# All Questions

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### The Roman numeral system continues to lack a zero digit today. Would zero ever get its own Roman numeral digit in the future? [duplicate]

This question is a follow-up to: Why didn't the number zero (0) have a Roman numeral of its own? The number zero did not have an official Roman numeral symbol in the first place, and it still ...
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### When and how was it discovered that the sun was in different positions depending upon longitude?

It seems to me that the ancient Greeks knew that geographic location affected the apparent position of the sun in sky but given the lack of rapid travel or communications or reliable clocks, how was ...
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### How did Yao came up with his minimum spanning tree algorithm?

I recently stumbled upon this text about Yao's algorithm for the minimum spanning tree (MST) and I was wondering if there are some preceding algorithms (other than Sollin's algorithm) that were ...
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### Did Kolmogorov complexity influence the development of communication complexity?

I was reading a wikipedia article about communication complexity and it seems to me that it bears some resemblance to Kolmogorov complexity. Was the founder of communication complexity influenced by ...
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### Who introduced the comma notation for partial derivatives?

In general relativity, it is common to use the comma notation for partial derivatives $$\frac{\partial g_{\mu\nu}}{\partial x_\rho} = g_{\mu\nu_,\rho}$$ Where did this notation first appear? Was it ...
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### Why do we use Leibniz's “version” of calculus instead of Newton's?

I understand that they invented calculus independently at roughly the same time, but why do we use Leibniz's terminology/notation rather than Newton's? For example, why don't we use "fluxion"...
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### What mathematical problems did the Sicilians need Arab help with in 1229? Did the Arabs solve these problems?

An incident in the negotations of the Sixth Crusade is described as Frederick II asking help from Arab scholars with some mathematical problems: ... and the sultan graciously allowed Frederick to ...
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### How did Kolmogorov came up with his formalization of intuitionistic logic?

According to this article Kolmogorov published a paper in 1925 in which he attempted to formalize Brouwer’s intuitionistic mathematics. In that paper there are the following logical formulas: \begin{...
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### When was the function 1 + cos(x), aka the vercosine, given a name?

Nowadays, when one searches for little-known trigonometric functions, one usually finds a list containing the versine, coversine, vercosine, and covercosine. When using this list, $1+\cos(x)$ is given ...
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### Have we exhausted all our experimental capabilities? [closed]

Currently high energy physics research has reached a physical plateau, with our current experimental capabilities stuck at 10^4 GeV, while quantum gravitational effects are predicted to appear at 10^...
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### What was the optical problem discussed and solved by Gauss in his 1831 letter to Brandes?

Volume 5 of Gauss's works contains a section which includes "Essays on various objects in mathematical physics". Just to emphasize the importance of this section, i'll mention that it ...
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### What are the direct predecessors of Lagrange's theory of quadratic forms?

I was reading Stillwell's Mathematics and its History, where Lagrange's theory of quadratic forms is synoptically presented, and I was wondering of what are the direct predecessors of the theory. ...
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### Where is this statement of Bourbaki's Dieudonné from and what does it mean?

In a few places, such as this web page, I have read the following statement about Jean Dieudonné, who was a founding member of the French "secret society" of mathematicians, Nicolas Bourbaki:...
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### Who discovered the thin lens equation $\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$?

According to Weisstein's webpage it was Halley in 1693 (quoting Steinhaus); but I've also seen it attributed to Cotes, Huygens, even Gauss (eg Britannica). Wikipedia's History of Optics does not give ...
77 views

### What was considered Evolutionary Science or Biology proper in 1880-1890 in the US?

I have a question that is more related to the history of evolutionary biology rather than the science itself, namely I am interested in knowing what might have been considered the 'orthodoxy' of the ...
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### Interpretation of a short note of Gauss on the resolution of a special system of inhomogeneous linear equations by roots of unity

My question refers to a 2-pages fragment of Gauss, entitled: "Note on the resolution of a special system of linear equations", which is found on pages 30-31 of volume 8 of his works. In this ...
81 views

### In which article/book chapter did Cantor, Hibert, and Poincare formally defined or directly discussed the term “potential infinity”?

Some media sources say that "Cantor claimed that there would only be potential infinity, not actual infinity" In addition, the following link claims that Hilbert, Poincare, and Cantor were ...
87 views

### What astronomy efforts required multiplication of large numbers around 1600?

I'm reading an article about the history of logarithms and it says: One problem that was plaguing people at the time, especially astronomers, was arithmetic. Astronomical calculations required the ...
153 views

### What mathematical theorems were known in the Americas prior to European contact?

A comment on another site brought the article How Does Race Affect a Student's Math Education? to my attention. In the article, the author observes (emphasis mine), But she’s also constrained by the ...
86 views

### How large were the differences in the orbit of Uranus which led to the calculation of the existence of Neptune?

After Uranus was discovered and its orbit calculated, its future orbit was calculated, and its future positions as seen from Earth were calculated. And observers of Uranus began to notice that Uranus ...
81 views

### Newton as the first one to establish numerical analysis as a new field of study

I was reading about the history of Newton's Method. Newton used a cubic equation, $x^3 - 2x - 5 = 0$, to show the efficacy of his method around 1670. I was wondering that why Newton would choose this ...
114 views

### Why are complex numbers called 'complex'?

I'm a high school teacher, and I was just wondering why complex numbers are called 'complex'. I have read that Gauss coined the term. But I couldn't find any reference where it was explained. I also ...
117 views

### Has Cantor's irregular enumeration of rationals ever been discussed?

Enumeration of all positive fractions recently has gained renewed interest (see the list below). By translation invariance we can be sure that in all intervals (n, n+1] of the real axis, there are the ...
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### When was compactness theorem for propositional logic first proven?

Compactness for first-order predicate logic was first proven as a corollary of (Gödel 1930). Does anyone know a reference for the first proof of the compactness of propositional logic? Some proofs ...
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### Why is William Playfair seldom heard about in mathematics?

William Playfair was a Scottish engineer and economist, who invented the pie and bar charts as well as the line graph, which have all played an indubitably ubiquitous role in modern statistics. I hadn'...
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### Who was Hans Bauer who worked on the Perron integral?

I'm referring to the Hans Bauer who is the author of this article from 1915 (H. Bauer, "Der Perronsche Integralbegriff und seine Beziehung auf Lebesguesschen" Monatsh. Math. Phys. , 26 (1915) pp. 153–...
84 views

### What was the content of Sakharov's research into cosmic rays?

According to Wikipedia, Sakharov in his early scientific career investigated cosmic rays. It offers no other details. It claims that it was for this work that he was awarded his doctorate. However ...
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### Who established that $K_e = \frac{1}{4 \pi \varepsilon _m}$?

Coulomb's Law states that : $$F_e = K_e\dfrac{q_1q_2}{r^2}$$ where $q_1$, $q_2$ are magnitudes of the two point charges, $r$ is the distance between them and $K_e$ is Coulomb's Constant (aka ...