History and Philosophy of Mathematics

Course manual 2017/2018

Course content

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.

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Study materials

Literature

• Plato’s Ghost by Jeremy Gray

Syllabus

• further material in Blackboard

Objectives

• 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.

Teaching methods

• Lecture
• Seminar
• Presentation/symposium
• Self-study

Lectures and seminars, including presentations by students.(details in blackboard)

Learning activities

Attendance

The programme does not have requirements concerning attendance (OER-B).

Additional requirements for this course:

Active participation in the seminar is essential. Lectures are interactive and are indispensable.

Assessment

Details of the assignments in blackboard.

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.uva.nl/plagiarism

Timetable

The schedule for this course is published on DataNose.

Contact information

Coordinator

• dr. G. Alberts

D.J. Beckers

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