Blaise Pascal was a brilliant seventeenth century mathematician. He made foundational contributions to statistics and to our understanding of how air pressure works. He was also a devout Catholic, and came up with an interesting argument for why one should believe in God, now known as Pascal's Wager.
Pascal laid out the wager in part 233 of his Pensées, a series of notes for an uncompleted defense of Christianity that were published posthumously.
Pascal argued that, while it's impossible to prove whether or not God exists, people should believe in God anyway. The essential component of the argument is the relative payoffs and costs for believing or not believing in God under either the assumption God exists or God doesn't exist.
If God exists, Pascal argued that belief would lead to eternal joy in heaven, while disbelief results in damnation and torture in hell for all time. If God doesn't exist, belief just leads to a finite cost: giving up sins and living a godly life. Disbelief brings only a finite benefit: sinning can be fun and sleeping in on Sundays is nice.
This is usually summarized in a table like the one below:
Business Insider/Andy Kiersz
The argument is based on the infinite nature of the afterlife. No matter what the costs in this life are of believing in God, they are always outweighed by the benefits, if God exists. Similarly, however large the benefits of atheism are, if God does exist, those benefits are massively countered by the infinite cost of going to hell.
Further, since the benefits of belief and the costs of disbelief are infinite in the case God exists, we don't need any actual estimate for the probability that God exists, so long as that probability is not zero. Even if there's only a one in a trillion chance for the existence of God, one in a trillion times infinity is still infinity.
This Is Not About Proving God's Existence
This is not an argument for the actual existence of God. Pascal states that, as to the question of the existence or non-existence of God, "Reason can decide nothing here." Instead, it's an argument for why, regardless of existence, one should believe in God.
As University of Wisconsin mathematics professor Jordan Ellenberg describes it in his new book "How Not To Be Wrong", "Pascal is not trying to convince you God exists; he is trying to convince you that it would be to your benefit to believe so."
This is, naturally, a very controversial argument. One of the biggest issues is that Pascal starts out with the enormous assumption that, if God exists, His system for deciding on who goes to heaven and who goes to hell is based entirely on personal belief.
It's entirely conceivable that there could be a God who doesn't care about personal belief, and instead decides on who gets to go to heaven based on people's actions in life. Or perhaps a religion different from your own is right, and by believing in the wrong God, you are still in a lot of trouble.
This line of thought has lead some thinkers to construct an atheist version of the wager. If God exists, we cannot have any idea of what His criteria are for going to heaven. This means that the case in which God exists can't affect our calculations. Instead, we just have to consider the possibility that God does not exist, in which case the benefits of atheism may well make it worthwhile to disbelieve.
Regardless of what assumptions you use, Pascal's Wager and the counterarguments against it are a wonderful example of using mathematical thinking - considering probabilities and outcomes - to wrestle with deep philosophical questions.