Technological singularity

Admit that artificial thinking will be able to work on research and development topics. Clues are given elsewhere on this site. Admit it for now. Artificial thinking will work on computer science. And it will particularly work on artificial thinking improvement. This work will result in reaching a critical threshold, so called singularity. See Wikipedia definition.

Chain reaction

The nuclear chain reaction is a good sample of a critical threshold. Below this critical threshold, the reaction decreases. As soon as the critical threshold is reached, the chain reaction starts.
Have a look at Wikipedia for a broader definition of critical threshold.
Have a look at this simulation of a nuclear chain reaction.

Progress leads to exponential progress

Enhancement after enhancement, artificial thinking algorithms will reach such a high level that they will overcome the capacities of human beings. Given that, what will stop the process? this enhanced artificial thinking algorithm will be smart enough to develop a smarter algorithm. At first glance, no limit.

Man will be clever enough...

No, never men will stop! Think of business competition. Think of military applications. Suppose you just reached the critical threshold. Your neighbor will do better in order to win, and you will do the same. The only way: Running ahead to the least appalling outcome.