A Miraculous Mistake
In the cloister of Basel's Peterskirche (St. Peter's Church), an epitaph commemorates the life of Jacob Bernoulli, who died on August 16, 1705. Bernoulli, a towering figure in the history of mathematics, liked the properties of the logarithmic spiral. He dubbed it the Spira mirabilis—the "miraculous spiral"—due to its unique characteristic of self-similarity. As the spiral grows, its shape remains unchanged with each turn. This mathematical constancy fascinated Bernoulli so much that he requested it be carved on his tombstone.
He paired the spiral with the Latin motto Eadem mutata resurgo, which translates to "Though changed, I rise again the same". The phrase was a double-entendre, referring both to the spiral's ability to retain its form as it expands and to his own hope for the resurrection of the body. However, a stonemason, unfamiliar with the subtleties of geometry, made a significant error. Instead of the requested logarithmic spiral, an Archimedean spiral was carved into the stone. The two are visually distinct: the turnings of an Archimedean spiral have a constant separation, whereas the distance between the turns of a logarithmic spiral increases in a geometric progression. The very symbol of mathematical constancy was rendered incorrectly for eternity.
A Dynasty of Thinkers
The memorial at Peterskirche is for Jacob and others. The outer walls of the church bear epitaphs for other members of this extraordinary family, including his younger brother Johann I and Johann's son, Daniel Bernoulli. The Bernoullis were a Basel dynasty that produced at least eight distinguished mathematicians and scientists in three generations.
Their family life was often marked by intense intellectual rivalry. Jacob and Johann famously feuded, posing complex mathematical problems to challenge and sometimes humiliate one another in the European academic community. This competitive spirit continued into the next generation, with Johann later competing fiercely with his own son, Daniel. Daniel Bernoulli is now best known for the Bernoulli Principle in fluid dynamics, a fundamental concept in physics and engineering. The collection of memorials at Peterskirche is the final resting place of a family whose contributions fundamentally shaped calculus, probability theory, and mathematical physics.