Last week on 17th September (1826) we celebrated Bertrand Riemann’s birthday. This is one of those mathematicians I have encountered so much during my study from high-school to university. I was always mesmerized by how many hard and interesting things he has accomplished during his life. I believe that reading about his life is an incredible experience and sometimes I think about how exactly was he outside mathematics.
Georg Friedrich Bernhard Riemann was an influential German mathematician who made lasting and revolutionary contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rigorous formulation of the integral, the Riemann integral, and his work on Fourier series. His contributions to complex analysis include most notably the introduction of Riemann surfaces, breaking new ground in a natural, geometric treatment of complex analysis. The mathematics behind these is not ‘piece of cake’ and this makes everything more mysterious and interesting. If you want to give it a try, the book An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces (Theoretical and Mathematical Physics) is a good ( but complex ) idea. To give color to this theory, here are some examples of Riemann surfaces:
1st is for arsin(z), then log(z) and the last one for z^(1/2)
His famous 1859 paper on the prime-counting function containing the original statement of the Riemann hypothesis, is regarded, although it’s his only paper in the field, as one of the most influential papers in analytic number theory. Riemann hypothesis is one of those unsolved problems that most of mathematicians talk. The hypothesis implies results about the distribution of prime numbers. Along with suitable generalizations, some mathematicians consider it the most important unresolved problem in pure mathematics (Bombieri 2000). The Riemann hypothesis, along with Goldbach’s conjecture, is part of Hilbert’s eighth problem in David Hilbert’s list of 23 unsolved problems; it is also one of the Clay Mathematics Institute’s Millennium Prize Problems. If you want to read more, the book Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics should be on your list.
Moreover, through his (along with his Göttingen colleague and mentor Gauss) pioneering contributions to differential geometry, Riemann laid the foundations of the mathematics of general relativity.
I hope you found this article interesting and that you will find some time to find out more about this great mathematician. Thank you for your help and support. You can find me on Facebook, Tumblr, Google+, Twitter, Instagram and Lettrs, I will try to post there as often as possible. Don’t forget that maths is everywhere! Enjoy!