16
votes
Accepted
How long has the order of priority of arithmetical operations been widely taught in high schools?
This question comes up often, but there is no up to date scholarly study of it that I know of. The most comprehensive recent accounts (and they are rather brief) seem to be Jeff Miller's Earliest Uses ...
- 80k
16
votes
Accepted
What did the study plan of an early 20th century mathematics undergraduate program look like?
Here is an example.
link https://iiif.lib.harvard.edu/manifests/view/drs:467220382$1i
Official Register of Harvard University
Volume VI, May 26, 1909, number 16
Announcement of the Courses of ...
- 10.6k
10
votes
Accepted
What algebra problem did Serge Lang give to calculus students?
In 1969 Lang wrote an article for the Columbia Daily Spectator, Don't
Blame Us if You Flunk Math (Volume III, Number 4, December 8, 1969). The phrasing of the subline illustrates how much the times ...
- 80k
9
votes
Accepted
What dialect of ancient Greek was taught to natural philosophers?
Attic, the highest prestige dialect, hands down. For centuries, this has been the mainstay of Greek language education in Europe.
There is no better reminder of this than Newton's Trinity College ...
- 1,949
8
votes
When exactly (and why) did matrices become a part of the undergraduate curriculum?
I would say that in Germany there was a gradual development towards the matrix notation of linear equation systems from the 1920s onwards. Courant certainly was a pioneer in this development as he ...
- 1,404
8
votes
Are there any sources of mathematicians talking about their research methods?
Cédric Villani's Birth of a Theorem does exactly that. A great read for scientists, even non-mathematicians.
Edit: The English title of the book is Birth of a Theorem and not Living Theorem (the ...
8
votes
Was such advanced content on set theory taught in American elementary schools back in 1965?
Yes. I was there.
I was at an American school in São Paulo, Brazil. Apparently, it was easier to introduce the new ideas in such foreign settings (a private school, no school boards to satisfy, ...
- 148
7
votes
Accepted
What were the typical ways students were taught the elements when it remained the prime textbook of mathematics?
Students learned theorems, propositions and their proofs. A teacher would call a student to the blackboard and ask to reproduce a proof. A shorter test would be just to state the theorem. Many ...
- 51.1k
7
votes
How long has the order of priority of arithmetical operations been widely taught in high schools?
but for how long has PEMDAS been widely taught in high school mathematics classes? I assume this will differ for different parts of the world, so please include what countries or regions you can speak ...
- 1,971
7
votes
Seeking sources: Catholic church and the development of mathematics
"Examples of the Catholic church commenting on, or intervening in, the development of mathematics:" Counter-reformation issues in the 17th century around transubstantiation/consubstantiation ...
- 6,684
7
votes
Seeking numbers of German mathematics professors in 1890
A relevant source to find answers to this questions is the book (out of print in Germany):
[Ferber 1956] Christian von Ferber: Die Entwicklung des Lehrkörpers der deutschen Universitäten und ...
- 690
6
votes
Accepted
Seeking numbers of German mathematics professors in 1890
I recommend the authoritative volume "Das Studium der Mathematik an den deutschen Universitäten seit Anfang des 19. Jahrhunderts" by Wilhelm Lorey, published in 1916. This digitalized edition can be ...
- 1,404
6
votes
Seeking sources: Catholic church and the development of mathematics
I would add, as example, that can be a bit investigated the work of Padre Girolamo Saccheri, a Jesuit priest, and his famous "Euclides ab omni naevo vindicatus" (Euclid Vindicated from Every Blemish) ...
- 1,738
6
votes
Seeking sources: Catholic church and the development of mathematics
You must tell them about the book Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World, by Amir Alexander. It's about, among other things, how the Jesuit priests stopped the ...
- 5,976
6
votes
Seeking sources: Catholic church and the development of mathematics
Cauchy, who gave calculus its modern formalization (cf. Grabiner's The Origins of Cauchy's Rigorous Calculus), was a "significant mathematician who was also a practicing Catholic." From Belhoste's ...
- 5,419
6
votes
Accepted
Are there any sources of mathematicians talking about their research methods?
Mathematicians rarely describe the process which led them to their discoveries.
One notable exception was Euler.
Some books on the subject written by great mathematicians are:
J. Hadamard, The ...
- 51.1k
6
votes
Why did the development of major Mathematics in America only start after 1900s?
It is absolutely irrelevant for the question when America was discovered. The first university on the US territory was founded in 1636. But until 20th century most universities taught mostly ...
- 51.1k
5
votes
Are there any sources of mathematicians talking about their research methods?
The first mathematician who did that was Archimedes, in his The Method of Mechanical Theorems (usually known as The Method).
- 5,976
5
votes
Where did the false "equal transit-time" explanation of lift originate from?
The popularity of the equal transit-time fallacy is a bit more complicated than a mistake spreading from a single source. It is simple, intuitively appealing (blowing over an airfoil is often invoked, ...
- 80k
5
votes
When and why did the concept of relativistic mass become outdated?
Interestingly, the shift in physics appears to have occured late in the 20th c. while philosophers were already discussing it as an exemple. Max Jammer's book Concepts of Mass remains an invaluable ...
- 2,462
5
votes
Blackboards as math tech!
If we ignore the "wall" part
"Pastel of Boy with Slate" 1822
Schoolboys would use these, since paper was too expensive to waste on practice or scratch work.
The exact origins of ...
- 10.6k
5
votes
Accepted
What books did Lavoisier read?
There is online a Panopticon Lavoisier which is a tool for searching the Archives de l’Académie des sciences, Fonds Lavoisier.
The link to "library"
is introduced thus:
The catalogue of ...
- 2,462
4
votes
Seeking sources: Catholic church and the development of mathematics
An interesting story is the one of Matteo Ricci, a missionary jesuit in China. He wrote the first Chinese translation of Euclid's Elements. He was also a cartographer.
Regarding real analysis, Pietro ...
- 175
4
votes
Why were 20th Century German scientists so impressive?
The German/Prussian education system was based on two pillars: The first was a mandatory comprehensive primary public school education with the aim to provide literacy, numeracy and good ...
- 541
4
votes
Where did the false "equal transit-time" explanation of lift originate from?
Klaus Weltner and Martin Ingelman-Sundberg (from the Department of Physics at the University Frankfurt) in an ultimately unpublished paper, “Physics of Flight — reviewed”, submitted to the European ...
- 155
3
votes
Where did the false "equal transit-time" explanation of lift originate from?
This explanation has probably been independently 'rediscovered' many times, and it is unlikely to be able to point to a particular origin.
Ackroyd says in 'Babinsky's Demonstration: The Theory of ...
- 191
3
votes
Where did the false "equal transit-time" explanation of lift originate from?
The asymmetric shape (not its explanation with "equal transit time"!) comes from the first mathematical theory that explained the lifting force (Chaplygin's formula, known in the West as "Blasius ...
- 51.1k
3
votes
Are there any sources of mathematicians talking about their research methods?
Alexander Grothendieck, without a doubt one of the most creative mathematicians in the last 100 years, wrote a voluminous manuscript Récoltes et Semailles about (among other things) his approach to ...
- 1,012
3
votes
Where did the false "equal transit-time" explanation of lift originate from?
"Hat der Körper eine gleichmäßige Geschwindigkeit in ruhender Luft, so wird auch in der den Körper umgebenden Luft eine gleichmäßige Bewegung eintreten, die im wesentlichen darin besteht, daß die Luft ...
- 31
3
votes
Seeking sources: Catholic church and the development of mathematics
Look up Bernard Bolzano, who should be known to all students of analysis through the Bolzano-Weierstrass theorem. His work became known largely after his death and after others had already ...
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