Sign-In
Cart
The Dream of Certainty: Hilbert and the Foundations of Knowledge
Paperback
Please select the version of book you would like to purchase.
ISBN13: 9798171947873
Publisher: Independently Published
Published: Sep 4 2026
Pages: 240
Weight: 0.72
Height: 0.51 Width: 6.00 Depth: 9.00
Language: English
Publisher: Independently Published
Published: Sep 4 2026
Pages: 240
Weight: 0.72
Height: 0.51 Width: 6.00 Depth: 9.00
Language: English
In 1888 a young German mathematician settled a problem that had defeated the best minds of Europe for twenty years. He did it without solving it. He proved that the answer existed, refused to say what it was, and sent the manuscript off with the serenity of a man who has just found a shortcut through a swamp. The greatest expert in the field read it and delivered a verdict that has outlived his own theorems: this is not mathematics, this is theology.
The young man was David Hilbert, and he had just performed the trick that would define him. Faced with a locked room, he did not look for the key. He walked around the outside of the building and came in through a window nobody had noticed was there. He did it again with geometry, insisting that the words point, line, and plane were empty vessels that would work just as well if you called them tables, chairs, and beer mugs. He did it again with the twenty-three problems he laid before the mathematicians of the world in Paris in 1900, a to-do list for the twentieth century that the twentieth century largely obeyed.
And then, in his sixties, he stopped walking around buildings. He demanded that mathematics prove its own consistency using nothing but its own most modest tools, and he staked his reputation and the reputation of his beloved Göttingen on the answer being yes. In September 1930 he told a radio audience that we must know and we shall know. The day before, in a room a few streets away, a quiet young Austrian had explained to an almost empty hall why we shall not.
This is the story of the most ambitious failure in the history of thought, and of what grew out of the wreckage: the computer, the limits of proof, the strange discovery that a system can be perfectly consistent and still contain truths forever out of its own reach. It follows Hilbert from a provincial Prussian schoolroom where his teachers thought him slow, through the golden years when Göttingen was the capital of the mathematical world, to the evening when a Nazi minister asked him how the mathematics institute was faring without its Jews, and he answered that there was no mathematics in Göttingen any more.
It also asks a question Hilbert would have recognized as his own. If a system cannot fully account for itself from the inside, what does that mean for physics, for cosmology, for the confident modern habit of naming things nobody has ever measured? The book carries that question into contemporary research, where a cosmological constant can be derived rather than declared, where an invariant turns out not to tell you what a thing is made of, and where a theorem shows that any consistent physics must contain structure no observer inside it can ever reach. Hilbert asked whether a system can justify itself from within. The answer is no, and the shape of that no is the most useful thing we have learned in a century.
Keywords: Hilbert, mathematics, foundations, certainty, Gödel, philosophy of science, cosmology
And then, in his sixties, he stopped walking around buildings. He demanded that mathematics prove its own consistency using nothing but its own most modest tools, and he staked his reputation and the reputation of his beloved Göttingen on the answer being yes. In September 1930 he told a radio audience that we must know and we shall know. The day before, in a room a few streets away, a quiet young Austrian had explained to an almost empty hall why we shall not.
This is the story of the most ambitious failure in the history of thought, and of what grew out of the wreckage: the computer, the limits of proof, the strange discovery that a system can be perfectly consistent and still contain truths forever out of its own reach. It follows Hilbert from a provincial Prussian schoolroom where his teachers thought him slow, through the golden years when Göttingen was the capital of the mathematical world, to the evening when a Nazi minister asked him how the mathematics institute was faring without its Jews, and he answered that there was no mathematics in Göttingen any more.
It also asks a question Hilbert would have recognized as his own. If a system cannot fully account for itself from the inside, what does that mean for physics, for cosmology, for the confident modern habit of naming things nobody has ever measured? The book carries that question into contemporary research, where a cosmological constant can be derived rather than declared, where an invariant turns out not to tell you what a thing is made of, and where a theorem shows that any consistent physics must contain structure no observer inside it can ever reach. Hilbert asked whether a system can justify itself from within. The answer is no, and the shape of that no is the most useful thing we have learned in a century.
