Leonhard Euler’s importance for the history of mathematics is undoubted. Not only was he the most prolific mathematician ever – his collected works so far run to 76 volumes and further editions of his correspondence are planned – he dominated the eighteenth century. He combined an extraordinary memory, a capacity for a huge range of interests, an exceptional technical facility, and an ability to work to a high level of abstraction with a natural clarity of expression. His importance extends beyond his many profound innovations in many fields, of which three can be mentioned here:
- mechanics, which he built up from the motion of point masses through the theory of rigid body motion to aero- and hydrodynamics, with applications to ship design, gunnery, optics, and celestial mechanics, where he did important work on the motion of the Moon and the three body problem;
- the calculus, where he successfully introduced the concept of a function as fundamental; and
- number theory, including the theory of quadratic forms and the zeta function.
It was also the force of his example that established the culture of publishing in mathematics, and replaced the markedly more secretive habits of Newton and Leibniz. His widespread correspondence stimulated others, his work at the head of the Academy of St Petersburg helped develop mathematics in Russia, and his textbooks on the differential and integral calculus and on algebra made the subject accessible to generations of students.
The orbital stability of a test body motion in the field of two massive bodies