It's possible to argue, mathematically, that there is a 95% chance of mankind's extinction within 9120 years. This calculation is derived from the Carter Prediction.
I first came across the "Carter Prediction" in Stephen's Baxter's SF novel "Manifold: Time". It's a real proposition by a real eminent physicist, Brandon Carter.
Wikipedia calls it the Doomsday Argument, and I recommend you to read their article on this.
So what is this prediction? It's about how many humans will ever be born. Suppose you are shown a magic records office which contains a special birth certificate for every human that will ever be born, either in the past, the present or the future. The certificates are all numbered, starting at 1. There's been about 40 billion people born so far. If we die out in the next century, the total that will ever be born is about 46 billion. However, if we go on to exist as a species for a million years, the total number could be 50000 billion or more.
Suppose you ask for one of the birth certificates, completely at random. Suppose the certificate you are given is number 41 billion. - that is - it belongs to somebody alive now. So what's more likely - that there are 46 billion certificates in there- or 50000 billion or more? It's much more likely that there are only 46 billion or so.
Now, let's think about people instead of birth certificates . You are about the 41st billion person born. If mankind was going to last one million years, it's amazingly unlikely , isn't it, that you were one of the first 0.008 percent to be born.
This argument, to say the least, is disputed. I don't believe it myself - because if the "first" human had considered it, he or she would have deduced that the total number of humans to be born would be about 5, and that the species would die out in a generation.
However, despite attempts to shoot it down , the Carter Prediction still has it's supporters. Maybe the mathematical answer to the 100 year questiion is "Yes, humanity will survive, but statistically the odd are against us lasting much longer".
Ah well, I'll be getting to the politics side of this soon...
