Yep! The mathematics is pretty simple and recurs in a bunch of other places, from the theory of evolution by natural selection, to the question of why things go viral on the Internet.

The basic idea is that these sorts of objects are routinely seeing spontaneous nuclear decays -- there might be billions per millisecond of these. What's important is that each nuclear decay is an explosion which releases debris that can cause other nearby nuclei to decay as a result. So it becomes important to know: what is the average number N of nuclei which fall apart as a direct result of getting hit by the shrapnel of one decaying nucleus?

Since nothing is terribly exact in physics there are two regimes to consider, N < 1 and N > 1. In that first regime we can roughly calculate that we need to multiply this baseline billions-per-millisecond rate of spontaneous decays by the number

    1 + N + N² + N³ + ... = 1/(1 - N)

The virality analogy is "Given one person shares it, what is the average number N of their friends who share it?" As you can see as this gets closer to N=1 it goes towards infinity.

For N > 1 the same multiplier holds but it cannot be summed infinitely: instead we realize that each term takes a slightly longer time period and thus the growth goes something like e^(k t) for some k, it's an exponential growth towards a majority of the sample reacting.

For fissile materials like plutonium, an easy way to increase N is to just bring two plutonium rods closer together: free debris from explosions in the one now cause new explosions in the other. This is called forming a "critical mass" hence the language about "criticality". Another way is to bring in these "neutron reflectors" that reflect the debris back into the same sample, it's basically the same principle.