Adventures in shape and space – and time

As a youth entering the sixth form to study Mathematics, Further Mathematics and Physics I enjoyed the riches of the school's mathematics library and in particular three books which appealed to me, A mathematician's apology [1], A book of curves [2] and On growth and form [3].Hardy's book [1] is one that an impressionable, young mathematician should not read unguided. It left me with the impression that the proper pursuit of mathematics was as a pure subject, of no use or application, to be studied for its own sake; to my regret, I held to this view for several years before finally being able to shake it off through teaching Newtonian mechanics. Looking across mathematics teaching today I seem to observe great interest in geometry, number and algebra ‘curiosities’ that are rooted entirely in mathematics. This in itself is no bad thing, since it clearly draws us and our students into the fascinating world of mathematics. But what of the applications of mathematics? Might they be equally fascinating? Surely we do not want to lure our students into Hardy's trap?

6. Rheticus

As Copernicus entered his sixties, he was still a busy canon, particularly with respect to his medical expertise. Martin Luther’s Reformation was gaining power at this time, and a young mathematician-astronomer from Wittenberg (home of Luther and his thriving university) became aware of Copernicus’s work. Georg Joachim Rheticus left Wittenberg early in May 1539 to travel to Varmia. Rheticus brought with him a gift: three technical books printed by Johannes Petreius in Nuremberg. He went on to assist Copernicus with observations of the planet Mercury and completion of De revolutionibus. In the autumn of 1541, Rheticus returned to Wittenberg armed with the manuscript of Copernicus’s magnum opus.

The Boussinesq Debate: Reversibility, Instability, and Free Will

ArgumentIn 1877, a young mathematician named Joseph Boussinesq presented amémoireto theAcadémiedes sciences which demonstrated that some differential equations may have more than one solution. Boussinesq linked this fact to indeterminism and to a possible solution to the free will versus determinism debate. Boussinesq's main interest was to reconcile his philosophical and religious views with science by showing that matter and motion do not suffice to explain all there is in the world. His argument received mixed criticism that addressed both his philosophical views and the scientific content of his work, pointing to the physical “realisticness” of multiple solutions. While Boussinesq proved to be able to face the philosophical criticism, the scientific objections became a serious problem, thus slowly moving the focus of the debate from the philosophical plane to the scientific one. This change of perspective implied a wide discussion on topics such as instability, the sensitivity to initial conditions, and the conservation of energy. The Boussinesq debate is an example of a philosophically motivated debate that transforms into a scientific one, an example of the influence of philosophy on the development of science.