Henrik Kragh Sřrensen (1973-)

Steno Institute, Aarhus

Niels Henrik Abel (1802-29)

K_{3,3} \geq 2

Some of my digital photos

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My interests in math 'proper'

Although now a Ph.D. student in the history of mathematics I remain very interested in mathematics proper. My main field of interest lies in discrete mathematics (parts of which are also known as combinatorics). Main interests in combinatorics include Ramsey theory and links between Ramsey theory and complexity theory.

K_{3,3}\geq 2 The hexagon on the right represents one of the simplest yet very beautiful results in Ramsey theory, a result which is completely elementary. It says, that no matter how you color the edges of the complete hexagon (all vertices joined by an edge) in two colors (red and blue), a monochromatic triangle (three vertices joined by edges colored the same color) will emerge. The proof indicated in the picture is a simple combinatorial argument. Choose any vertex V with blue degree at least 3 (such a vertex exists...). The edges which join the three vertices adjacent to V cannot be colored blue without producing a blue triangle together with V. Thus, these edges must be red to avoid a blue triangle, thereby producing a red one instead!

Of course, this argument can be generalized. For instance, in order to see that every 3-coloring of a complete 17-gon must produce a monochromatic triangle, pick a vertex of 1-degree at least 6. Take six 1-adjacent vertices; if any two of them are joined by a 1-edge, a monochromatic triangle is found. Otherwise, we have a two-coloring of a complete 6-gon, and the result proved above applies.
Since my good friend Thomas Britz (PhD) is working in combinatorics specializing in Matroid Theory, I have become interested in the subject (at a beginners level).
Because of its philosophical significance, I have taken up an interest in the Four-Colour-Theorem (4CT) and its proofs.

Four colors are required to color this mapThe four color theorem states that it is possible to color the regions of a (sufficiently well-behaved) planar map (the countries in a regular map) using no more than four colors in such a way that two neighbouring regions always have different colors. This result which was conjectured for more than a century was proved in 1973 using extensive computer power. The simple figure on the right shows that three colors do not suffice.

I have developed an interest in the Prime Number Theorem (PNT), and in particular in Atle Selberg's elementary proof of it. In due time, I hope to investigate the proof and its 'elementariness' in order to describe the concern for purity of method in modern mathematics which has many similar ideas through history. Both Selberg and Erdös gave elementary proofs of the PNT, and I would also like to investigate their differences, as well as the motivations of the IMU for awarding Selberg the 1950 Fields Medal for his work (including the PNT).
But I am also very interested in other fields such as harmonic analysis, complex analysis and the theory of Lie groups.
 
And of course I am also interested in fields of current mathematics relating to or reflecting on the history of mathematics that I study. This includes algebraic geometry (which is the current environment for studying elliptic functions), Galois theory (for the study of the theory of equations), and basic mathematical analysis (which gives the framework for my studies in the history of infinite series).
You can find good information on current mathematical topics on the internet. Some of my favorite sites include:
I have uploaded a few simple mathematical papers: