Bernhard Riemann - Студенческий научный форум

XI Международная студенческая научная конференция Студенческий научный форум - 2019

Bernhard Riemann

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Bernhard Riemann made profound, far-sighted discoveries with lasting consequences for mathematics and our understanding of space, gravity, and time.

Riemannian geometry completely reformed the field of geometry and became the mathematical foundation of Einstein’s general theory of relativity.

Finding a proof or disproof of the Riemann hypothesis continues to be the greatest, deepest, unsolved problem in number theory – the search for a solution has become the holy grail of mathematics.

Another of Riemann’s innovations, Riemann surfaces, made a strong link between topology and complex function theory.

Riemann was the first person to rigorously define the integral.

Beginnings

Georg Friedrich Bernhard Riemann was born on September 17, 1826 in the rural village of Breselenz, in northern Germany. He was the second of his parents’ six children.

His mother was Charlotte Ebell, the daughter of a government employee in the city of Hanover. His father was Friedrich Bernhard Riemann, a Lutheran pastor.

Life was harsh for the family – they lived in near poverty. In accordance with Lutheran practice, a solemn mood pervaded the home at all times. Although it was austere, Bernhard’s home was also loving and caring.

The threat of death from tuberculosis was present in the very air the family breathed. Their diet and nutrition was poor and young Bernhard was plagued with persistent constipation. Although his brother and his four sisters reached adulthood, they all, except for his sister Ida, died at relatively young ages.

Homeschool

Bernhard grew up 10 miles from Breselenz in the tiny village of Quickborn, where his father became the pastor when Bernhard was a toddler.

Bernhard’s parents believed the most important thing they could give their children was a solid education. Bernhard attended some classes in the village school, but most of his education came from homeschooling with his father.

In his earliest years Bernhard was interested in history, particularly ancient history. But it was always clear that this stuttering, painfully shy boy had one exceptional talent: mathematics. His father enlisted a local teacher by the name of Schultz to teach 10-year-old Bernhard arithmetic and geometry, but soon Bernhard was teaching his teacher!

Homesick at High School

In the spring of 1840, age 13, Bernhard was sent to live with his maternal grandmother in the city of Hanover. There he attended the Tertia des Lyceums Gymnasium, a school whose students were expected to go to college.

Bernhard was behind his classmates in most subjects, and he suffered terribly from homesickness. Hanover was about 90 miles from Quickborn – too far for him to travel home to see his cherished family. Despite his homesickness, he worked hard and made good progress academically.

Johanneum Gymnasium as it looked when Bernhard Riemann attended it.

Bernhard’s grandmother died two years after Bernhard arrived in Hanover to live with her.

Bernhard moved again, this time to the Johanneum Gymnasium in the small city of Lüneburg.

Lüneburg was about 45 miles from Quickborn, close enough for him to walk home for vacations. These treks strained his frail body badly, but knowing he could get home to Quickborn took the edge off his appalling homesickness. His mother agonized over his safety and health when he was on the road.

Mathematical Genius to Serve God

More than half of Bernhard’s school day was devoted to Latin, Greek, Hebrew, and German, but Mathematics formed a significant part of his curriculum: his ability in this subject was outstanding.

One of his teachers, Herr Schmalfuss, recognized Bernhard’s flair and began lending him advanced college-level mathematics texts, including works by Leonhard Euler and Adrien-Marie Legendre. The first time he did this, Herr Schmalfuss was astonished when Bernhard, after just a few days, returned the book to him. He questioned Bernhard about the book’s themes, and it became clear that his student truly had read and understood mathematical material that a typical advanced college student would have taken weeks or months to absorb.

In addition to his love of mathematics, Bernhard was also passionate about his religion. A devout Lutheran, he decided to study Theology and Philology at the University of Göttingen, hoping to follow in his father’s footsteps and become a pastor.

This was a curious decision, because Bernhard was introverted, terrified of public speaking, and generally uncomfortable around people. On the other hand, his father was his hero, and trying to emulate his hero was probably instinctive.

Interestingly, Leonhard Euler was also the son of a Protestant pastor and also seemed destined to join the clergy.

Mathematics Chair, Marriage, and Ill Health
In 1859, Göttingen’s chair of mathematics, Lejeune Dirichlet, died. He was replaced by Riemann, who was 32 years old.

In 1862, Riemann found the courage to propose marriage to 27-year-old Elise Koch, one of his sister’s friends. Elise accepted, and they had one daughter, Ida, born in 1863.

A month after his wedding, Riemann suffered an attack of pleurisy, a painful inflammation of the lungs that, among other things, can be caused by tuberculosis.

An Italian Finale
In his final years, Riemann made several trips to Italy, where the milder climate eased his tuberculosis. Indeed, his daughter Ida was born in Pisa. Riemann enjoyed life in Italy; he loved the artworks he saw there, and he felt more carefree and relaxed than he did in Göttingen.

On his final day of life, he knew the end was near. He sat under a fig tree, working on mathematics, and enjoying the view. His Christian faith remained strong to the end. He died just after saying, “forgive us our debts,” while he and his wife Elise recited the Lord’s Prayer together.

Bernhard Riemann died, age 39, of tuberculosis on July 20, 1866 in Selasca, Italy. He was buried in Selasca.

His friend Richard Dedekind collected Riemann’s surviving papers and published them in 1868, bringing most of Riemann’s work to a wider audience for the first time. Sadly, however, much of Riemann’s research never came to light, because a cleaner, unaware of its importance, burned it shortly after his death.

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