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Georg Friedrich Bernhard Riemann
  1826 - 1866
 

Georg Friedrich Bernhard Riemann was a profoundly original thinker. In the span of a very brief life, he left us with a host of methods, theorems and concepts named after him, including the still unproven Riemann hypothesis.

Riemann's portrait includes graphical representations of some of Riemann's most complex concepts.

Riemann surfaces, an instance of one overlaying the lower right of Riemann's portrait, are a Riemann invention arising from multi-valued functions -- a not uncommon conundrum in mathematics. They resolve problems in which, essentially, two different values of 'y' correspond to the same 'x', as can often arise in complex operations, and even in relatively simple square root operations and logarithm.  Riemann essentially increased the number of 'x's", so that there were enough for each possible y. The solution is not only ingenious, but after-the-fact, it is seems somewhat obvious -- the mark of true insight.

Pictured over Riemann's shoulder is another, and quite different depiction of this very versatile tool, the Riemann surface.

In his 1859 paper On the Number of Primes Less Than a Given Magnitude, Reimann dealt with a formula for the identification and track the occurrence of prime numbers ( a prime number being one which has no factor except itsef and 1).   Prime numbers not only have an almost mystical fascination, but seem to hold the keys to many perplexing riddles.

Riemann examined the properties of the Zeta function, (inscribed at the lower left of Riemann's portrait).  And he advanced a riddle of his own, the Riemann hypothesis, essentially positing that the Zeta function has infinitely many non-trivial roots, with the vast majority of the roots lying between 0 and 1. This still unproven hypothesis remains of the most important, and beguiling, unresolved problems in mathematics.

(And if you study the portrait for a moment, you may notice in the upper left hand area a "skewed" rectangular area which hasn't fully "shifted" into place -- an homage to the still unresolved Riemann hypothesis!).

 
 
 
 
       
 
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