# The Genius Of the Bernoulli Family

## A family’s mathematical and scientific mastery

Have you ever wondered what it would be like to have a family reunion where everyone’s discussing calculus over dinner? No? Well, neither have I, until I dived into the saga of the Bernoulli family. This isn’t just any family; this is a dynasty of mathematicians whose penchant for numbers reshaped the scientific landscape. But let’s cut through the legend: were they geniuses, or just at the right place at the right time? The family produced eight prominent academics, most notably Jacob, Johann, and Daniel Bernoulli, who were among the pioneers of calculus, differential equations, probability theory, and fluid mechanics. In this article, we will explore the life and work of each member of the Bernoulli family, and how they influenced the development of mathematics and physics during the early modern period.

# Jacob Bernoulli (1654–1705)

Let’s start with Jacob Bernoulli, the family’s opening act in the late 17th century. Jacob, the man who introduced us to the mathematical constant *e*, was clearly a brainiac. His magnum opus, *“Ars Conjectandi,”* was a game-changer in probability theory. Jacob Bernoulli, also known as James or Jacques, was the eldest son of Niklaus Bernoulli, a spice merchant and alderman of Base. He studied theology and philosophy at the University of Basel, but his interest in mathematics was sparked by reading the works of René Descartes and Blaise Pascal. He became a professor of mathematics at the University of Basel in 1687, and corresponded with many leading mathematicians of his time, such as Gottfried Leibniz, Christiaan Huygens, and Guillaume de l’Hôpital.

He is best known for his work on the theory of probability and combinatorics, especially his book *Ars Conjectandi* (The Art of Conjecturing), which was published posthumously in 1713. In this book, he introduced the concept of expected value, the law of large numbers, the Bernoulli distribution, and the Bernoulli trials. He also proved the binomial theorem for any rational exponent, and derived many important formulas and identities involving binomial coefficients, such as the Pascal’s triangle, the Vandermonde identity, and the Chu-Vandermonde identity.

Jacob Bernoulli also made important contributions to the calculus of variations, a branch of mathematics that deals with finding the optimal shape or function that minimizes or maximizes a given quantity. He was the first to pose and solve **the brachistochrone problem**, which asks for the curve of fastest descent between two points under the influence of gravity. He also solved the isoperimetric problem, which asks for the curve of maximum area enclosed by a given length. He coined the term “*lemniscate*” for the figure-eight shaped curve that bears his name, and studied its properties.

Jacob once quipped,

“I recognize the lion by his paw.”

Well, we recognize genius by its brainpower, but was it genius or just Jacob capitalizing on the burgeoning field of mathematics? Jacob died of tuberculosis in 1705, at the age of 50. He was buried in the cloister of the Münster of Basel, where his epitaph reads: “Eadem mutata resurgo”* (I rise again, changed but the same)*. His grave is marked by a lemniscate, symbolizing his mathematical achievements.

# Johann Bernoulli (1667–1748)

Then came Johann, Jacob’s younger brother. Ever lived in the shadow of a brilliant sibling? Johann didn’t just live there; he thrived. While he might have been seen as riding on Jacob’s coattails, he was, in fact, carving his own niche, particularly in the world of calculus. He was the kind of guy who would challenge Leibniz to a math duel via snail mail. Johann Bernoulli, also known as Jean, was the younger brother of Jacob Bernoulli, and the most prolific and influential member of the Bernoulli family. He studied medicine and mathematics at the University of Basel, where he became a professor of mathematics in 1695, succeeding his brother. He also held positions at the University of Groningen, the Academy of Sciences in Paris, and the Imperial Academy of Sciences in St. Petersburg. He was a close friend and collaborator of Gottfried Leibniz, and a fierce rival of Isaac Newton.

Johann Bernoulli was one of the first and foremost proponents of the infinitesimal calculus, which he learned from Leibniz. He threw calculus at everything: particle motion, pendulum swings, the way a chain dangles, and even how light bends. Not to mention, he was a whiz at separation of variables, exponential calculus, and the calculus of finite differences. He discovered the fundamental theorem of calculus — that whole *“derivative of an integral is the integrand”* spiel.

Johann Bernoulli also contributed to the calculus of variations, along with his brother Jacob. He solved the brachistochrone problem independently, and posed and solved* the tautochrone problem*, which asks for the curve along which a particle falls to the lowest point in the same time, regardless of its initial position. He also introduced the Euler-Lagrange equation, which is the main tool for finding the extremals of a functional.

Johann wasn’t just about calculus. He dipped his toes in number theory, geometry, algebra, and analysis. He proved e is irrational, played around with harmonic series, exponential functions, and logarithms. He invented the polar coordinates, and used them to study the curves generated by the motion of a point attached to a rotating arm. He also introduced the concept of the envelope of a family of curves, and the evolute and involute of a curve.

