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History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.

7 votes
0 answers
321 views

Gauss, Cantor, and infinite confusion

There is an interesting comment by Gauss on "infinite magnitude as a complete thing" that has invited varying interpretations. In a well-known passage, Gauss criticized the use of infinity in mathema …
Mikhail Katz's user avatar
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7 votes
0 answers
76 views

Earliest historical work on Cauchy's infinitesimal delta functions?

As early as 1981, Hans Freudenthal briefly mentioned Cauchy's work on "singular integrals (i.e., integrals of infinitely large functions over infinitely small paths [$\delta$ functions])" on page 135 …
Mikhail Katz's user avatar
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2 votes
0 answers
113 views

Robinson's views on Heyting's work?

Abraham Robinson and Arend Heyting had mutual respect (though holding differing philosophical views on the nature of mathematics). Heyting repeatedly expressed admiration for Robinson's work; see for …
Mikhail Katz's user avatar
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4 votes
2 answers
914 views

Priority for lemniscate of Gerono?

The Lemniscate of Gerono is a special case of the Lissajous curves. The dates for the two mathematicians are fairly close: Gerono (1799-1891) and Lissajous (1822-1880). There seems to have been earl …
Mikhail Katz's user avatar
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18 votes
2 answers
1k views

New articles by Errett Bishop on constructive type theory?

Recently two formerly unknown articles by Errett Bishop (1928-1983) were posted online by Martín Escardó. One is entitled "A general language", deals with constructive type theory, and is 28 pages lon …
Mikhail Katz's user avatar
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7 votes
1 answer
284 views

Sophus Lie's contribution to solution of problems of variational type as in Euler and Lagrange

The original impetus for Sophus Lie's work was apparently to streamline the solution of certain problems of variational type such as those treated in the work of Euler and Lagrange. This presumably i …
Mikhail Katz's user avatar
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11 votes
1 answer
792 views

Lalouvère's activities as censor

Fermat had a friend at Toulouse named Lalouvère. Lalouvère was censor, jesuit, and mathematician (in alphabetical order). Antonella Romano writes on page 512 of her book La Contre-Réforme Mathémat …
Mikhail Katz's user avatar
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0 votes
1 answer
165 views

de Waard volume on Fermat

Fermat's works were published by Tannery and Henry in four volumes, the last of which appeared in 1912. An additional volume was edited by de Waard in 1922: Fermat, P. Oeuvres de Fermat: Suppléme …
Mikhail Katz's user avatar
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3 votes
0 answers
148 views

Whatever became of d'Espagnet's library?

The library at Bordeaux where Pierre de Fermat learned enough mathematics by his predecessors to develop his technique of adequality was owned by Jean d'Espagnet who passed it on to his son Etienne d' …
Mikhail Katz's user avatar
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13 votes
4 answers
993 views

Source for analysis of identification of structures in learner's mind and mathematical struc...

Concerning the structure of the learner's mind, psychologist Piaget claimed that There exists, as a function of the development of intelligence as a whole, a spontaneous and gradual construction of e …
Mikhail Katz's user avatar
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17 votes
1 answer
2k views

Did Lagrange change his mind about infinitesimals?

Lagrange is famous for his attempt to found analysis algebraically using power series expansions, an approach that, as we know today, is limited to analytic functions. Lagrange is also known as the in …
Mikhail Katz's user avatar
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7 votes
3 answers
5k views

Was Cauchy prescient?

Cauchy proved a sum theorem for series of continuous functions in 1821, and published another article on the subject in 1853. Michael Segre, writing in Archive for History of Exact Sciences, claimed …
6 votes
1 answer
727 views

Did Bishop make those comments in his oral presentation?

The 1975 published version of a 1974 talk at a workshop by Errett Bishop contains the following comment: "A more recent attempt at mathematics by formal finesse is non-standard analysis. I gather …
Mikhail Katz's user avatar
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19 votes
2 answers
2k views

Did Hilbert discuss his 23 problems with Felix Klein?

Hilbert's lecture at the ICM in Paris in 1900 presented 10 of the famous 23 open problems. It is well known that the idea of the lecture came from Hermann Minkowski. Hilbert was at Göttingen at the ti …
Mikhail Katz's user avatar
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13 votes
2 answers
2k views

Fermat's opponents

It is well known among historians of Fermat that, while his technique of adequality prepared the ground for the general framework later developed by Leibniz and Newton, Fermat himself gave very little …
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