No, on their own computers can not solve the problems of humanity, only humans can do that. However, computers are powerful tools that can be used to model various aspect of the real world. If human have managed to to get these model correct then computers are now fast enough to calculate what these models will predict in the future. Armed with these predictions humans may be capable of making choices that help to solve human problems.
The error rate and slowness of human computers trying to solve large problems.
both computer and humans can do work and solve problems in mathematics
Solving computationally intensive problems that were beyond the capability of human computers to solve.
technology
Primarily bytes.
Computers can reach much higher levels of cryptography than the human brain can process. There are cryptographic formulas that a computer can solve in seconds that a human could take decades to solve.
To help people solve large tedious computational problems.
Sense and to solve human problems.
Because those ancestors which could not solve problems mostly died before actually becoming ancestors.
I'd call geek squad for help.
To have an "intention" requires human thought and a human brain. A website is not human; it has no brain; it cannot think, plan, or intend anything. So the whole idea of the "mystery of intentions by computers" is rather ridiculous.
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