Johann was also a renowned teacher and mentor. He mentored the next-gen math whizzes like Leonhard Euler, Jean le Rond d’Alembert, Pierre Louis Maupertuis, and Joseph Louis Lagrange. Not to mention his sons, Daniel and Johann II, who didn’t fall far from the math tree.

Johann Bernoulli died in 1748, at the age of 80. He was buried in the same cloister as his brother Jacob, where his epitaph reads: **“Archimedes, Newton, and he”** *(Archimedes, Newton, et ille)*.

# Daniel Bernoulli (1700–1782)

And how can we forget Daniel Bernoulli, Johann’s son? You know, the *‘Bernoulli Principle’* guy? His work in fluid dynamics was nothing short of revolutionary. But let’s be honest: was he standing on the shoulders of giants? His *“Hydrodynamica”* wasn’t just a stroke of genius; it was a compilation of a family’s lifelong obsession with numbers.

Daniel Bernoulli was a mathematician and physicist who is best known for his work on fluid dynamics and probability theory. He studied medicine and mathematics at the University of Basel, where he obtained his doctorate in 1721. He also traveled to Italy, France, and Russia, where he met and worked with many eminent scientists, such as Leonhard Euler, Alexis Clairaut, and Christian Goldbach. In 1725, he snagged the role of mathematics professor at the University of St. Petersburg, and by 1733, he was diving into the worlds of anatomy and botany as a professor at the University of Basel.

Daniel is most famous for his book *Hydrodynamica* (Hydrodynamics), which was published in 1738. In this book, he applied the principles of conservation of energy and momentum to the flow of fluids, and derived the equation that bears his name, which relates the pressure, velocity, and height of a fluid in a pipe or a channel. He also explained the phenomenon of the *Venturi effect*, which is the reduction of pressure and increase of velocity of a fluid when it passes through a narrow section of a pipe. He also studied the flow of blood in the human body, and the effect of air resistance on the motion of projectiles.

He also made important contributions to the theory of probability and statistics, especially in relation to the applications of mathematics to social and natural sciences. He developed the concept of *expected utility*, which is a measure of the value of a risky outcome based on the probability of its occurrence and the utility of its consequences. He used this concept to resolve the **St. Petersburg paradox**** ***(which was invented by his own cousin Nicolas Bernoulli)*, which is a problem that involves a game with an infinite expected value, but a finite expected utility. He also introduced the concept of the standard deviation, which is a measure of the dispersion of a set of data around its mean.

Daniel died in 1782, at the age of 82. He was buried in the cloister of the Münster of Basel, near his father and uncle. His epitaph reads: **“He was the greatest of the Bernoullis”*** (Ille fuit maximus Bernoulliorum)*.

## Other members of the Bernoulli family

Nicolaus Bernoulli, another family star, often gets overshadowed. But his contributions to probability and statistics were significant. His exchange with Pierre Rémond de Montmort on probability was more than just scholarly banter; it was the intellectual equivalent of a fencing match.

As the 18th century rolled on, the family’s mathematical flame didn’t flicker. Johann II, Daniel II, Johann III — the sequels kept coming. But here’s the kicker: were they innovating, or just iterating?

Reflecting on this, one can’t help but wonder: was the Bernoulli family’s success a product of sheer genius, or were they just riding the wave of the scientific revolution? Did they shape the course of mathematical history, or were they simply at the right place in the right chronological order? It’s easy to get lost in the romanticism of a family of geniuses pushing the boundaries of science. But maybe, just maybe, the Bernoullis were a product of their time — a perfect storm of opportunity, intellect, and yes, a bit of familial competition.

In the end, whether they were geniuses or just incredibly well-positioned, the Bernoullis left an indelible mark on science. Their story isn’t just about formulas and theorems; it’s about ambition, rivalry, and the relentless pursuit of knowledge. And perhaps, that’s the real genius of the Bernoulli saga.

*References:*

Bernoulli, Jakob I. “THE BERNOULLI FAMILY.” *The 17th and 18th Centuries: Dictionary of World Biography, Volume 4* 4 (2013): 122.

Eves, Howard. “Historically Speaking — : The Bernoulli Family.” *The Mathematics Teacher* 59.3 (1966): 276–278.

Senn, Stephen. “Bernoulli family.” *Encyclopedia of Statistics in Behavioral Science* (2005).

Thank you so much for reading. If you liked this story don’t forget** to press that clap icon as many times as you want.**

*If you like my work and want to support me then you can*

**Buy me a coffee**☕️. Keep following for more such stories!