31
votes
Accepted
How did Ramanujan learn to do mathematics?
First hand testimony and insightful thoughts on Ramanujan's background and way of doing mathematics can be found in Hardy's lecture Indian Mathematician Ramanujan. Hardy is the British mathematician ...
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17
votes
Accepted
What kind of mathematical education did Leibniz have?
Mauro Allegranza's comment pretty much says it all but to elaborate a bit one could mention that Leibniz came to mathematics rather late in his intellectual career and was essentially a self-educated ...
- 5,062
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 ...
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14
votes
Accepted
Examples of good research mathematicians that did poorly in exams
Well Ramanujan was such a mathematician. He was not so poor in math exams but he scored somewhat unbelievable marks in mathematics. In $1907$, he appeared in FA Examination at Pachaiyappa College, ...
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13
votes
Accepted
What did the study plan of a 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 ...
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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 ...
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10
votes
Accepted
When were problem sets included in Science/math textbooks?
I can only talk about math books. Problems in the end of the chapters is a British-American custom. German, French and Russian books do not have them.
Instead they publish separate problem books, ...
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9
votes
Examples of good research mathematicians that did poorly in exams
The most famous case of this sort is Galois failing the entrance exam to Ecole Polytechnique.
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9
votes
Why were 20th Century German scientists so impressive?
Given the historical circumstances the German education system might or might not have played a significant role in the formation of these scientists. In his collection of essays entitled "Brocas ...
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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 ...
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7
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 ...
- 1,364
7
votes
When were problem sets included in Science/math textbooks?
Here is one data point. (It does not contradict Alexandre's assertion that this is an American innovation, but does provide an earlier starting date.)
Day's Algebra (I picked this volume up in a ...
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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 ...
- 680
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 ...
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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 ...
- 1,901
7
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 ...
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 ...
- 1,364
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 ...
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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) ...
- 1,717
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 ...
- 5,718
6
votes
Examples of good research mathematicians that did poorly in exams
Newton somewhat infamously failed his examinations at Cambridge: he was questioned orally about the proofs in Euclid, and since he had looked at Euclid once and thought it a total waste of time, and ...
- 161
6
votes
Where can I learn more about lesser known mathematicians?
There is a large list of links to biographies here. Most mathematicians on the list are not as well known as Gauss and Euler, and they link to MacTutor, which is more reliable than Wikipedia.
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6
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 ...
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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 ...
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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 ...
- 47.6k
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 ...
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5
votes
Examples of good research mathematicians that did poorly in exams
G.H. Hardy. From http://www-history.mcs.st-and.ac.uk/Biographies/Hardy.html
"While at Winchester Hardy won an open scholarship to Trinity College, Cambridge, which he entered in 1896. At Cambridge ...
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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, ...
- 73.6k
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 ...
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5
votes
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 ...
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