#foundations of geometry

[mirtitles]

Hilbert's Fourth Problem by A. V. Pogorelov

Hilbert’s fourth problem, which involves finding all geometries where “ordinary lines” are “geodesics,” is both accessible and profound. While the problem can be appreciated by beginning graduate students, its solution requires tools from various branches of mathematics, including geometry, analysis, and the calculus of variations. A partial solution was provided by Georg Hamel in 1901. Later, A.…

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[pythagorag]

Most Satisfying Part of my Major:

After 4 hours finally finding what the simple 3x3 reflection matrix you need is.