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I would say that no area of mathematics has ever been completely abandoned. The areas go in and out of fashion, but nothing seems to be completely abandoned. For example, approximately in 1940's most mainstream mathematical journals stopped to consider papers on elementary geometry. But the area is not abandoned in any way. First of all, there are "non-...


8

Geometry I'm not sure you can really call geometry abandoned, but it certainly was much more popular a few hundred years ago (discovery of spherical geometry and hyperbolical geometry, parallel axiom debate) and a few thousand years ago (the old Greeks developed a lot of geometry). Nowadays, there are very few papers about just plain Euclidean geometry (or ...


7

"Examples of the Catholic church commenting on, or intervening in, the development of mathematics:" Counter-reformation issues in the 17th century around transubstantiation/consubstantiation interpretation of the eucharist directly influenced attitudes toward the techniques of indivisibles that were seen as closely related to atomism and therefore opposed on ...


6

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 biography of him, p. viii: "Truth," he wrote in 1842, "is a priceless treasure which, whenever we manage to acquire it, cannot bring us remorse and sorrow; ...


6

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) in which he first discovered many theorems of what will then be called hyperbolic geometry. He however ended his books by saying that such theorems were ...


5

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 progress of Infinitesimal Calculus in Italy because the foundations of the subject were shaky at the time (to say the least). Perhaps that you might also mention ...


5

One of the greatest mathematical controversies arguably is the one concerning infinitesimals: are they contradictory? are they useful? did Leibniz really use them? is there a connection between Leibniz's infinitesimals and Robinson's? are Euler's infinitesimal procedures sheer madness? are they chimeras, as alleged by authors ranging from Berkeley to Moigno ...


4

History of Mathematics Classification To see how the classification of mathematics has developed historically, compare the ancient classification of mathematics: Arithmetic (discrete math) Geometry (continuous math) to that of Descartes' era: Analytic Geometry Arithmetic (discrete math) Geometry (continuous math) to the 1868 classification in Jahrbuch ...


4

Edmund Whittaker's A history of the theories of aether and electricity, vol. II (Harper Brothers, NY, 1960) has a chapter on the history of general relativity with a lot of mathematical details.


4

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 Mengoli proposed one of the most influential problem in the early days of calculus: the Basel problem, famously solved by Euler. Also, Francesco Faà di Bruno ...


4

The closest I can think of is Pais's Subtle is the Lord, although it is not a history textbook but rather Einstein's scientific biography, which literally retraces his steps based on the author's own interviews, among other things. He does also go into some mathematical details unlike the usual "literary" biographies. On differential geometry and the role ...


3

To have one man’s steps distilled into textbook form is a lot to ask: who teaches a course on that? The next best thing might be the proceedings and collections in Einstein Studies (with contributions of the same John Norton):    1. Einstein and the history of general relativity (1989),    3. Studies in the history of general relativity (1992),    5. The ...


3

Yes, there is: https://archive.org/details/historyoftheorie00whitrich A history of the theories of aether and electricity : from the age of Descartes to the close of the nineteenth century by Whittaker, E. T. It also contains history of optics, quantum mechanics and relativity.


3

There is a second sentence to the quote:"The energy of the universe is constant. The entropy of the universe is increasing". The conservation of energy law. The second law of thermodynamics. The quote became famous because from the conjuction of the two conclusion about the heat death of the universe appears to follow. The idea was expressed earlier by ...


3

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 rediscovered his results independently.


3

This is not a list of controversies, but you might be interested in Imre Lakatos' book Proofs and Refutations which describes the mathematical progress. For example it provides a discussion of Euler's Polyhedron Formula as a discussion between a teacher and some students. The arguments the students use in this discussion are arguments which have been brought ...


3

I recommend Norton's History of Chemistry by William Brock. For a history of the periodic table try my own: Eric Scerri, The Periodic Table, Its Story and Its Significance, OUP, 2007.


3

I agree that there are (surprisingly?) few books on the history of chemistry. The most succinct one is probably C. Cobb, H. Goldwhite; "Creations of Fire - Chemistry's Lively History from Alchemy to the Atomic Age" Much more detailed, although somewhat old now, is A. Ladenburg; "Lectures on the History of the Development of Chemistry Since the Time of ...


2

Another example is the study of configurations; its history is given in §1.2 of Branko Grünbaum's Configurations of Points and Lines, Graduate Studies in Mathematics volume 103, American Mathematical Society, 2009. Broadly, this area of combinatorics, though not defined in full generality until 1876 by Theodor Reye, encompasses work of Pappus and Desargues. ...


2

I suppose the prime example would be classical invariant theory (CIT), although agreeing with Alexander, and despite exaggerated news of its death it had some bursts of revival recently. It is interesting to note that in the 19th century this subject was almost inseparable from classical elimination theory (CET). There has been a revival of CIT without CET (...


2

A History of Mechanics, by Dugas (1955) is available from Dover; Part V is an introduction to Quantum Theory. Some experiments are discussed, but it is mostly a scholarly discussion of ideas and how they evolved over time, with proper references, as explained by a trained engineer and historian of science. The scope is well described by the preface and ...


2

If you're interested in reading more about the history of quantum mechanics, one of the most comprehensive works is Mehra's six-volume epic. Other than that, I can personally recommend reading scientific (rather than "informal") biographies of some of the individually involved scientists. I thoroughly enjoyed Pais' accounts of both Bohr's and Einstein's (...


2

See links at Online resources for history of physics, History and Philosophy of Biology Resources, Chemical Heritage Foundation, Math Archives: History and Websites relevant to the History of Mathematics, also Teaching with Original Historical Sources in Mathematics puts an interesting spin on it. I like Sean Carroll's blog on physics, Phil Plait's blog on ...


2

There are gigantic lists (Wikipedia) of men of the cloth in Mathematics and Science: (1) https://en.wikipedia.org/wiki/List_of_Catholic_clergy_scientists (2) https://en.wikipedia.org/wiki/List_of_Christians_in_science_and_technology


2

Although not a text book, a very enjoyable account that covers the history of general relativity from Einstein (and before) to the current research and understanding is "The Perfect Theory: A Century of Geniuses and the Battle over General Relativity" by Pedro G. Ferreira1 .


2

I don't think there is a systematic way to search for handwritten manuscripts, and they are rarely available on the web. One collection is here: http://www.claymath.org/node/1370 If you press on the pop-up menu "Publications" in the top, you find manuscripts of Klein, Quillen, Riemann and others. University of Uppsala has Beurling's archive: http://www.math....


1

See the hefty § "Magnetism and Electricity", pp. 387-616 of A Source Book in Physics by William Francis Magie. It contains selections, prefaced with a biography, of 37 scientists including Gilbert, Franklin, Coulomb, Galvani, Volta, Ørsted, Biot and Savart, Arago, Ampère, Ohm, Faraday, Lenz, Gauss, Joule, Maxwell, Hall, Hertz, et al.


1

If French works for you, O. Darrigol's Les équations de Maxwell: de MacCullagh à Lorentz (2005) is such an anthology, with comments drawn from his earlier book. Such collections are likely a dying breed, as all papers (in this case, nine by MacCullagh, Maxwell, Lorenz, Heaviside, Hertz, Lorentz) become freely available online.


1

For thermodynamics: Clifford Ambrose Truesdell, The Tragicomical History of Thermodynamics, 1822-1854 (New York, NY: Springer New York, 1980).


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