Keywords: Hilbert, mathematics, foundations, certainty, Gödel, philosophy of science, cosmology
Also from
Kriger, Anna
Féminisme Au-Delà de la Colère: Un Avenir Fondé Sur La Solidarité, Pas Sur l'Indignation
Kriger, Anna
Paperback
$27.37
The Brain That Lives Tomorrow: Anokhin, Experience, Predictive Processing, and the Development of Intuition
Kriger, Anna
Paperback
$13.20
When Generosity Becomes a Wound: How Giving Too Much Can Become a Way of Asking to Be Loved
Kriger, Anna
Paperback
$15.60
Le Cerveau Qui Vit Demain: L'Expérience, Le Traitement Prédictif Et Le Développement de l'Intuition
Kriger, Anna
Paperback
$31.50
Also in
Biographies General
Bluesland: Portraits of Thirteen Major American Blues Masters
Pete Welding (ED.)
Toby Byron (ED.)
Hardcover
$11.99
Karl Popper - The Formative Years, 1902 1945: Politics and Philosophy in Interwar Vienna
Hacohen, Malachi Haim
Hardcover
$236.28
The Children of Athena: Greek Intellectuals in the Age of Rome: 150 Bc0-400 AD
Freeman, Charles
Hardcover
$30.40
Make It a Double: From Wretched to Wondrous: Tales of One Woman's Lifelong Discovery of Whisky
Sackier, Shelley
Hardcover
From $12.99
The Code Breaker: Jennifer Doudna, Gene Editing, and the Future of the Human Race
Isaacson, Walter
Hardcover
$12.99
An Enemy Such as This: Larry Casuse and the Fight for Native Liberation in One Family on Two Continents Over Three Centuries
Correia, David
Hardcover
From $12.99
Agents of Chaos: Thomas King Forçade, High Times, and the Paranoid End of the 1970s
Howe, Sean
Hardcover
From $12.99
The Secret Life of the Savoy: Glamour and Intrigue at the World's Most Famous Hotel
Williams, Olivia
Paperback
$17.05
The Badger: The Life of Bernard Hinault and the Legacy of French Cycling
Fotheringham, William
Paperback
$20.89
The Devil's Diary: Alfred Rosenberg and the Stolen Secrets of the Third Reich
Wittman, Robert K.
Kinney, David
Paperback
From $10.99
Florence Kelley and the Nation's Work: The Rise of Womens Political Culture, 1830-1900
Sklar, Kathryn Kish
Paperback
$88.50
The Rise and Fall of Anne Boleyn: Family Politics at the Court of Henry VIII
Warnicke, Retha M.
Paperback
$29.45
A Woman of No Importance: The Untold Story of the American Spy Who Helped Win World War II
Purnell, Sonia
Hardcover
$10.99
Living with a Wild God: A Nonbeliever's Search for the Truth about Everything
Ehrenreich, Barbara
Paperback
$9.99
Seafaring Women: Adventures of Pirate Queens, Female Stowaways, and Sailors' Wives
Cordingly, David
Paperback
$17.10
The Butcher, the Embezzler, and the Fall Guy: A Family Memoir of Scandal and Greed in the Meat Industry
Cherington, Gretchen
Paperback
$17.05
Gift of Power: The Life and Teachings of a Lakota Medicine Man
Erdoes, Richard
Lame Deer, Chief Archie Fire
Paperback
From $8.99
My Own Devices: True Stories from the Road on Music, Science, and Senseless Love
Dessa Wander
Hardcover
$9.99
Nobody's Girl: A Memoir of Surviving Abuse and Fighting for Justice
Giuffre, Virginia Roberts
Hardcover
From $14.99
How to Be Okay When Nothing Is Okay: Tips and Tricks That Kept Me Alive, Happy, and Creative in Spite of Myself
Lawson, Jenny
Hardcover
$26.10
Family of Spies: A World War II Story of Nazi Espionage, Betrayal, and the Secret History Behind Pearl Harbor
Kuehn, Christine
Hardcover
$28.49
Dangerous, Dirty, Violent, and Young: A Fugitive Family in the Revolutionary Underground
Dohrn, Zayd Ayers
Hardcover
$29.69
A Walk in the Park: The True Story of a Spectacular Misadventure in the Grand Canyon
Fedarko, Kevin
Paperback
$19.80
Catch the Devil: A True Story of Murder, Deception, and Injustice on the Gulf Coast
Colloff, Pamela
Hardcover
$28.80
Through Mom's Eyes: Simple Wisdom from Mothers Who Raised Extraordinary Humans
Jones, Sheinelle
Hardcover
$26.10