# Tagged Questions

Use this tag for questions concerning history of mathematics, historical primacies of results, and evolution of terminology, symbols, and notations. Consider if History of Science and Mathematics Stack Exchange is a better place to ask your question.

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### Why are $\pi$ and $e$ simply referred to as “pi” and “e”?

I'm aware of the names "Archimedes' constant" and "Euler's number" for $\pi$ and $e$ respectively, but these don't seem to be used very commonly. Even in school I remember $\pi$ and $e$ being almost ...
379 views

### Generalizing complex numbers: Is there a mathematical system isomorphic to 3 dimensional space?

As I understand it, complex numbers: $ax+i$ are isomorphic to two-dimensional space. Quaternions consist of $4$ dimensions. Is that right? Wikipedia says "quaternions form a four-dimensional ...
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### Prime Counting: In truncation rule #2 mentioned in an AMS.org article, I'm unclear how “special leaves” work?

I'm reading through an AMS.org article on prime counting. The article covers the history of prime counting and focuses on improvements to the Meissel-Lehmer method. It is the improvement on page ...
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### Did Ackermann produce a finitary consistency proof of second-order $PRA$?

In Wilhelm Ackermann's Doctoral Thesis (it is claimed, by Richard Zach, for one, in his paper "The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program", arXiv: math/...
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### What are the disadvantages of non-standard analysis?

Most students are first taught standard analysis, and the might learn about NSA later on. However, what has kept NSA from becoming the standard? At least from what I've been told, it is much more ...
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### What is the origin of the name Hermitian and Unitary matrix?

A matrix $H$ is Hermitian if $H ^\dagger = H$. A matrix $U$ is Unitary if $U^\dagger=U^{-1}$. My question is: Why do we name matrices of such properties Hermitian and Unitary? These names are non-...
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### Where do hash functions come from?

I have some basic understanding of how hash functions work, however, I have no idea of how mathematicians created them. Were them a byproduct of a non cryptografics related research or were them a ...
1k views

### What's an example of an infinitesimal?

If you want to use infinitesimals to teach calculus, what kind of example of an infinitesimal can you give them? What I am asking for are specific techniques for explaining infinitesimals to students, ...
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### Trying to understand how Lehmer's method represents a simplification of Meissel's method for counting primes

My question stems from a wikipedia article on prime counting. The details on Meissel's method can be found in the wikipedia article. As I understand, Meissel proposed two formulas which I asked ...
139 views

### Peano Arithmetic before Gödel

If I understand correctly, Gödel was the one to discover how to encode finite sequences of integers in Peano Arithmetic, with his Chinese Remainder Theorem trick (his "beta function"). As a ...
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### What did Whitehead and Russell's “Principia Mathematica” achieve?

In philosophical contexts, the Principia Mathematica is sometimes held in high regard as a demonstration of a logical system. But what did Whitehead and Russell's Principia Mathematica achieve for ...
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### Why Frobenis concerned the groups which today called “Frobenius Group”?

From their work, it seems that the Ancient mathematicians were investigating a mathematical object not as a fun, but to solve some problem occurred in earlier work of someone. Lagrange, Galois, Abel ...
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### Unclear on why Meissel's approach to counting primes works

I am reading through the Wikipedia article on prime counting. The following is presented to describe Meissel's approach: Let $p_1, p_2, \dots, p_n$ be the first $n$ primes. Let $\Phi(m,n)$ be the ...
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### Deriving the wave equation in 3 dimensions and the history of it

I'm trying to find how the wave equation was derived in 3 dimensions. Surprisingly, there isn't much information available on this apart from wikipedia of all places https://en.wikipedia.org/wiki/...
140 views

### Who is “R. Drabek”?

The book "Algebra für Einsteiger" bei Bewersdorff (I think the English edition is called "Galois Theory for Beginners") starts with a nice quotation: Math is like love; a simple idea, but it can ...
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### Proofs of Simplicity of $A_n$

