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Suggested Citation:"Epilogue." John Derbyshire. 2003. Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics. Washington, DC: Joseph Henry Press. doi: 10.17226/10532.
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EPILOGUE

Bernhard Riemann died on Friday, July 20, 1866, a few weeks short of his 40th birthday. He had caught a heavy cold in the fall of 1862, and this had accelerated the tuberculosis from which he had probably suffered since childhood.138 The efforts of Göttingen colleagues had secured a series of government grants to enable Riemann to travel to a better climate, this being the only way known for a TB sufferer to obtain relief from the disease and slow its progress.

Thus, Riemann’s last four years had been spent almost entirely in Italy. When he died he was staying in Selasca, on the western shore of Lago Maggiore in the Piedmontese Alps. His wife, Elise, and their three-year-old daughter, Ida, were with him. Richard Dedekind recorded the event in the brief biography of his friend that he appended to the Collected Works.

On June 28 he arrived at Lago Maggiore, where he lived at the Villa Pisoni in Selasca, near Intra.139 Swiftly his strength ebbed away, and he himself perceived with full clarity that his end was approaching. Still, on the day before his death, resting in the shade of a fig tree, full of joy at the beautiful scenery laid out before him, he was at

Suggested Citation:"Epilogue." John Derbyshire. 2003. Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics. Washington, DC: Joseph Henry Press. doi: 10.17226/10532.
×

work on those papers that, sad to say, he left unfinished. His end was very peaceful, with no struggle or death-spasm. It seemed as though he watched with interest the separation of the soul from the body. His wife brought bread and wine to him. He asked her to take his greetings to those at home, and said to her: “Kiss our child.” She recited the Lord’s Prayer for him, but he himself could no longer speak. At the words “forgive us our trespasses” he directed his eyes devoutly upward. She felt his hand become colder in hers, and after a few breaths his pure, noble heart ceased beating. That pious sense that was planted in him under his father’s roof, stayed with him all his life, and he served God faithfully, in his own way. With devotion of the highest kind, he never interfered with the faith of others: the main thing in religion was, in his opinion, daily self-examination before the face of God.

He rests in the churchyard of Biganzolo, in the parish of Selasca. His gravestone carries the inscription:

HERE RESTS IN GOD

GEORG FRIEDRICH BERNHARD RIEMANN

PROFESSOR AT GÖTTINGEN

BORN IN BRESELENZ, SEPT. 17, 1826

DIED IN SELASCA, JULY 20, 1866

ALL THINGS WORK TOGETHER FOR GOOD TO THEM THAT LOVE GOD

The inscription is all in German. The epitaph is from St. Paul’s epistle to the Romans, 8:28. (In German, Denen die Gott lieben müssen alle Dinge zum Besten dienen.) Riemann’s grave site no longer exists. It was destroyed in a later reorganization of the church property. The inscribed stone survived, though, and has been set in a nearby wall.

Elise Riemann returned to Göttingen with her daughter. They lived there with Bernhard Riemann’s one surviving sister, also named Ida, at Weender Chaussee 17. The next door house, No. 17A, was occupied by Hermann Schwartz, a professor of mathematics at the Uni-

Suggested Citation:"Epilogue." John Derbyshire. 2003. Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics. Washington, DC: Joseph Henry Press. doi: 10.17226/10532.
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versity.140 Riemann’s chair at the University was taken by Alfred Clebsch, who wrote the founding text of modern algebraic geometry.

In 1884, Riemann’s daughter Ida, then 20 years old, married Carl David Schilling, who had taken his doctor’s degree under Schwartz in 1880 and remained friendly with him. Soon after this, Schilling took up a position as director of the marine academy in Bremen. In September 1890, Riemann’s widow and his sister went to live with the Schillings in Bremen. Riemann’s daughter lived until 1929, her husband until 1932. They seem to have produced a large family, but the precise number of their children has eluded me. The descendants of Bernhard Riemann are, at any rate, now merged into the general mass of humanity.

Few as were the years of work allotted to him, and few as are the printed pages covered by the record of his researches, his name is, and will remain, a household word among mathematicians. Most of his memoirs are masterpieces—full of original methods, profound ideas and far-reaching imagination.

—George Chrystal, from the article headed “Riemann” in the 1911 Encyclopœdia Britannica

Suggested Citation:"Epilogue." John Derbyshire. 2003. Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics. Washington, DC: Joseph Henry Press. doi: 10.17226/10532.
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Suggested Citation:"Epilogue." John Derbyshire. 2003. Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics. Washington, DC: Joseph Henry Press. doi: 10.17226/10532.
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Page 363
Suggested Citation:"Epilogue." John Derbyshire. 2003. Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics. Washington, DC: Joseph Henry Press. doi: 10.17226/10532.
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Page 364
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In August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: "On the Number of Prime Numbers Less Than a Given Quantity." In the middle of that paper, Riemann made an incidental remark — a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false?

Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic — defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark — the Riemann Hypothesis — that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows — subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age.

It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many — the veritable "great white whale" of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution.

Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, the Riemann Hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof — and those who have been consumed by it.

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