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

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
  • 16.6k
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
  • 16.6k
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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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
  • 16.6k
10 votes
2 answers
979 views

Who was the first to discover that the curvature of an embedded surface is the product of th...

The invention of intrinsic differential geometry is usually attributed to Gauss in the context of his theorema egregium but the notion of the curvature of an embedded surface existed before. Who was t …
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
  • 16.6k
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
  • 16.6k
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 …
Mikhail Katz's user avatar
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2 votes
1 answer
451 views

Levi's book on Leibnizian calculus

Raphael Levi learned from Leibniz at a late stage in Leibniz's career. This might be a definite advantage for understanding Leibniz. Leibniz did not elaborate some of the philosophical principles behi …
Mikhail Katz's user avatar
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3 votes
3 answers
786 views

Lapses of "the early proponents of the doctrine of limits"

I have a question that I have been wondering about for a long time without finding any answer. Concerning the period around 1900, Robinson commented in his 1966 book that "there is in the writings of …
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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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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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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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 …
41 votes
4 answers
7k views

Did Euler prove theorems by example?

In his 2014 book, Giovanni Ferraro writes at beginning of chapter 1, section 1 on page 7: Capitolo I Esempi e metodi dimostrativi Introduzione In The Calculus as Algebraic Analysis, Craig Fraser, r …

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