There are different proofs of simplicity of the group $A_n$, and one can get at least two proofs by choosing randomly 10 books of the subject, so I will not go into what are these proofs? Rather, I ...
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### Separability and second countability is the same thing to Halmos

I was browsing through Paul Halmos' classic book on measure theory, when I came by the following definition of separability on page $3$ in the chapter on prerequisites: Today a separable space is ...
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### Characterizations of Nilpotent Groups

There are several characterizations of finite nilpotent groups (they are, as in wiki): $G$ is (finite) nilpotent group. Normalizer of every proper subgroup is bigger than the subgroup. Every ...
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### History of graph minor concept

I can't find the correct reference to the first introduction of graph minor. There are plenty of strong results on minors (Kuratowski theorem, well-quasi-ordering by Robertson and Seymour, ...) and ...
572 views

### Serendipitous mathematical discoveries in recent times

As of today, most important results in mathematics are conjectured long before they are proven. Are there any examples of (important) mathematical discoveries that were proven by chance rather than ...
4k views

### Past open problems with sudden and easy-to-understand solutions

What are some examples of mathematical facts that had once been open problems for a significant amount of time and thought hard or unsolvable by contemporary methods, but were then unexpectedly solved ...
629 views

### Why is the word associative used to represent the concept of the associative property?

For the commutative property ... According to wikipedia: The word "commutative" is a combination of the French word commuter meaning "to substitute or switch" and the suffix -ative meaning "...
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### What is the origin of the distinction between assignable and inassignable number?

Leibniz described his infinitesimals as being inassignable numbers in a number of texts, e.g., in his Cum Produisset that was analyzed in detail by H. Bos in a seminal text dating from the 1970s. The ...
307 views

### Errors in math research papers [duplicate]

Have there been cases of errors in math papers, that were undetected for so long, that they caused subsequent errors in research, citing those papers. ie: errors getting propagated along. My ...
37 views

### Reference on the history of ergodic theory

I'm looking for some good books on the history of ergodic theory. I'm a Ph.D student in the field, and I am taking Steven Weinberg's advice to learn about the history of my field: http://math....
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### Local Solid Angle Units

This is a cultural question: Are there any, even moderately or historically used, units that measure solid angles which are not steradians? Basically, is there a unit x such that x:sr::grad:rad?
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### Where is the definition of the derivative formula derived from?

I know what the definition of the derivative is , however, I am curious where this comes from mathematically.
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### What “linguistic and philosophical problems” might be inherent in trigonometry?

In "A Mathematician’s Lament", Paul Lockhart derides the "status quo" of math education, claiming that "mathematics is an art form done by human beings for pleasure" but instead is taught "devoid of ...
22 views

### Did the symbol for expectation value originate in bra-ket notation?

I was just wondering, whether the common $\langle x \rangle$ symbol for the expectation value of a variable originates in the bra-ket notation of quantum physics? I would think that a fundamental ...
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### On non-modular lattices and orto-modularity

I would like to have a definition for non-modular lattices which clearly sets them appart from their modular counterparts, thereby focusing on their main distinctive feature. Besides, I would be very ...
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### Why did Euclid call 6 a perfect number?

The old Greek did not consider $1$ a number. Nevertheless Euclid called $6 = 1+2+3$ a perfect number. How could he use $1$ which was not a number?
101 views

### Connection of Fourier's work with Fredholm's

Im trying to formulate for myself in what sense Fredholms work on the Dirichlet problem is connected to Fouriers work on the heat equation. Fourier idea seems to have fundamental problems with ...
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### Why do we use a single 'dash' for difference : $-$ and a double 'dash' for sum: $+$? [closed]

Why do we use a single 'dash' for difference : $-$ and a double 'dash' for sum: $+$? Just a shower thought: Who came up with this notation? It kind of makes it look like the difference is simpler ...