Can One Machine Do It All?
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Every question of mathematics can be answered: there is no “we will not know.” All of mathematics can be written in one system of symbols and rules that proves every true statement, and a mechanical procedure can decide, for any statement, whether it can be proved.
In any consistent system of rules strong enough for arithmetic, there are true statements that the rules can neither prove nor disprove. So no one system can answer every question of mathematics.
Truth for a language rich enough for arithmetic can be defined only in a richer language, never within the language itself. So no one system of symbols and rules can even say which of its own statements are true: there’s no universal criterion of truth.
Some problems can’t be solved by any effective calculation: I’ve found one in elementary number theory. So no mechanical procedure can decide, for every statement of logic, whether it can be proved.
No machine can decide, for every statement of logic, whether it can be proved. If one could, it could decide whether any machine ever prints a 0, and a machine that asked it that about itself could be made to do the opposite.