the atmosphere
outiside the fireball, surrounding the sphere with a penumbra of lightning
strikes.