Daniel Bernoulli was the son of Johann Bernoulli, a mathematician, and his brother Nicolaus and his uncle Jacob were also mathematicians. Daniel was sent to Basel University at the age of 13 to study philosophy and logic. Daniel really wanted to study mathematics, and during his time there he was learning calculus from his father and his older brother. His father insisted he take up a trade and sent Daniel back to Basel University to study medicine. Daniel completed his doctorate in medicine in 1720, writing his doctoral dissertation on the mechanics of breathing.

Failing to obtain an academic post, Daniel went to Venice to study practical medicine.
There he worked on mathematics, and with Goldbach's assistance, published his first mathematical work *Mathematical Exercises*, in 4 parts. The first part described faro, a game of chance. The second part was on the flow of water from a hole in a container. The third part was on the Riccati differential equation, while the final part was on a geometry question concerning figures bounded by two arcs of a circle. Daniel attained fame due to *Mathematical Exercises*, and consequently he and his brother were offered mathematics positions in St. Petersburg in 1725.

Soon after they arrived, his brother Nicolaus died of fever. To cheer him up, Johann Bernoulli sent one of his pupils, Leonard Euler, to St. Petersburg to work with Daniel in 1727. This time was very productive for the both of them. He studied vibrating systems, showing that the movements of strings of musical instruments are composed of an infinite number of harmonic vibrations all superimposed on the string. He also produced an important work on probability and political economy.

Undoubtedly the most important work which Daniel Bernoulli did while in St Petersburg was his work on hydrodynamics, a term he invented. This work contains for the first time the correct analysis of water flowing from a hole in a container. This was based on the principle of conservation of energy which he had studied with his father in 1720. Daniel also discussed pumps and other machines to raise water. He also discussed the basis for the kinetic theory of gases. He was able to give the basic laws for the theory of gases and gave the equation of state discovered by Van der Waals a century later.

Daniel returned to Europe and lectured on botany from 1733 to 1743. In 1734, Daniel Bernoulli submitted an entry for the Grand Prize of the Paris Academy giving an application of his ideas to astronomy. He and his father were declared joint winners of the Grand Prize. As a result, his father was furious to think that his son was considered his equal, and banned him from his house.

Meanwhile, Daniel and Euler continued to correspond. Euler used his great analytic skills to put many of Daniel's physical insights into a rigorous mathematical form. Daniel continued to work on his hydrodynamics book, and it was published in 1738. In 1743, he began lecturing on physiology. In 1750, he was appointed to the chair of physics and taught physics at Basel for 26 years until 1776. He gave some remarkable physics lectures with experiments performed during the lectures. Based on experimental evidence he was able to conjecture certain laws which were not verified until many years later. Among these was Coulomb's law in electrostatics.

Daniel Bernoulli did produce other excellent scientific work during these many years back in Basel. In total he won the Grand Prize of the Paris Academy 10 times, for topics in astronomy and nautical topics. He won in 1737 for work on the best shape for a ships's anchor; 1740 (jointly with Euler) for work on Newton's theory of the tides; in 1743 and 1746 for essays on magnetism; in 1747 for a method to determine time at sea; in 1751 for an essay on ocean currents; in 1753 for the effects of forces on ships; and in 1757 for proposals to reduce the pitching and tossing of a ship in high seas.

Another important aspect of Daniel Bernoulli's work that proved important in the development of mathematical physics was his acceptance of many of Newton's theories. Daniel worked on mechanics and used the principle of conservation of energy which gave an integral of Newton's basic equations. He also studied the movement of bodies in a resisting medium using Newton's methods. He also continued to produce good work on the theory of oscillations and in a paper he gave a beautiful account of the oscillation of air in organ pipes.

Daniel Bernoulli was much honoured in his own lifetime. He was elected to most of he leading scientific societies of his day including those in Bologna, St. Petersburg, Berlin, Paris, London, Bern, Turin, Zurich and Mannheim.