Assignment: History and Philosophy of Mathematics
Coursework essay assessment
Either:
Describe a topic from modern mathematical research which can have implications for philosophy and culture. Specify what implications for culture one can find in the results of the chosen mathematical research. Make observations on the ways research in mathematics can advance
cultural and philosophical development.
Or:
Discuss any issue from fields of philosophy and culture which could be important for and could have an impact on modern mathematics. In what sense the development of non-mathematical and non-physical sciences, art politics etc, can be used in order to influence, enhance or advance mathematical research.
1] Plan of essay. Statement of objectives and main ideas which will be developed and defended in essay. Clear structure of essay: introduction, main body, conclusion to be expected.
2] Concise account of the case-study or particular problem in mathematics and culture, in sufficient detail to support your main arguments concerning their differences and possible points of impact.
3] Demonstration of the ability to relate the problems discussed in the course to the chosen subject for the essay.
4] Demonstration of the ability to provide a reasoned argument, using appropriate references and other evidence, to support the case made. Appraisal of the success, or otherwise, of the various positions with respect to the interaction between mathematics and culture.
5] References and evidence of independent literature search.
The size of essay is 2000 words [4 pages]. Please do not exceed this limit.
1) Platonism in contemporary mathematical physics: its cultural, sociological and artistic implications.
2) Mathematics describes best the non-existential realm of the world where no humanity is possible. How this statement can be reconciled with a point of view that mathematics is human invention? Discuss.
3) How the interest to mathematics and its study affects your picture of the world and ability to engage relationships with people who have no interest in mathematics. In other words, If mathematics influences your personality, how can you position it with respect to other persons who are formed under the influence of human sciences, art etc. Is there any existential difference between professional mathematicians and artists (for example).
4) Is there any intrinsic ethics in mathematics?
5) Mathematics and theology: does mathematical rationality of the universe point towards the underlying reason of the universe.
6) Structural realism as a modern option for philosophy of mathematics.
You can suggest your own topic but, please, negotiate it with the lecturer.