Bernoullis

Bernoullis refers to the Bernoulli family, a prominent Swiss clan of mathematicians and scientists from Basel, active in the 17th and 18th centuries. Over several generations they produced leading figures in probability, calculus and fluid mechanics, helping to shape early modern applied mathematics.

Jakob Bernoulli (1654–1705) and his brother Johann Bernoulli (1667–1748) were central early members. Jakob's Ars Conjectandi (1713, published after his death) laid foundations for probability theory, introducing ideas such as Bernoulli trials, the Bernoulli distribution, and what would later be called the law of large numbers; he also wrote on mathematical series and probabilities.

Johann Bernoulli, a renowned teacher and mathematician, advanced calculus and mechanics and mentored a generation of scholars, including Leonhard Euler. He helped propagate analytic methods in physics and mathematics across Europe and fostered a culture of rigorous problem solving.

Daniel Bernoulli (1700–1782), son of Johann, is known for Hydrodynamica (1738) and for Bernoulli's principle, which relates fluid speed to pressure in moving streams. His work linked mathematics with physical intuition and engineering applications, illustrating the power of mathematical modeling in natural phenomena.

Together the Bernoullis contributed to the growth of probability theory, calculus, and fluid dynamics, and helped establish Basel as a center of mathematical science in early modern Europe. Their interdisciplinary legacy continues to influence mathematics, physics, and engineering.