Bernhard Riemann was an outstanding German mathematician, who made an invaluable contribution to the development of science.
Childhood and early years
Riemann was born in Brzezelenz, a village in the vicinity of Dannenberg in the Kingdom of Hanover. Friedrich Bernhard Riemann, his father, was a poor Lutheran priest who took part in the Napoleonic wars. His mother, Charlotte Ebell, died early. Bernhard was the second of six children in the family. From an early age, the boy showed amazing mathematical abilities and incredible success in the account, but he was shy and suffered many nervous breakdowns. He was a pathologically timid person and suffered from fear of public speaking.
In high school, Riemann diligently studies the Bible, but he invariably draws on mathematics. Teachers were impressed by his ability to solve complex mathematical problems, in which, often, he surpasses his teachers.
In 1846, at the age of 19, Riemann began to study theology and philology, intending to become a priest, but his teacher Gauss, shocked by the young man’s abilities to mathematics, strongly advises him to abandon the theological path and concentrate his efforts on exact sciences.
In 1854, his first lecture was held, which outlined the region of the geometry of Riemann, underlying the general theory of relativity of Einstein. In 1857, at the University of Göttingen, attempts were made to confer on the scientist a special professorial title. And, although the attempts do not end in success, they open up a prospect for stable earnings before Riemann. In 1859, all in the same Göttingen, Riemann was promoted to the head of the department of mathematics, and in the same year he was elected a corresponding member of the Berlin Academy of Sciences. The newly-minted Corresponding Member presents to the Academy his report “Determination of the number of prime numbers smaller than a given value”, which will become the key in the development of number theory. Riemann is also one of the first to apply the measurement system above three – and four-dimensional measurements to explain physical reality.
In 1866, as a result of the clash between the armies of Prussia and Hanover during the Austro-Prussian War, Riemann was forced to flee from Göttingen.
The contribution of Riemann
Innovative works of Riemann laid the foundation of modern mathematics and various research fields, including mathematical analysis and geometry. His work has found application in the theories of algebraic geometry, Riemann geometry and the theory of complex manifolds. Adolf Hurwitz and Felix Klein have expounded the theory of Riemann surfaces. This aspect of mathematical knowledge is the basis of topology, and to this day is widely used in modern... mathematical physics. Riemann also made a series of pivotal discoveries in the theory of “real analysis.” He introduced the “Riemann integral”, found by means of “Riemann sums”, and derived a theory of trigonometric series that is different from the Fourier series, the first step on the path to the theory of generalized functions, and also defined the “Riemann-Liouville di erentintegral”.
He did a lot for the development of modern analytic number theory. He introduced the “Riemann zeta function” and explained its significance for understanding the distribution of primes. He also put forward a number of assumptions about the properties of the zeta function, one of which are the famous “Riemann hypotheses.” His works inspired the work of Charles Lutwijd Dodgson, better known as Lewis Carroll, a mathematician who wrote popular books “Alice in Wonderland” and “Alice in the Looking-Glass”.
Geometry of Riemann
The mentor of Riemann, Gauss, in 1853 advises him to write “Habilitationsschrift” on the fundamentals of geometry. After several months of work, Riemann puts forward his own theory of multidimensional spaces and in 1854 he reads in Göttingen a lecture known as “Über die Hypothesen welche der Geometrie zu Grunde liegen”. It was published in 1868, that is, two years after the forced flight of Riemann from his native city, and produces a furore in the world of mathematics. The theory was recognized as one of the most significant achievements in geometry.
The concept of multidimensional spaces
Riemann worked on obtaining a multidimensional table of numbers at any point in space, with the help of which one can analyze the degree of its bending and curvature. In the end, Riemann comes to the conclusion that in a four-dimensional space, no matter how distorted, a multidimensional table of ten numbers is needed to determine the properties of its set. This becomes one of the important foundations of geometry, known as the “Riemann metric”.
In June 1862 Riemann married Eliza Koch. The daughter who was born in the family was their only child.
Death and heritage
In the autumn of 1866, Riemann picked up a severe cold, which had developed into an incurable form of tuberculosis. This happens during the journey of Riemann with his wife and three-year-old daughter in Italy. The scientist has only a few weeks to live. Riemann was buried in the cemetery of Bigansolo. Soon, in Göttingen, in his house, the maid will take up putting in order. Among the garbage, it will throw out and several unreleased works of the scientist. Riemann never allowed to publish his unfinished works, and therefore some of the most valuable mathematical knowledge can be lost for us forever.