**Guarino Guarini** was an Italian mathematician who worked in geometry and philosophy.

- Trained as a theologian in the small but elite order of Counter-Reformation Clerics Regular, commonly known as the Theatines and the immediate model for the Jesuit Order, Guarini was also deeply interested in mathematics following in turn the Jesuit pursuit of all the arts and especially the new discoveries that surrounded the curious-minded of the Age of Discovery.
- Guarini spent his novitiate in Rome where he learned at first hand what Bernini and Borromini, now recognised as great masters of Baroque architecture, were doing, and their example presumably caused him to practise architecture, then considered as a mathematical art but not strictly a member of the Quadrivium, the mathematical division of the Liberal Arts, still supreme in the world of learning.
- Even from the beginning of the eighteenth century there was a turn against the triumphs of the Baroque, so that we now have great difficulty in understanding such a figure as Guarini and his work, which also includes his mathematical philosophy and figural meaning, or geometrical iconography.
- The line that Guarini refuses to cross is to pass from Universal Mathematics to mathesis, a term which for him seemed to represent the rising physico-mathematics of the Cartesian school.
- Guarini referred to Wallis among the few authorities for his mathematics - both were involved in summation to infinity.
- Guarini was adept at most applications of advanced curvature and projective techniques, if not indulging outright in the projective geometry of Desargues as his modern admirers have alleged, confusing 'projection' with 'projective geometry'.
- Guarini was therefore proficient in the French tradition of stone cutting using most difficult procedures, as well as gnomonics, or the study of sundials, devoting many published pages to each discipline.
- The key to such attitudes can be found in the Jesuit Bolognese belletrist and mathematical encyclopedist, Mario Bettini, who Guarini implicitly relied upon in much of his work.
- However while there are some indications of rationalising the elements of architecture more geometrico, found in his Architectura civile, Guarini accepted the traditions of Vitruvius and the High Renaissance with a bracing freedom in the decorative development of the orders, as well as a innovative appreciation of the daring of Gothic structure, exceptional at this date.
- Guarini wrote a great summa of philosophy which carried a treatment of light, strictly discursive in manner, and he was reluctant to separate light from its traditional transcendental interpretation.
- Guarini was aware of the transformative implications of geometrical processes, especially through light, optics and projection so rhetorically advanced by Bettini.

Born 1624, Modena (now Italy). Died 1683, Milan (now Italy).

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Origin Italy

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive