Search Results

Just a few remarks: I doubt that we know that Thales "certainly knew" the concept of a planar angle. All we know about pre-Euclidean mathematics is basically based on histories written long after Eu …

As Sesiano writes in his book, the first three books that once existed in Arabic translation (by Qusta ibn Luqa) are lost. But al-Karaji quoted extensively from Diophantus Book III (and gives almost a …

Both Euler and Goldbach counted 1 as a prime in certain situations (variants of Goldbach's conjecture), and did exclude 1 whenever it suited them (arithmetical functions). The question whether 1 is pr …

The cuneiform tablet MS 2351 from the 19th century BC contains the 15-digit sexagesimal number 13 22 50 54 59 09 29 58 26 43 17 31 51 06 40, which happens to equal $20^{20}$. I also seem to remember t …

It seems that the first published proof of the result in the title is due to the Banu Musa, two brothers from Baghdad living in the 9th century. In their book on The measurement of plane and solid fig …

In his letter to Zimmermann (March 12, 1797; Werke X), Gauss wrote May God give the noble Duke a long life, and what may Science expect from him since he deems a work that is only a little interestin …

I don't think that there's a good answer to this. The following episode at least shows that people have been thinking about the problem of capitalizing Abelian for quite a while. In her letter to Has …

The ancient Greeks were quite strict in their separation of pure mathematics (mathematics) and applied mathematics (logistics). Euclid in his elements covered the basics of pure mathematics: line segm …

Let me start with your first quotation: "In 1763, Euler started a thorough study of curvature of embedded surfaces. In 1767, he found an expression of the curvature in terms of the product of princip …

KConrad's answer is correct, and the analytic class number formula is due to Dedekind. Yet the whole story is a little bit more complex and it is fair to say that Dedekind's analytic class number form …

In 1801, Gauss certainly was aware of the general procedure to obtain the class number formula (or asymptotic results) via counting lattice points. As a matter of fact, the approach using lattice poin …

Please allow me to put my question on top of the list again by turning my comment into an answer. FC's remarks led me to the article "Transcendental values of the digamma function", J. Number Theory 1 …

This makes a little bit more precise what has already been said in the comments. This list of emigrants (most of them were forced to leave since they lost their jobs; this applies to Emmy Noether, R …

In absence of any evidence (she has collected works, and there are various people who have studied her biography) this is nonsense. In addition, this would not at all be compatible with Emmy Noether's …

In his early days, Fermat realized that a natural number that can be written as a sum of two rational squares actually is a sum of two integral squares, but he did not come back to this claim when ev …