The problems arena
The world's questions stand beside seven challenges issued by the book. An attempt earns a place in the ledger; verification stays rare and visible.
Choose a problem at the desk| No. | Problem | The question | Status | Source |
|---|
The world's open questions
Each page holds its question, the attempt cards attached to it, and a solutions area that stays ready for a checked proof or witness.
The book's own problems
These problems belong to the book. The difficulty claims are the book's. If a house problem turns out to have been solved before, the ledger records the source and the problem retires with honors.
Margin notes
Each quarrel stays close to its mathematics, with the ending stated as cleanly as the record allows.
x³ + px = q
Tartaglia guarded a cubic solution as a sworn secret and shared it with Cardano under a promise of silence. Cardano printed the method in Ars Magna after learning that del Ferro had found it earlier. The oath was broken in print, and the credit is shared among the discoverers and the algebra that carried the result.
x = a(t − sin t), y = a(1 − cos t)
Johann Bernoulli posted the brachistochrone as a public challenge, asking for the curve of quickest descent under gravity. Both Bernoulli brothers answered, and Newton is said to have solved it overnight after the challenge reached him. The winning curve is a cycloid, while the overnight story survives as a reported episode rather than a timed record.
dy/dx versus fluxions
Newton developed fluxions and Leibniz published the notation dy/dx, with independent calculus programs taking shape in the seventeenth century. A priority dispute turned their followers into rival camps and burdened British mathematics for decades. The modern record recognizes both as independent founders, while the dispute never produced a single uncontested victor.
x⁴ → x³ resolvent
Ferrari's quartic method reduces a general fourth-degree equation to a cubic resolvent. The surviving letters document Ferrari's contest with Tartaglia, while del Ferro's heirs belong to the earlier guarded story Cardano inherited. The record does not show a direct Ferrari-versus-del-Ferro-heirs duel; the solution entered print in Cardano's Ars Magna.
Attempts, not trophies
Each attempt records a name, a date, a link, and the exact claim. The status ladder runs from attempted → under review → verified, or withdrawn. A published peer-reviewed result or a checked formal proof is the only path to verified.