An extensive biography of Euler, mathematician and theoretical physicist.
Backstory: I’ve been reading biographies recently. Often, biographies of physicists, mathematicians, or popular musicians.
Euler was in the generation following Newton and Leibnitz — Leonhard Euler 1707-1783, Isaac Newton 1642-1726, Gottfried Wilhelm Leibnitz 1646-1716. Newton and Leibnitz had “invented” calculus, the theory of gravity, the theory of optics, etc.
The new math/science was elaborated by a large community of (primarily European) scholars. Euler was probably the most productive and influential in his generation.
What I found fascinating is that many of the names I remember from my Physics education were active during this timeframe — Bernoulli (3 generation’s of them), Maclaurin, Lagrange, etc.
Also fascinating is the way research was done and how it was shared. Many countries had scientific societies funded by the rulers — England, Russia, Prussia (Berlin), etc. Euler was primarily involved/funded in Prussia and Russia. Each published research, but the publishing often lagged the work by years. (Some of Euler’s papers were published decades after his death). Researchers presented their work locally and letters were exchanged with remote scientists.
The impression I got is that these letters were complete — a form of peer review. Often, the letter content that was received and forwarded on. Related to this is that there were many arguments on precedence — who was the first to “invent” a concept/formula. Euler was often a participant in the debate, both as a possible inventor, and also as an influential “judge” since he knew all the participants and was aware of their research.
Newton’s Theory of Gravity: Euler (and others) debated whether the force at a distance was real or was actually transmitted via an invisible “ether”. The idea of vortexes in the ether explaining the astronomical observations was a possible option.
Three-body problem and perturbation approaches: Observational astronomy of the moon, planets, and their moons was actively pursued by Euler and others in this time frame. Euler (and others) did extensive calculations to see if Newton’s theory could predict the observations. The staring point was to actually develop the differential equations that predicted the orbits. Then, they would search for analytic solutions and if not possible, would develop finite-difference equations (series expansions) that could be evaluated to compare to the observations.
People published tables of numbers calculated in this way. There were discrepancies, and it was debated whether gravity corrections (e.g., an inverse-fourth-power term) was needed.
The question about whether an analytic solution to the 3-body problem was possible or not was still open. (It’s not).
Fluid mechanics: Euler (and others) developed the differential equations that described fluid flow. This had real-world applications in ballistics and ship design, so was of particular interest to the rulers that funded the research institutes. Solving analytically is really not possible, so a large part of Euler’s work (and others) was to produce numerical calculations.
Differential equations and their solutions: Writing down the differential equations that described curves (e.g. of ropes and beams) in space and mechanics of rigid (and elastic) bodies was first done during this era.
Mechanics and the concept of least action: The concept was a useful approach to finding actual solutions to mechanics and orbit problems, but it was debated whether it was true or not.
Infinite series expansions and summation: Euler described many of the series expansions (e.g. of triginometric functions) that I’ve dealt with in Physics and Maths coursework. Analytic solutions to infinite series were one area of his research. Alternative equivalent series were also useful to develop. The point was to come up with series that converged faster if numeric solutions had to be calculated. Examples actively pursued were the calculation of pi, of e, and the production of tables of logarithms,
Real-world applications: I’m aware of Euler from theoretical Physics and Mathematics, but a large proportion of his research and calculations were applying this theory to real-work problems. This includes telescope/microscope design; the use of astronomical observations for map-making and navigation; the use of fluid mechanics (static and dynamic) for ship design; solid body mechanics applied to architecture and bridge design; etc.
Summary: I did enjoy reading the book, but it was a ‘slog’ to get through. The author attempted to give a chronological summary of all available information about Euler. The book is a mixture of personal information/anecdotes, mathematics and physics research and publications, inter-personal political disputes of the times, etc.
One particular annoyance was the huge number of names mentioned through the book. Keeping in mind who was who was tough. Interestingly, people’s names varied when referenced from different countries. E.g., is it Johann of Jacques Bernoulli? and was it Johann I, Johann II, or Johann III? One was Euler’s teacher, one his peer, one his student.
Aside: In an article I read recently, the author mentioned that one of the key things that emerged out of the “enlightenment” was the sharing of scientific theories, observations, and results. Specifically mentioned Newton, who published his theory of gravity and other scientific investigations. But Newton was also heavy into alchemy. Alchemists in general did not share their investigations publicly, and Newton did not either. So progress in the alchemical arts was severely limited. Basically, alchemy turned into chemistry once the practitioners started sharing their results.