"Reason" is one of the most powerful tools human culture has developed. It has various forms, including sophisticated verbal argumentation (like law, philosophy, and the analytical portions of "humanities" generally), and the numerous species of mathematical logic.
In plotting our course toward the future, it's important that we try to be as reasonable as we can. Thinking carefully is a wonderful way (though not the only way: meditative disciplines help with this too) of avoiding being pushed around by the more animalistic portions of our brains. And reason is the best tool we have for figuring out likely conclusions from our observations and assumptions.
But overvaluing reason would be just as foolish as ignoring it. Reason is a powerful tool but in some contexts it is so inefficient it is impractical to apply. It is especially inefficient at arriving at conclusions based on massive amounts of heterogeneous data. Sometimes the most reasonable thing to do is to set aside detailed reasoning about a certain matter and make a judgment by intuition!
And reason can never be a complete solution to understanding the world, because reasoning always relies upon certain assumptions -- which must come from somewhere besides reason.
As human beings, we need to rely on reason plus intuition -- the latter being a crudely-defined shorthand for "certain human brain/mind processes that synthesize some processes in the theater of reflective awareness and some outside it, aimed at arriving at solutions to problems based on holistically integrating all the information available to the mind, or at least a large percentage thereof."
Intuition's conclusions may not always be easy for us to justify by reason, in practice. A question is whether, in principle, given enough space and time resources and enough visibility into the unconscious mind, one could always justify a good intuitive conclusion based on rules of sound reasoning. I suspect this is true -- but even if so, it's not a very helpful thing, because in practice we don't have arbitrarily much space and time resources to carry out this sort of experiment, and we also don't have the capability to suck all the contents of a human's unconscious into some reasoning engine's theater of reflective awareness.
As a scientist, I have great interest in understanding the workings of reason -- for instance, I do research on the application of probability theory and formal logic to reasoning about fuzzy everyday events. But at the same time, when I do science, I rely on a mixture of reason and intuition just like everybody else!
Will Intuition Go Obsolete?
Perhaps future AI minds will have greater capability to reason than us -- associated, perhaps, with much larger and more flexible theaters of reflective awareness. But even so, I strongly suspect they will still need a mixture of reason with some form of intuition. I suspect that reason will always be a resource-intensive, complex approach to solving problems that depend on large, heterogeneous pools of information -- so that it will always be supplemented with other methods with different strengths.
But I freely admit that this is conjecture -- perhaps new forms of reason will be admitted that don't have the shortcomings of human reason. Perhaps future minds will solve everything using some transhuman form of logic, even the choice of where to place their little toe when they walk, and the choice of which key to play next on the piano (or whatever analogous choices they have to make).