There are 40 quintillion black holes in the observable Universe. More or less. - Syfy

What they really wanted is the black hole mass function across cosmic time.

That's what we call a stellar mass function: how many stars are in a bin of a given mass.

There's an initial mass function, which is, say, how many stars of what mass are born out of a single giant cloud of gas and dust at the same time.

It's a little different, for two main reasons: One is that black holes take time to form, after massive stars explode and their cores collapse to form black holes.

That messes things up because now you have one black hole of higher mass, which removes two lower mass ones from their bin in your function.

Their goal was to figure out the spread of masses of black holes, how many are in a given mass bin — like, say, 3-5 times the Sun's mass, 5–10, and so on, up to supermassive black holes that can have billions of solar masses to them — and moreover how that changes over time.

Hence that line above about the black hole mass function across cosmic time.

The details are… complex, but what they did is used a well-known suite of software to calculate how stars are born — the stellar mass function — and couple it with software that looks at data for galaxies and how they change over time.

Some stars make black holes when they explode, but some are in binary systems, orbiting another star.

Cranking all this through their code, the end result is table with a lot of numbers: How many black holes of a given mass there are at different points in the history of the Universe.

This shows the region around a black hole with a mass 6.5 billion times that of the Sun, located 55 million light years away from Earth in the core of the galaxy M87.

For example, in the nearby Universe, they see the number of black holes in a given bin is pretty flat from 5–50 times the mass of the Sun; for any given mass in that range you'll see roughly the same number of black holes.

In the early Universe there were fewer heavy elements — these are made in massive stars which explode and scatter them, and early there hadn't enough time for this to happen much.

Stars with fewer heavy elements can be more massive, so the black holes they make are bigger, too.

And, once they have the number of black holes per mass over time, they can then add them all up!

The total number over all time isn't nearly as scientifically interesting as the mass function is, but it's certainly interesting in a whoa that's so cool kind of way?