The quote about how Grothendieck solved mathematical problems—emphasizing his approach of finding a standpoint where there are no special cases—is quite general. Without knowing enough about your experience, it’s difficult to provide a precise answer. For instance, I know several quotes related to that topic, but here is one.
During the 1966 celebration of Grothendieck's Fields Medal, Dieudonné remarked (Les travaux de Alexandre Grothendieck):
S'il fallait chercher une parenté spirituelle à Grothendieck, c'est
à Hilbert, me semble-t-il, qu'on pourrait le mieux le comparer :
comme Hilbert, sa devise pourrait être : « simplifier en généralisant »,
en recherchant les ressorts profonds des phénomènes mathématiques ;
mais, comme Hilbert aussi, lorsque cette analyse en profondeur
a conduit à un point où seule l'attaque de front reste possible, il
trouve presque toujours dans sa riche imagination le bélier qui
enfonce l'obstacle. La comparaison est peut-être lourde à porter,
mais Grothendieck est de taille à n'en pas être accablé.
~ (If one had to seek a spiritual kinship for Grothendieck, it seems to me that the best comparison would be with Hilbert: like Hilbert, his motto could be 'simplify by generalizing,' seeking the profound mechanisms behind mathematical phenomena. But, also like Hilbert, when this in-depth analysis leads to a point where only a direct frontal attack remains possible, he almost always finds, in his rich imagination, the battering ram to break through the obstacle. The comparison may be a heavy one to bear, but Grothendieck is well capable of shouldering it without being overwhelmed.)
Hilbert is often credited to said (Quoted in N Rose Mathematical Maxims and Minims (Raleigh N C 1988)):
The art of doing mathematics consists in finding that special case which contains all the germs of generality.
Luckily enough for Grothendieck, the special cases were wisely (and primarily) suggested by Serre! (See their correspondence)
