Aim of the course
Students acquire a firm knowledge of the history and philosophy of mathematics. They will recognize the various views on modern mathematics in its cultural context.
Through the experience of thinking along the lines of different disciplines (i.c. history, philosophy), students of mathematics get the habit of making their own discipline the subject of reflection in a systematic way.
Mathematics in the 20th century: can we do better than fragmented histories?
Two persistent problems in the philosophy of mathematics are, according to Mannoury, its applicability and its beauty. Today history confronts us with another philosophical problem, the unity of mathematics.
History & Philosophy:
The written history of mathematics seems to stop at the middle of the 20th Century. Mathematics did not stop there, so why should its historiography. In this course we set the challenge of gaining a coherent view of mathematics in the whole 20th century. Fragmented histories of subfields of mathematics allow continuing stories, but mathematics as a whole does not.
Here comes in the role of philosophy of mathematics. We will explore newer views on the nature of mathematics to gain a more encompassing view of the history of mathematics. This question of unity will be the challenge of the present lecture course.
Also, the question of applicability will be specified by an historical interpretation of the rise of modern mathematics. The emerging practice of pure mathematics around 1800 and further changes in the twentieth century show the historical dynamics of mathematics. Applied mathematics emerged in the 19th century as the companion to the pure --and how applicable was it really? Typical of twentieth century science is modeling. Mathematicians played a novel role in mathematical modeling. As quants they got involved in stock markets and big data in the 21st century.
These questions demand a fresh look on mathematics, philosophically and historically. We will zoom out and reflect on the importance of mathematical thought in culture (and in the economy for that matter). We will study philosophers and historians who help us understand the cultural role of mathematical thought.
The course is developed for mathematics and will be attractive for students of computers science and physics as well. And for quants.
Without setting strict prerequisits, we assume that this course is not the student’s first ever confrontation with history of mathematics. The first weeks will be devoted to students (re)reading their favorite among the better introductory textbooks (D.J. Struik, M. Kline, I. Grattan-Guinness). Having established common ground in that way, we will continue lectures and seminars based on the literature under Studiemateriaal.
Registration via https://elo.mastermath.nl/course/view.php?id=258.
dr. G. Alberts (UvA); dr D.J. Beckers (VU)