In Jacques Hadamard's book The Psychology of Invention in the Mathematical Field the author advances a view of innovation or invention in mathematics, based on evidence and personal reflection of many mathematical luminaries such as Einstein, Pascal and Wiener and with much reliance on the self-reflection of Poincaré. Hadamard himself was a notable mathematician in his own right. His survey of the process involved in mathematical innovation highlights significant similarities among practicioners across the centuries, and this gives his work weight, in my opinion.
Briefly, he argues that mathematical discovery typically occurs in two steps: an intuitive step and a rational step (my terms). In the former, the mathematician 'sees' or somehow grasps an abstract entity and some property of it. Mathematicians often speak of the 'beauty' of mathematics, and this is in direct reference to the structures and objects that are discovered and incorporated into mathematics. I use the word 'discovered' advisedly, as it is my belief that mathematical objects and their properties somehow exist independently of our minds and are capable of being discovered by us. I do not agree that mathematical objects and structures are purely expressions of our minds or consciousness, but this is the other major view held. Both views have many proponents, though I'd guess that the former is predominant.
The intuitive step thus is an apprehension or glimpse into this abstract realm, inviting study and investigation. But one cannot conduct further study by intuiting; rather, further study is conducted by formalizing a definition, property or theorem to be proved. In other words, the rational step takes the opening provided by the intuitive step, formalizes it with definitions and proofs, and presents it to our rational faculties for examination and approval. As well, in this form, the new realization is conveyed to other mathematicians.
In my own limited mathematical experience, I can testify that there is a kind of 'knowing by seeing' the object in some abstract vision in the mind. This precedes useful interaction on a formal level with such entities. The two modes of knowing/seeing and formal interaction are real.
This leads me to advance and apply Hadamard's conclusions to theology, namely, in theology as in mathematics there is an intuitive element of knowing or seeing a spiritual or biblical truth, followed by a more rigorous support and defense of some truth, by appeal to the Scriptures, and possibly to church tradition and other writers. There are significant differences between theology and mathematics: a theological truth is not susceptible to rigorous formal proof, as are the truths of mathematics. A theological truth is more like a theory in the physical sciences, in which a theory gains increasing stature by cumulative agreement and support from experiment, and by lack of counterexamples. In the realm of theology, some truths may seem radical at first, yet they gain prominence by various means of support and agreement from the Scripture, from the opinions of others looking at Scripture, and from their explanatory power. An example might be the notion of 'covenant' which is certainly present in Scripture and which, on further examination, seems to permeate God's dealing with us in redemptive history. In theology as in science, no proposition is ever proved with absolute formal certainty (but what would such a proof in theology mean, in any case?), but ever-closer approximations to truth seem possible.
In theology, as in mathematics, it is not sufficient to intuit or grasp with some inner vision a spiritual truth. While in mathematics the intuitive vision must be validated by rigorous proof, in theology the intuitive vision must be validated by explicit appeal to the words and text of Scripture. Only after that occurs can we rely on the theological truth, even if it is somehow 'obvious' to others. Thus, we do not wish to deprecate or disparage the role of intuition in grasping spiritual truths, but we wish to assert that it is not complete until passing some form of rational and cognitive muster. Neither, incidentally, is it valid to assert some theological truth purely based on rational considerations. No, if it is true, it will be true intuitively and rationally.
Theological inquiry and spiritual understanding require both (spiritual) intuition and (a sanctified) rational capability. Our practice of theology is impacted negatively by the effects of sin, making the joint application of intuition and rationality more urgent. Rationality can check and counterbalance imperfect and inaccurate intuitions, and intuition can inform and direct formal inquiry.
In the body of Christ, there will be those excelling in spiritual intuition and also those excelling in rational methods of inquiry. It is critical to note that neither camp can say to the other, "I have no need of you." These two faculties form complementary parts of an overall enterprise, one that God has given to us to do.
Reference: The Psychology of Invention in the Mathematical Field by Jacques Hadamard; 1945, Dover 1954.