If I have excelled in the art of the mathematician, it is due less to my facility or my persistence in working to find solutions for problems delegated to me by my predecessors, than to the natural propensity which drives me to envisage questions , ones that are clearly critical, which others don't seem to notice, and to come up with "good ideas" for dealing with them ( while at the same time no-one else seems to suspect that a new idea has arrived), and "original formulations" which no-one else has imagined. Very often, ideas and formulations interact in so effective a manner, that the thought that they might be incorrect does not arise, (apart from touching them up a bit). Also as well, when its not a matter of putting the pieces together for publication, I take the time to go further, or to complete a proof which, once the formulation and its context have been clarified, is nothing more than what is expected of a true "practitioner", if not simply a matter of routine. Numberless things command our attention, and one simply cannot follow all of them to the end! Despite this it is still the case that the theorems and propositions in my written and published work that are cast into the proper form of a demonstration number in the thousands. With a tiny number of exceptions they have all joined the patrimony of things accepted as "known" by the community, and are used everywhere.
Yet, even more than in the discovery of new questions, notions and formulations, my unique talent appears to consist of the entertainment of fertile points of view which lead me to introduce and to, more or less, develop completely original themes. It is that constitutes my most essential contribution to the mathematics of my time. To speak frankly, these innumerable questions, notions and formulations of which I've just spoken, only make sense to me from the vantage of a certain 'point of view' - to be more precise, they arise spontaneously through the force of a context in which they appear self-evident: in much the same way as a powerful light ( though diffuse) which invades the blackness of night, seems to give birth to the contours, vague or definite, of the shapes that now surround us. Without this light uniting all in a coherent bundle, these 10 or 100 or 1000 questions, notions or formulations look like a heterogeneous yet amorphous heap of "mental gadgets", each isolated from the other- and not like parts of a totality of which, though much of it remains invisible, still shrouded in the folds of night, we now have a clear presentiment.
The fertile viewpoint is that which reveals to us, as so many parts of the same whole that surrounds them and gives meaning to them, those burning questions that few are aware of, ( perhaps in response to these questions) thoroughly natural notions yet which none had previously conceived, and formulations which seem to flow from a common source, which none had dared to pose despite their having been suggested for some time by these questions, and, and for which the ideas had yet to emerge. Far more indeed, than what are called the "key theorems:" of mathematics, it is these fertile viewpoints which are, in our particular craft(*) the most powerful tools for discovery- rather they are not tools exactly, but the very eyes of the researcher who, in a deeply passionate sense, wishes to understand the nature of mathematical reality.
Yet, as the word itself suggests, a "viewpoint" implies particularity. It shows us but a single aspect of a landscape or a panorama out of a diversity of others which are equally valuable, and equally "real". It is to the degree that the complementary views of the same reality cooperate, with the increasing population of such "eyes", that one's understanding of the true nature of things advances. The more complex and rich is that reality that we wish to understand, the more the necessity that there be many "eyes" (**)for receiving it in all its amplitude and subtlety.
Otherwise stated: Vision is, to the viewpoints from which it springs, and which it unites, like the clear, warm light of day is to the different frequencies of the solar spectrum. A vision that is both extensive and profound is like an inexhaustible wellspring, made to inspire and illuminate the work, not only of the person in whom it first sees the light of day and becomes its servant, but that of generations, fascinated perhaps ( as he was also) by those distant boundaries which it opens up.