Cramer’s rule provides a general formula for solving linear equation systems with a unique solution using determinants, remaining a standard tool in linear algebra today. This contribution emerged during a career defined by the rigorous advancement of mathematical analysis within the Republic of Geneva, where the subject operated under the evolving influence of eighteenth-century scientific discourse.
Academic Career at Geneva
Born in 1704, Cramer remained deeply embedded in the intellectual life of his home city. He earned his doctorate from the University of Geneva by 1722. By the age of twenty, he secured a co-chair position for mathematics at the university. He transitioned to the sole professorship of mathematics in 1734 and eventually accepted a professorship of philosophy at the institution in 1750. Beyond his university appointments, he participated in local governance, serving on the Council of Two Hundred beginning in 1734 and the Council of Sixty by 1750.
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Cramer published his most influential work, a treatise on algebraic curves, in 1750. This text provided the first demonstration that a curve of the n-th degree is determined by n(n + 3)/2 points. His research also introduced Cramer’s paradox, which emerged from investigations into the intersections of curves. In 1728, he proposed a solution to the St. Petersburg Paradox, anticipating elements of expected utility theory. Additionally, he edited the works of the Bernoulli family and published analysis on Newton’s treatment of cubic curves in 1746.
Physics and International Recognition
Though primarily remembered for his mathematical output, Cramer applied his expertise to physical problems. In 1730, he authored research regarding the spheroidal shape of planets and the motion of their apsides. His scientific standing earned him entry into several international bodies, including the Royal Prussian Academy of Sciences and the Academy of Sciences of the Institute of Bologna. In 1749, he attained the status of Fellow of the Royal Society. His life concluded on 4 January 1752 in Bagnols-sur-Cèze, where he had traveled to seek medical recovery.
Fast facts
- Born: 1704, Geneva
- Died: 1752, Bagnols-sur-Cèze
- Citizenship: Republic of Geneva
- Education: University of Geneva
- Primary Employer: University of Geneva (1724-1751)
- Notable Recognition: Fellow of the Royal Society (1749)
- Religion: Reformed
- Language: French
Questions readers ask
What is Cramer's rule?
It is a formula used to solve linear equation systems that have a unique solution by utilizing determinants.
What was Cramer's professional focus?
He worked as a mathematician, physicist, and university teacher, specializing in the field of analysis.
Achievements
- Fellow of the Royal Society — 1749
- Notable work: Cramer's rule
- Notable work: Cramer-Castillon's problem
- Notable work: Cramer's paradox
- Held posts at University of Geneva
- Fields: mathematics and physics
