None of these things are enough by itself. It's rather that they have now solved so many things that the sum total has (arguably) crossed the threshold. As for

None of these things are enough by itself. It's rather that they have now solved so many things that the sum total has (arguably) crossed the threshold. As for solving math problems, that is an important part of recursive self improvement. If it can come up with better algorithms and turn them into code, that will translate into raising it's own intelligence.