Beniamino Segre Quotes (1903-1977)

“A nonsingular cubic surface F can be rationally represented upon a plane α if and only if F contains a rational point.”

“Non vi sarebbe quindi da stupirsi se le geometrie di Galois venissero and avere in futuro applicazioni anche al campo della fisica, da cui attualmente sembrano molto lontane esce anzi tali spazi finiti portassero alla costruzione di schemi a modelli dove i fenomeni fisici trovassero interpretazioni matematiche più semplici di quelle consuete. (It would not be much of a surprise if Galois geometry in the future came to have applications in the field of the physics, from which these finite geometries are currently far removed. These finite geometries might lead to the construction of models in which physical phenomena have simpler mathematical interpretations than the models now used. — modified from the original translation by Tallini)”

“The study of the geometry of a Galois space S_r,q, i. e. of a projective r-dimensional space over a Galois field of order q = p^h. where p, h are positive integers and p is a prime (the characteristic of the field), has recently been pursued and developed along new lines ... In it, both algebraic-geometric and arithmetical methods have been applied, including the use of electronic calculating machines; moreover, some of the problems dealt with are deeply connected with information theory, especially with the construction of q-ary error-correcting codes. It is actually a chapter of arithmetical geometry, which reduces to the investigation of certain questions on congruences mod p in the particular case when h = 1.”