Grothendieck on mathematician’s prowess and beauty of math

Although I am not even remotely acquainted with algebraic geometry (or any maths, for that matter), I found Récoltes et Semailles by Grothendieck a vastly interesting and insightful read. The analysis, reflection combined with metaphors in the book, much reminds me of many thoughts of my own I would just like to put the work of understanding topology in my own schedule, and quote a few paragraphs here, for readers’ knowledge.

*The dream I’m referring to had no scenario, no specific acts or activities.
It contained but a single frozen image, one that was at the same time
remarkably alive. It was a human head seen in profile, scanned from left
to right. The head was of a mature man, beardless, with wild head wrapped
around its brow like a bright powerful halo. The strongest impression made
by this head was of a joyous, youthful vitality, which seemed to spring
directly from the supple and vigorous arching of its neck (sensed more
than seen). The facial expression was more that of a mischievous
delinquent than of a responsible or settled adult, thrilled by the
recollection of some trick he’d gotten away with or was about to do. It
gave off an intense love of life, playful, content with itself.

Nobody else was present, no-one to play the role of observer, and “I” to
look at or contemplate this being, of whom one saw only the head. Yet the
perception of this head, or let us say of the atmosphere which it evoked,
was extremely intense. Nor was anyone else present to record impressions,
comment on them, or give a name to the person being observed, to call him
“this or that”. There was only this intensely vital object, the man’s head,
and an awareness of that vitality.

When I awoke and reviewed the various dreams which had passed that night,
the one with the man’s head did not seem of any particular significance,
there was nothing in it that might make me cry out: you ought to be looking
at me! Reviewing this dream in the quiet comfort of my bed, I was driven
by the natural desire to put a name to this apparition. Nor did I have
far to search: once the question was posed it was more than obvious that
the head I’d seen in my dream was none other than my own.

It’s not a bad thing, I told myself, it takes some doing to see one’s own
head in a dream as if it were that of another! The dream gave the impression
of having arisen by accident, much as when one finds a 4-leaf clover, (or
even one of 5 leaves), yet aroused no other reaction, so that shortly
afterwards I felt free to go on my way as if nothing had happened. *

……

*It is also the case that the most totally consuming ambition is powerless
to make or to demonstrate the simplest mathematical discovery - even as
it is powerless ( for example) to “score” ( in the vulgar sense) . Whether
one is male or female, that which allows one to ‘score’ is not ambition,
the desire to shine, to exhibit one’s prowess, sexual in this case. Quite
the contrary!

What brings success in this case is the acute perception of the presence
of something strong, very real and at the same time very delicate. Perhaps
one can call it “beauty”, in its thousand-fold aspects. That someone is
ambitious doesn’t mean that one cannot also feel the presence of beauty
in them; but it is not the attribute of ambition which evokes this
feeling….

The first man to discover and master fire was just like you and me. He
was neither a hero nor a demi-god. Once again like you and me he had
experienced the sting of anguish, and applied the poultice of vanity to
anaesthetize that sting. But, at the moment at which he first “knew” fire
he had neither fear nor vanity. That is the truth at the heart of all heroic
myth. The myth itself becomes insipid, nothing but a drug, when it is used
to conceal the true nature of things. *