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Mathematician, astronomer, and cosmographer, b. at Florence in 1397; d. there, 10 May, 1482. Toscanelli, who was one of the most distinguished scientists of the fifteenth century, was the son of the Florentine physician Dominic Toscanelli. He began his mathematical studies at Florence under Giovanni dell'Abacco. At the age of eighteen he entered the University of Padua where he studied mathematics, philosophy, and medicine. In this period he formed his life-long friendship with Nicholas of Cusa who studied law and mathematics at the same university. The two probably met at the college Prosdocimos de'Beldomandi. Both left the university in 1424, Nicholas with the title of doctor decretorum and Paolo as a doctor of medicine. In consequence of this Toscanelli afterwards was frequently called Paolo fisico. While Nicholas of Cusa went back to Germany Toscanelli returned to Florence, where he spent the remainder of his life with the exception of short journeys in Tuscany and brief sojourns at Todi and Rome. At Florence Toscanelli took up scientific studies in various directions which brought him into connexion not only with distinguished artists, as Brunelleschi, but also with the greatest scholars of Italy and other countries. He may indeed be said to have been the centre of the learned world of that era. His contemporaries pronounced him one of the most distinguished mathematicians of his time. Regiomontanus and Cusa sought his opinion in the most abstruse questions of theoretical mathematics, or supported their assertions by his authority. Thus Nicholas of Cusa, even at the height of his fame, admired in his friend the thorough mathematician, as is shown by his treatise "De transformationibus geometricis" which was dedicated "Ad Paulum magistri dominici Physicum Florentinum". The same admiration is evident when Cusa wrote as a dialogue between himself and Toscanelli the latter's adverse criticism of Cusa's "Mathematica complementa". In this dialogue Toscanelli says that like Regiomontanus he found the "Mathematica complementa", which investigated the squaring of the circle, obscure and lacking in positiveness.

Toscanelli's services to astronomy are shown by the painstaking and exact observations and calculations, preserved in manuscript, of the orbits of the comets of 1433, 1449-50, of Halley's comet of 1456, of the comets of May, 1457, of June-July-August, 1457, and that of 1472. According to his own testimony these observations cost him immense labours and long vigils. He could not entirely throw off the influence of astrology, although two of his contemporaries, Marsilio Ficino and Giovanni Pico, disbelieved in it. A monument to his astronomical skill still exists at the Cathedral of Santa Maria del Fiore at Florence in the well-known gnomon, which he constructed about 1468 and which was later improved by Cardinal Ximenes. A marble slab having a small opening in it was placed at a height of 277 feet in the dome over the middle of the left transept; by the shadow he could determine midday to a half-second, and could also settle with much precision the altitudes of the solstices. Toscanelli also gave much attention to cosmography. It seems indeed that he was the most distinguished scholar of the fifteenth century in this branch of science, the aim of which was to gain knowledge of the world in its widest extent. The estimation in which he was held as a cosmographer is shown by the generally accepted belief, resting on traditions respecting Columbus, that Columbus before undertaking his dangerous western voyage asked Toscanelli's advice. Toscanelli had a thorough knowledge of the writings of Ptolemy, he had studied the travels of Marco Polo, and had gained personal information from merchants and seamen, above all from the Italian traveller Nicolo Conti. All that he had thus learned had brought him to the conviction that the transverse extent of Europe and Asia covered nearly two-thirds of the earth, that is 230 degrees of latitude, so that the western route across the ocean could only cover 130 degrees. For a half century the Portuguese had sought to sail around Africa towards the east. Toscanelli seems to have made them repeated proposals as to the possibility of a western route, without, however, being able to convince the Portuguese of the feasibility of his theory.

If we may believe the tradition connecting Toscanelli and Columbus, then Toscanelli wrote, in answer to repeated requests of King Alfonso, the celebrated letter dated 25 June, 1474, to the confessor Canon Ferdam Martins of Lisbon whom he knew. In this letter, which was accompanied by a map, he suggested clear directions for the carrying out of his scheme. This letter had no decisive effect upon the king but probably influenced the adventurous Christopher Columbus, then in the full vigour of manhood. Columbus, who had lived in Lisbon from 1476, heard of the correspondence between Toscanelli and the Court. According to the tradition it was only through the intervention of the friend of Columbus, Lorenzo Giraldi, that the former obtained from Toscanelli, in answer to a personal inquiry, an explanation of his scheme of a voyage westwards. Toscanelli is said to have sent Columbus, for this purpose, a copy of his letter and chart. At the beginning and end of the letter Toscanelli added a few words addressed especially to Columbus. The two biographies of Columbus, that of his son Fernando and that of Bishop Las Casas, both include and give the text of another letter from Toscanelli in reply to second letter sent him by Columbus. Unfortunately Toscanelli's two letters no longer exist in an authentic form. Both apparently have been greatly altered in the Italian translation of Fernando's "Historie", and in the Spanish biography by the Bishop Las Casas of Chiapaz. However, by good fortune, the middle part of Toscanelli's first letter, that is a copy of the letter of 25 June, 1474, has been preserved in its original form. Harrisse discovered in the "Bibliotheca Colombina" at Seville a copy, made by Columbus himself, of the letter to Martins on the cover of an edition of the "Historia rerem ubique gestarum" of Æneas Silvius. This document makes it possible to determine fairly accurately Toscanelli's opinion, which has been so variously interpreted, concerning the western route and the distance apart of the coasts of the two mainlands.

Toscanelli's chart, however, has not been preserved, either in the original or in a copy. A successful reconstruction of this chart was made by Hermann Wagner of Göttingen which shows that Toscanelli covered the customary nautical chart of the fifteenth century with the reticulations of a square flat chart, upon which direction and distance would be correctly measured by means of the spaces. It is not surprising that Columbus was overwhelmed with delight when he saw it, that he took it with him on his first westward voyage, and had absolute confidence in it. Consequently his two biographers are right in laying so much emphasis on the controlling influence of Toscanelli over Columbus. They even praise the Florentine scholar as the actual father of the great idea of sailing to India by the western route. A diametrically opposite opinion has been expressed by the French scholar Henri Vignaud, who since the holding of the American Congress at Paris in 1900 has attempted to prove that Toscanelli's correspondence with Martins and Columbus, including the accompanying chart, is a forgery. This has led to a violent controversy over the "Toscanelli question", in which Italian, American, English, French, and German scholars have supported the traditional belief of the connexion between Toscanelli and Columbus. Notwithstanding this, Vignaud in 1905 and 1911 published monographs on the life of Columbus for the purpose of maintaining his views. Vignaud's arguments, however, are not decisive. Even though the correspondence between Toscanelli and Columbus be proved to be apocryphal, still Toscanelli's knowledge and ability as a cosmographer does not suffer in the slightest so long as the letter of 1474 is taken as the expression of his cosmographic ideas, and so long as the letter of Duke Ercole of Este, written to his ambassador Manfredo of 26 June, 1494, is regarded as authentic. This letter says that Toscanelli had really occupied himself with the idea of a voyage towards the west. The titles of only three of Toscanelli's works are known, none of them, unfortunately, have been preserved: the "Prospettiva", the "Meteorologia agricola", and also, according to Uzielli, a translation of Ptolemy's geography. A single manuscript is one of the treasures of the Bibliotheca Nazionale centrale of Florence; this was published in 1864 and pertains to astronomy, geodesy, and geography.