Please choose three topics you could imagine working on for your project. Just type the title into the text fields. If you want to suggest an own topic, describe it concretely with a few words.

Suggested topics

Fashions in Mathematics

Are fashions relevant in mathematics? If you think so, base your argumentation on two examples of fashionable topics from different time periods.

Sofia Kovalevskaya

Sofia Kovalevskaya was the first female professor in mathematics and lived in Stockholm in the latter part of her life, in the late 19th century. Analyze what her life and her career say about society and equality in Sweden around that time, comparing it where suitable to other places in Europe.

Mathematical errors

How do mathematical errors affect the further development of a subject? Discuss and illustrate with two examples.

Fin-de-siècle

Discuss the following claim: The fascination with the foundations of mathematics (logic, set theory, axioms, and precise definitions) in the late 19th century is a fin-de-siècle phenomenon.

Bourbaki

The Bourbaki movement in France (from the mid 1930s) aims at giving a definitive account of all mathematical knowledge. Discuss where this desire came from and what it led to.

School students

In different periods of time, the expected mathematical abilities of students at high school age were different. Why? Discuss with regard to two different time periods, one which which may, but does not need to be, the present.

Collaboration

Today, most (but not all) mathematicians work together with others and write articles with one or more collaborators. This was not the case in the past. Why did this transition occur and how did it develop?

Pure and applied

Many mathematical institutions (also at KTH) are divided into "pure" and "applied" mathematics, but that was not the case in the past. What led to this distinction? Is it a natural distinction, that can be projected further back into the history of mathematics?

New Math

Discuss the "New Math"-movement in the US mathematics education in the 1960s. Why did it occur and why did it not succeed? What can we learn from this?

Fascination

Some new mathematical discoveries generate great fascination with the subject outside of academia. Why? Discuss with regard to two examples. Analyze both mathematical and nonmathematical sources.

Competitions

From the Nordic Mathematical Contest to the International Mathematical Olympiad, there are now a large number of mathematical competitions. When and why did this start? Compare the problems from competitions with research mathematics.

Hobby

Find two examples of mathematicians that had another daytime job. (Do not choose Fermat, who we talked about quite in class.) Was mathematics a hobby to them, or was the job in some way related to mathematics?

Cartography

How did cartography (for navigation) and mathematics affect each other? Which practical problems occurred that mathematics was hoped to be able to solve? Was it successful?

To infinity and beyond

Discuss how mathematicians have dealt with the concept of infinity before and after Cantor and its popular reception.

Programming languages

Discuss: "Mathematics played an essential role in the the development of the first programming languages.". Base your argumentation on primary sources.

School syllabi

Discuss the causes and motivations for changes in the mathematical syllabi at high school or comparable level. You can focus on a time period and place of your choice, Sweden and the present included. What determines what should be taught?

Invention or discovery

Discuss the developments that led to complex numbers and beyond -- quaternions and octonions. Were they invented or discovered? Would you say that mathematical concepts in general are discovered or invented?

Functions

Discuss: There are parallels between the historical development of the concept of a function and the development of the understanding of that concept in school students during their mathematical education.

Eastern mathematics

Due to the limited scope of the course, we did not study mathematical developments outside of the Western world and ancient Arabia/North Africa. Find and discuss a mathematical development in China, India, or elsewhere and its transmission or non-transmission to Europe.

The platonic solids

The five platonic solids (tetrahedron, cube, octahedron, dodecahedron, and icosahedron) are the only polyhedra composed of equal faces, all of which are regular polygons. Discuss the history of their classification and the roles they played within some mathematical and/or extra-mathematical areas (e.g. art, esoterics, astronomy, …)

Unsolvable

The unsolvability of polynomial equations of degree greater than 5 by radicals as well as Gödel's incompleteness theorem are examples of results that show the definitive impossibility of solving a problem, no matter which way we try it.

Which novel thoughts come into such an unsolvability result, and how are they perceived, both within and outside the mathematical world? Discuss this with respect to a suitable example, but not one of the above.

Puzzles

Since long ago, people found pleasure in mathematical puzzles. Who were the persons who invented those, and who solved them? Discuss also if there are some links between puzzles and "real" mathematics. Base your discussion on two historical examples from different time periods.

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