Cortés himself was half-educated

From Carnage and Culture by Victor Davis Hanson. Page 206.

Cortés himself was half-educated, and for a time worked as a notary, studied Latin, and read Caesar’s Gallic Wars, Livy, and other classical military histories. At least some of his success in the darkest hours of the Mexica wars was due to his mesmerizing oratory, laced with classical allusions to Cicero and Aristotle and punctuated with Latin phrases from the Roman historians and playwrights. Spain, we must remember, in the first century B.C. during the latter days of the Roman Republic and early years of the Principate, was the intellectual center of Europe, producing moral philosophers such as the elder and younger Senecas, the poet Martial, and the agronomist Columella.

Although the Inquisition and religious intolerance that were sweeping Spain would soon isolate the Iberian Peninsula from the main centers of learning in northern Europe, leading to clear decline by 1650, in the sixteenth century the Spanish military was still at the cutting edge of military technology and abstract tactical science. Many of the men who marched with Cortés were not merely notaries, bankrupt hidalgos, and priests acquainted with Latin literature but avid readers of contemporary Spanish political and scientific tracts. More important, they were trained as bureaucrats and lawyers in the inductive method of adducing evidence, prior precedent, and law to prove a point before an audience of supposedly disinterested peers.

Cortés’s conquistadors may not have been intellectuals, but they were equipped with the finest weapons of sixteenth-century Europe and buttressed by past experience of fighting the Moor, Italian, and Turk. The fundamentals of some two millennia of abstract Western military science, from fortification, siegecraft, battle tactics, ballistics, and cavalry maneuver to logistics, pike and sword fighting, and medical treatment in the field ensured that it would take literally hundreds of Mexicas to kill each Castilian. When rushed and swarmed, the Spaniards fell in rank and file, fought in unison with unquestioning discipline, and fired group volleys. In the myriad sudden and unexpected crises that arose each week, Cortés and his close advisers—the brilliant Martín López, the courageous and steady Sandoval, and the mercurial Alvarado—did not merely pray but coolly met, argued, and worked out a tactical or mechanical solution to salvage their blunder of marching into an island fortress of thousands. Cortés also worried that his actions would be recorded, criticized, audited, and made known to thousands back in Spain.