Bernhard Riemann

Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse

In this short paper, his only paper on number theory, and possibly the most famous paper in the whole of mathematics, Bernhard Riemann outlined in 1859 a method for proving the Prime Number Theorem.  In the paper he defined what is now referred to as the Riemann Zeta Function and made an hypothesis about the location of its zeros that is sometimes referred to as the most significant unsolved problem in mathematics.

The paper may be found at pages 136 to 144 of his collected works (see separate page for link).  Links to an English translation and also to a copy of Riemann’s original handwritten manuscript can be found at this page on the Clay Mathematics Institute website.

Ferdinand Lindemann

Ueber die Zahl π

Lindemann’s proof that pi is transcendental appeared in volume 20 of Mathematische Annalen at pages 213-225 in 1882.  See journals page for a link to the journal.

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