**Daniel Bernoulli** was a Dutch-born member of the Swiss mathematical family. His most important work considered the basic properties of fluid flow, pressure, density and velocity, and gave the *Bernoulli principle*.

- All three sons would go on to study mathematics but this was not the course that Johann Bernoulli planned for Daniel.
- First however Daniel was sent to Basel University at the age of 13 to study philosophy and logic.
- Johann was determined that Daniel should become a merchant and he tried to place him in an apprenticeship.
- Johann declared that there was no money in mathematics and so he sent Daniel back to Basel University to study medicine.
- This Daniel did spending time studying medicine at Heidelberg in 1718 and Strasbourg in 1719.
- The next chair to fall vacant at Basel that Daniel applied for was the chair of logic, but again the game of chance of the final selection by drawing of lots went against him.
- Having failed to obtain an academic post, Daniel went to Venice to study practical medicine.
- In Venice Daniel was severely ill and so was unable to carry out his intention of travelling to Padua to further his medical studies.
- The first part described the game of faro and is of little importance other than showing that Daniel was learning about probability at this time.
- Daniel had not solved the problem of pressure by this time but again the work shows that his interest was moving in this direction.
- While in Venice, Daniel had also designed an hour glass to be used at sea so that the trickle of sand was constant even when the ship was rolling in heavy seas.
- Daniel had also attained fame through his work Mathematical exercises and on the strength of this he was invited to take up the chair of mathematics at St Petersburg.
- Johann Bernoulli was able to arrange for one of his best pupils, Leonard Euler, to go to St Petersburg to work with Daniel.
- Euler arrived in 1727 and this period in St Petersburg, which Daniel left in 1733, was to be his most productive time.
- One of the topics which Daniel studied in St Petersburg was that of vibrating systems.
- Bernoulli determined the shape that a perfectly flexible thread assumes when acted upon by forces of which one component is vertical to the curve and the other is parallel to a given direction.
- Daniel makes the assumption that the moral value of the increase in a person's wealth is inversely proportional to the amount of that wealth.
- Daniel applied some of his deductions to insurance.
- Undoubtedly the most important work which Daniel Bernoulli did while in St Petersburg was his work on hydrodynamics.
- Even the term itself is based on the title of the work which he produced called Hydrodynamica and, before he left St Petersburg, Daniel left a draft copy of the book with a printer.
- Daniel also discussed pumps and other machines to raise water.
- One remarkable discovery appears in Chapter 10 of Hydrodynamica where Daniel discussed the basis for the kinetic theory of gases.
- Daniel Bernoulli was not happy in St Petersburg, despite the obvious scientific advantage of working with Euler.
- The post was neither one in mathematics nor physics but Daniel preferred to return to Basel and give lectures on botany rather than remain in St Petersburg.
- Daniel Bernoulli submitted an entry for the Grand Prize of the Paris Academy for 1734 giving an application of his ideas to astronomy.
- The result of this episode of the prize of the Paris Academy had unhappy consequences for Daniel.
- Whether this caused Daniel to become less interested in mathematics or whether it was the fact that his academic position was a non mathematical one, certainly Daniel never regained the vigour for mathematical research that he showed in St Petersburg.
- Although Daniel had left St Petersburg, he began an immediate correspondence with Euler and the two exchanged many ideas on vibrating systems.
- Euler used his great analytic skills to put many of Daniel's physical insights into a rigorous mathematical form.
- Daniel continued to work on polishing his masterpiece Hydrodynamica for publication and added a chapter on the force of reaction of a jet of fluid and the force of a jet of water on an inclined plane.
- The 1737 prize of the Paris Academy also had a nautical theme, the best shape for a ship's anchor, and Daniel Bernoulli was again the joint winner of this prize, this time jointly with Poleni.
- Hydrodynamica was published in 1738 but, in the following year Johann Bernoulli published Hydraulica which is largely based on his son's work but Johann tried to make it look as if Daniel had based Hydrodynamica on Hydraulica by predating the date of publication on his book to 1732 instead of its real date which is probably 1739.
- Botany lectures were not what Daniel wanted and things became better for him in 1743 when he was able to exchange these for physiology lectures.
- Daniel Bernoulli did produce other excellent scientific work during these many years back in Basel.
- 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 and his use of these together with the tolls coming from the more powerful calculus of Leibniz.
- Daniel worked on mechanics and again used the principle of conservation of energy which gave an integral of Newton's basic equations.
- Daniel Bernoulli was much honoured in his own lifetime.

Born 8 February 1700, Groningen, Netherlands. Died 17 March 1782, Basel, Switzerland.

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Analysis, Astronomy, Origin Netherlands

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive