A Statesman with a Mathematician’s Mind
Johan de Witt is remembered as a political leader, but before he ever entered government, he was a prodigy in mathematics. Educated at Leiden University, he excelled in both law and math, moving in circles that included prominent scholars like Frans van Schooten.
In his early twenties, he wrote a work that would quietly shape the way curves — and later, financial risks — were understood.
Drawing Curves with Algebra
In 1646, at just 23, De Witt composed Elementa Curvarum Linearum, later published in 1661 in the second volume of van Schooten’s Latin translation of René Descartes’ La Géométrie.
This text, often called the first textbook in analytic geometry, took geometric shapes and described them using algebraic equations. De Witt focused on conic sections — curves like ellipses, parabolas and hyperbolas, formed by slicing a cone.
Earlier thinkers such as Archimedes, Proclus and his contemporary Claude Mydorge had described these curves kinematically, by imagining moving lines and angles. De Witt advanced this tradition:
- He described the hyperbola using a rotating line and a sliding angle.
- He described the parabola with a rotating angle and a sliding line.
In the second book of his treatise, he systematically applied the new analytic methods of Descartes and Pierre de Fermat, giving what is considered the first fully systematic treatment of conic sections using algebra.
Both Fermat and Descartes had reached similar conclusions, but De Witt supplied a crucial missing element: the detailed steps to solve the locus problem for quadratic equations — essentially, determining all the points that satisfy a given algebraic condition.
Turning Math into Money
His mathematical talents did not remain in the classroom. As a senior statesman in a small, capital-hungry republic, De Witt turned his analytic skills to a pressing practical problem: how to value government debts.
In his work “The Worth of Life Annuities Compared to Redemption Bonds”, he compared two financial instruments used by the state:
- Life annuities, where someone paid a lump sum up front in exchange for a regular income until death.
- Redemption bonds, more like ordinary state loans, paying a fixed interest.
Using early probabilistic reasoning, De Witt calculated that a bond yielding 4% produced roughly the same profit as a life annuity paying 6% (a rate of 1 in 17). Yet the Dutch States at the time were paying over 7% (1 in 14) on life annuities.
In other words, the state was overpaying for risk.
This analysis — later discussed in correspondence between Leibniz and Bernoulli — is regarded as one of the first applications of probability in economics. It showed how mathematical thinking could be used not just to trace elegant curves, but to weigh life, death and public finance on the same analytic scales.
A Mind Ahead of Its Time
By uniting geometry and government bonds in the same career, De Witt foreshadowed entire modern fields: actuarial science, financial mathematics, and quantitative economics.
He died violently in a political storm, but the quiet calculations he made about curves and annuities pointed toward a future where numbers would rule markets as surely as princes once ruled states.
