The original statement was by V.S. Ramachandran where he stated there are 100 billion neurons and anywhere between 1000 to 10000 POSSIBLE connections from each neuron. This refers to the plasticity of the human brain where new connections are formed and old connections are sloughed on to be reformed again at a different site later again.
There is an estimated 10^85 atoms in the known universe from classic matter (not dark matter, antimatter, nor even photons)
I believe the the proper equation for this problem would be nCr where n = total sample size and r = number of items to be selected from the sample. You would use the combinatorial function because it is all possible outcomes in any given order. Therefore:
n= number of neurons = 100,000,000,000
r = number of possible connections (assuming any neuron can connect to any other neuron) = 10000
However, the website I am using can only do:
n= 100 billion
r = 10 but...
nCr = 2.75573e+103 (http://www.calctool.org/CALC/math/probability/combinations)
2.75573e+103 is greater than 10^85
This is flawed though because the human brain does not in fact connect at every point and cannot send connections everywhere. It is a mass of order and chaos that lies somewhere in the middle . There are many scientists working out the human connectome as we speak as well as connectomes for mouse, rat, cat, monkey, dog, etc. The full connectome of C. elegans has in fact been sorted out and is easier to find on google.
Another flaw with the statement is that glial cells are not accounted for at all in the estimate which is unfortunate because they outnumber neurons 10 to 1. Astrocytes are capable of forming gap junctions with their neighbors as well as storing, synthesizing, and releasing glutamate, GABA, and ions within the extracellular space. There are even recently discovered glial cells within the white matter tracts that send and receive signals through a traditional synapse.
Lastly, any prediction as to the size of the universe and the atoms contained with it relies on what we can observe of the universe. Much of our knowledge about the universe comes from distant star systems many thousands and millions of lightyears away. The light is just reaching our tiny planet now after millions of years and there could potentially be new star systems, new galaxies, collapsed systems, black holes that eat up all the atoms (such as that at the center of the milky way) or new particles forming on the edge of a black hole. We cannot be certain of the extent of the universe nor do we know how the human brain fully connects yet. Although, all else being said its a fun mind exercise to grapple the enormity of both the universe and the mind. I have also read that the number of snow flakes that fall in one year on earth outnumber the stars in the milky way galaxy (10^23 stars).