*Leonhard Euler: Mathematical Genius of the Enlightenment*

By Ronald S. Calinger, what a beautiful book, clearly written, conceptual in nature, placing Euler in the broader history of mathematics, the funding of science, and the Enlightenment, all in a mere 536 pp. of text.  Here is one bit:

At midcentury Leonard Euler was at the peak of his career.  Johann I (Jean I) Bernoulli had saluted him as “the incomparable L. Euler, the prince among mathematicians” in 1745, and Henri Poincaré’s later description of him as the “god of mathematics” attests to his supremacy in the mathematical sciences.  Euler continued to center his research on making seminal contributions to differential and integral calculus and rational mechanics, and producing substantial advances in astronomy, hydrodynamics, and geometrical optics; the state projects of Frederick II required attention especially to hydraulics, cartography, lotteries, and turbines.  At midcentury, when d’Alembert and Alexis Claude Clairaut in Paris, Euler in Berlin, Colin Maclaurin in Scotland, and Daniel Bernoulli in Basel dominated the physical sciences, Euler was their presiding genius.

Nor had I known that Rameau sent his treatise on the fundamental mathematics of music to Euler for comments.

Definitely recommended, you can order it here.


TC: "Nor had I known that Rameau sent his treatise ..." Me: I don't even know who Rameau is...time to Google it.

Bonus trivia (that I doubt you find in Google): some of Euler's works *still* have not been translated yet, he was that prolific.

The joke when I was getting my math degree was always that equations and axioms were named after the first person to write a paper using Euler's work, because otherwise everything would be named after Euler.

Some eccentric billionaire (not in the Epstein way) should build a new Institute for Advanced Study in a more attractive place than New Jersey.


Princeton is a very nice place, and it is well located there.

Euler also discovered (or invented, if you prefer) the favorite equation of mathematicians: e^i.pi + 1 = 0, which uses exactly once with nothing else each of the two numerical identities and zero, each of the two most famous transcendental numbers, and each of the three arithmetic operations in an equation. Euler himself considered the equation to prove the existence of God.

I'm glad you called attention to the "God equation".

The implications and applications of this equation are astounding. I am awestruck.

I remember once struggling in class about circuit theory and my professor (Timo Rahkonen) came to me and told me to read Euler' Letters to German Princess.

Now let's look at the state of maths in Africa (10 times more populated than europe bach then)

Don't be a bigot.

The progress of Africa was set back by colonialism.

I had heard that the Bernoulli brothers were paid to invent and give a mathematical formula to some rich noble who just wanted his name on it. Anyone remember the formula? It’s basic calculus, just isn’t coming to mind right now.

L'hoptital if I remember correctly. If you want a readable introduction to some of Euler's math check out How Euler Did It (here)[http://eulerarchive.maa.org/hedi/]

Mind blown, reading about L'Hopital and Bernoulli. L'Hopital was already a legitimate mathematician, but he recognized Bernoulli's brilliance and paid him to work on difficult mathematical problems.

I’m cumming at the though of a Buttigieg victory!!!

It has nothing to do with Brazil's innovative healthcare system at all.

Bolsonaro will be a great bottom for President Buttigieg

No, he will not.

He also invented the Tonnetz, an alternative arrangement to the black and white piano keyboard for musical notes. It brilliantly reveals the harmonic relationship of the tones isometrically and is much easier to navigate and understand than a piano keyboard. It would make music theory much easier to understand if adopted properly, I think.


Would even a math genius like Euler have been able to count Iowa caucus votes no more than twelve hours after the voting ended?

Is it cheating or just clownishness? The Dems are on a roll for both.

"... a mere 536 pp. of text ..."

I wonder what you consider to be a long book.

Interesting point about music. One of the things about music theory or at least western music theory is about how mathematical it is, the octave, or really 12 note, scale with all the keys one can play the same melody in, is very complicated. Harmonics, as well as astronomy, were the first sciences that were given the rigorous mathematical treatment that is usual in science since Descartes. I don't think it's an accident that Galileo's father was a court musician.

Euler was supposedly the last mathematician who 'knew it all', so I guess he'd have done music too.

I suspect that if Euler had learned that an otherwise respectable person referred to his work with the verbiage

continued to center his research,

he'd have challenged Mr. Calinger to a duel and shot him.

Generally known among mathematicians, but not to others - he had a medical background too and he walked from Basel to St. Petersberg to take up his appointment at Catherine the Great's court.

He went most of the way by boat, up the Elbe and across the Baltic Sea.

Math? You mean the thing that was "developed by Greeks and other Europeans" and "operates with unearned privilege in society, just like Whiteness"?

No, math must reformed to be "an intersectional, anti-racist, and class-consciously feminist enterprise" by using "critical math pedagogy".


Or is it /s? The AMS seems to believe it. First step, a feminist math department.


Between this and the recent post about the Berkeley ideological test I tend to think academia is lost. Then I read the link you posted and see this comment on that absurd commentary:

"I think your beef is less with maths, than with the fact that most people don’t use maths to forward a social “justice” agenda. As someone who is non-white, I take umbrage with the soft racism of the very idea of “social justice”, as it absolves the individual of any responsibility for her situation, instead, gratuitously blaming external forces for her failings.

The maths in our examples are not faulty. They merely fail to have givens that fit with the “victimhood” narrative. The “answer” is to let maths be maths, and not the social science that you seem to want it to be.



Maybe there is hope we can restore sanity to academia.

It must be nice to have the privilege of having AMS give you a platform to throw what is basically a tantrum (invariably from sour grapes but couched in the language of pretentious nonsense). What better sign of a slowly dying culture. This is what you get for simple-mindedly distributing 'self esteem' among school children. Now instead of taking responsibility of their own pedestrian shortcomings they make a hot air balloon bounce house of obsolete injustices.

Hopefully this disease won't come to my developing country. We can't afford such indulgences.

Your children will kick their wimpy whining asses.

We did this to ourselves.

I bought it on Kindle. What's the point of the Europe comments?


A placeholder concept that Europeans needed to have explained to them.

Euler was brilliant, but some of his mathematics was based on a lot of assumptions. For example, he assumed that the difference between the sum of the harmonic series and the natural logarithm converged on a limit. As it turns, out, it does, but Euler cranked out volumes about that limit, now known as gamma, before anyone bothered to prove that it existed. As one writer - I think in Euler: The Master of Us All - put it, Euler was the most advanced and powerful high school level mathematician ever.

He was also the quintessential nerd. Frederick the Great and Voltaire used to tease him about his clothes. For a true nerd, that kind of criticism is a serious compliment. Even better, he was good with children and would often work on his mathematics with one of his younger children on his lap. If you've ever tried to do math with a two year old on your lap, you'd understand Euler's sheer excellence.

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