The Simulation Hypothesis was first published by Hans Moravec (of the Robotics Institute, Carnegie Mellon University, US) in 1998. See Simulation, Consciousness, Existence

Then, in 2003, Professor Nick Bostrom, Director of the Future of Humanity Institute, Faculty of Philosophy & James Martin 21st Century School, Oxford University, published his paper 'Are You Living In a Computer Simulation?' (Philosophical Quarterly, 2003, Vol. 53, No. 211, pp. 243-255.)

This paper argues that at least one of the following propositions is true: (1) the human species is very likely to go extinct before reaching a 'posthuman' stage; (2) any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof); (3) we are almost certainly living in a computer simulation. It follows that the belief that there is a significant chance that we will one day become posthumans who run ancestor-simulations is false, unless we are currently living in a simulation.“

The paper has since generated much philosophical debate - according to some philosophers, it's impossible to construct a proof or disproof. More info. here on the professor's website.

Further discussion from professor Yuval Noah Harari writing in 'Homo Deus - A Brief History of Tomorrow' (Penguin Books, 2016) :

According to current scientific dogma, everything I experience is the result of electrical activity in my brain, and therefore it should be theoretically feasible to simulate an entire world that I could not possibly distinguish from the 'real' world. Some brain scientists believe that in the not too distant future, we shall actually do such things.”

And, from a mathematical viewpoint :

[…] since there is only one real world, whereas the number of potential virtual worlds is infinite, the probability that you inhabit the sole real world is almost zero.“

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