Roger Bacon was born 1214 in Ilchester, Somerset, England, and he died 1294 in Oxford, England. Roger Bacon studied geometry, arithmetic, music and astronomy as a young man. He received a degree from the University of Paris around 1241. After taking his degree he lectured at Paris on Aristotle's ideas but at this stage he showed little interest in science.
His interest in mathematics and science was acquired at Oxford to which he returned in 1247. He was much influenced by Grosseteste and worked most of his life on languages, mathematics, optics and sciences. In particular he concentrated on studying these topics at Oxford between has arrival in 1247 and 1257.
His most important mathematical contribution is the application of geometry to optics. He said:-
Mathematics is the door and the key to the sciences.
Bacon followed Grosseteste in emphasising the use of lens for magnification to aid natural vision. He carried out some systematic observations with lenses and mirrors. He seems to have planned and interpreted these experiments with a remarkably modern scientific approach. However many experiments are described in his writings which he never carried out in practice.
In 1257, perhaps largely due to ill health, Bacon left the University of Oxford and entered the Order of Friars Minor. However he continued his interest in the sciences and this was not appreciated by his superiors. Bacon wrote to Pope Clement IV in 1266, writing what looks remarkably similar to a grant proposal that a mathematician or scientist might make today. His proposal was for an encyclopaedia of all the sciences worked on by a team of collaborators, coordinated by a body in the Church.
Pope Clement IV, however, not being accustomed to receive proposals of this nature, misunderstood what Bacon was proposing, believing rather that Bacon's proposed encyclopaedia of science already existed. He asked to see it and Bacon, who could not disobey the Pope, rapidly composed the Opus maius (Great Work), the Opus minus (Smaller Work) and the Opus tertium (Third Work).
This remarkable achievement was carried out in secret since Bacon's superiors were violently opposed to what he was doing. Bacon was aiming to show the Pope that sciences had a rightful role in the university curriculum. He wrote down in Opus maius an astounding collection of ideas, for example he gives a proposal for a telescope:-
For we can so shape transparent bodies, and arrange them in such a way with respect to our sight and objects of vision, that the rays will be reflected and bent in any direction we desire, and under any angle we wish, we may see the object near or at a distance ... So we might also cause the Sun, Moon and stars in appearance to descend here below...
In 1268 Pope Clement IV died and Bacon's chances of seeing his great project come to fruition vanished. About this time however Bacon embarked on another great project himself, starting to write the Communia naturalium (General Principles of Natural Philosophy) and the Communia mathematica (General Principles of Mathematical Science).
Only parts were ever published, probably most was never written, but again there was some remarkable insights on astronomy and calendar reform which Bacon had formed after making observations. It was reported that Bacon
... did sometimes use in the night season to ascend this place (his study on Folly Bridge, on an eyot midstream in the Thames) invironed with waters and there to take the altitude and distance of stars and make use of it for his own convenience...
Bacon believed that the Earth was a sphere and that one could sail round it. He estimated the distance to the stars coming up with the answer 130 million miles.
Around 1278 Bacon was put in prison by his fellow Franciscans, the charge being of suspected novelties in his teaching. Clearly from his writings Bacon did not meekly refrain from putting forward his views after this. They were as aggressively stated in his last writings of 1293 as at any time in his life.