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Cursus: WISM481
WISM481
Seminar History of Mathematics
Cursus informatie
CursuscodeWISM481
Studiepunten (EC)7,5
Cursusdoelen
After completion of the seminar, the student is able to:
* use and interpret assigned literature (including primary sources)
* extract from this literature interesting contexts, interpretations and problems,
* present and discuss such issues in class meetings,
* report on the research in a written essay,
* work together with a fellow student to achieve the above.
Inhoud
Greek geometry as constructive mathematics

Ancient Greek geometry is a "maker's knowledge." Euclid never proves a single theorem about objects he has not first carefully shown how to construct by ruler and compass. A large part of higher Greek geometry is similarly devoted to producing specific geometrical objects, such as duplicating a cube, trisecting an angle, or squaring a circle. Why this obsession with making? Shouldn't geometry be about proving theorems rather than giving recipes for how to draw things using mechanical tools?
 
Growing interest in constructive mathematics in recent decades has shed new light on this aspect of classical geometry. Many authoritative editions and interpretations of Greek mathematics from a century ago were arguably coloured by the Platonic philosophy of mathematics of the time---"Cantor's paradise," as Hilbert called it. This point of view played down the role of constructions, relegating it to minor subsidiary functions such as existence proofs. But renewed recognition of the value of constructive and operational modes of thought in modern mathematics has revealed rich foundational parallels with the Greek style of geometry. This suggests that the Greeks may well have focussed on constructions due to a philosophically sophisticated conception of mathematical method and foundations, rather than as quasi-applied problems pursued largely for reasons of tradition, as had previously been supposed.
 
In this seminar we read Greek geometrical works in this tradition and, informed by modern insights, try to reconstruct their conception of mathematics and its foundations. Since the classical Greek corpus is completely void of any explicit foundational reflection, we must study their technical works with an eye to try to extract the implicit assumptions they make in terms of what constitutes worthy research goals and legitimate mathematical method and rigor.
 
Attention to these questions are a longstanding focus of the Utrecht school in the history of mathematics, going back to the work of Henk Bos. It remains a burning question in recent scholarship, and one on which mathematically trained students have much to contribute to historical understanding.
 
The topic also affords ample connections to current research in logic and philosophy of mathematics. This includes formalisations of diagrammatic reasoning, constructive mathematics, and the philosophy of mathematical practice.

Schedule
In consultation with participants.
 
Format
The first few meetings will be used to introduce the students to the topic and to distribute research tasks among pairs of students. In the next meetings pairs of students report on their research. Each of these meetings is a mix of presentation, excercises and discussion, prepared en presided by the reporting pair. This pair also hands out a homework excercise for the other participants and grades the returned homework. Each pair will report twice and produce a written account (essay) of their research.
 
Grading
20% homework
30% presentation
50% essay
 
Attendance is mandatory
 
Entry level
General mathematics at bachelor level. History of Mathematics is preferred but not strictly necessary. The seminar is suitable for Bachelor Math students in their last year as well as Master students, HPM students with sufficient mathematical background (depending on the subject, please contact in advance) and historically interested Physics students.

Evaluation matrix
 
  homework
20%
presentation 30% essay 50%
use and interpret assigned literature (including primary sources) x x x
extract from this literature interesting contexts, interpretations and problems   x x
is present and is able to discuss such issues in class meetings   x  
is able to report on the research in a written essay     x
can work together with a fellow student to achieve the above   x x
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