He was a precocious child, early delving into serious problems in mathematics and even publishing astronomical tables at the age of ten, Camuelis primus calamus (Madrid 1617).

Through Don Ferdinand, Caramuel became friends with Marie de' Medici, the exiled former queen-mother of France (1630–1642), who lived in Bruxelles, though she visited her daughter, the queen of England, for a period of three years.

[12] Having learned more of the doctrines of Cornelius Jansen, who had died earlier in that year, Caramuel embarked on a preaching crusade through Belgium and Germany, especially Mainz.

[20] Caramuel was in active correspondence with famous scholars:[21] the philosophers René Descartes and Pierre Gassendi; the Jesuit polymath Athanasius Kircher; the Czech Capuchin friar and astronomer Anton Maria Schyrleus of Rheita, the Bohemian doctor Jan Marek Marci, Pope Alexander VII (Fabio Chigi), who was a great admirer of his work; the Belgian astronomer Godefroy Wendelin, the theologians Franciscus Bonae Spei and Antonino Diana, Giovanni Battista Hodierna, Johannes Hevelius, Valerianus Magnus, Juan Eusebio Nieremberg, and many others.

According to Jean-Noël Paquot, he published no fewer than 262 works on grammar, poetry, oratory, mathematics, astronomy, architecture, physics, politics, canon law, logic, metaphysics, theology, and asceticism.

Although educated in the Thomist tradition, he firmly believed in the humanist ideal of nullius addictus iurare in verba magistri (‘not to swear slavishly by the words of any master’).

He refused to be enrolled in a specific school of thought and felt free to choose among all the authorities that would best suit his project of constructing a renovated Christian philosophy.

Caramuel loved to defend novel theories, and in Theologia moralis ad prima atque clarissima principia reducta (Leuven, 1643) tried to solve theological problems by mathematical rules.

He was a leading exponent of probabilism and his permissive moral opinions were criticized in Pascal's Provincial Letters and gained for him from Alphonsus Liguori the title of "Prince of the Laxists".

[27] Caramuel was also the first mathematician who made a reasoned study on non-decimal counts, thus making a significant contribution to the development of the binary numeral system.