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Reference requests: Jitsuro Nagura

I spent some time today looking for any biographical information on Jitsuro Nagura and came up empty-handed. Any suggestions welcome. Also, the Wiki note on the Chebyshev $\psi$ function says that ...
9
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2answers
721 views

Original source for a quote by Lobachevsky

Lobachevsky is quoted in many places to have once written (said?) "There is no branch of mathematics, no matter how abstract, which may not someday be applied to phenomena of the real world." (In the ...
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5answers
398 views

What is a good book about math history?

Which is a good book on math History? I want to give it as a gift to a mathematician.
10
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3answers
838 views

The pronuncation of “Tychonoff” and “Alaoglu”

I am not quite sure this is the place to ask this sort of question, but I am gonna give a talk on Banach algebra in which I will use theorems named after these two mathematicians whose names I can not ...
6
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4answers
836 views

History of analysis?

Any sites detailing the history of analysis post 1820 (to mid 1900s?) - vis-à-vis Cauchy, Weierstrass, Riemann, Bolzano, ..., Kuratowski, Hilbert? It's something that appears quite interesting and I ...
13
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6answers
659 views

Read old articles instead books.

I'd like to know if there is a site, or maybe a collection of books, where I can read old articles in mathematics in order to study topics directly from the source, instead reading books in the field. ...
8
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4answers
3k views

Math story: Ten marriage candidates and 'greatest of all time'

I remember a story about a famous mathematician who was offered ten marriage candidates and had to pick one of them, with the condition he had to meet them in turn and propose during that meeting, ...
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2answers
85 views

Searching for math encyclopedia with inventor / date / source by topic.

I remember to have seen an encyclopedia-type-of mathematics book that describes for each topic contained in it when and by who it was invented or when it was first mentioned. I.e. quaternion: Hamilton,...
0
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2answers
180 views

In which part of the history the man jumped from the intuitive concepts to the most complex ones? [duplicate]

This question explains better what this one tried: Understanding the intuition behind math In the history mathematics we always see how the numbers were created and for what purpose. Like ordering,...
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2answers
760 views

In what senses are archimedean places infinite?

According to Bjorn Poonen's notes here (§2.6), we should add the archimedean places of a number field $K$ to $\operatorname{Spec} \mathscr{O}_K$ in order to get a good analogy with smooth projective ...
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0answers
122 views

When was the term 'ramification' first used in math literature?

In my studies so far, I have had the word 'ramification' come up in Algebraic Number Theory and Complex Analysis. The Wikipedia article tells me that 'ramification' is also used in some other fields. ...
2
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1answer
255 views

What is the origin of the (nearly obsolete) term “binary decimal”?

What is the origin of the (nearly obsolete) term "binary decimal"? At least two important publications in the 1930s used this oxymoron to mean what is now ...
8
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1answer
177 views

Historical reference request: Young tableaux

I am writing up an article on the RSK correspondence. To this end, I want to understand the history behind the invention of the Young tableaux and how it was introduced into the study of the symmetry ...
7
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1answer
263 views

When did free modules first appear?

We study free modules in a Modern Algebra course or by reading a book on Algebra. In any case a free module looks like a vector space, for we consider the generating set and basis... My questions are ...
9
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2answers
729 views

What interview of G. H. Hardy by P. Erdős does Wikipedia refer to?

Quoting from the Wikipedia article on G. H. Hardy (emphasis mine): Starting in 1914, he was the mentor of the Indian mathematician Srinivasa Ramanujan, a relationship that has become celebrated.[...
5
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2answers
201 views

Trig reciprocal function nomenclature?

The fact that the reciprocal of $\sin\theta$ is $\csc\theta$, and the reciprocal of $\cos\theta$ is $\sec\theta$ messed with my head for the longest time when I was taking trig. Why are the functions ...
0
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1answer
464 views

Resurrection of my Tamagawa numbers Question, to understand the Formulation of BSD

My previous question was closed very badly for asking the broad and deep things, so I now understand the consequences of asking such questions, so I refrain from asking such questions, so this is not ...
9
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2answers
450 views

The history of set-theoretic definitions of $\mathbb N$

What representations of the natural numbers have been used, historically, and who invented them? Are there any notable advantages or disadvantages? I read about Frege's definition not long ago, ...
5
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0answers
696 views

Mac Lane and Eilenberg's motivations for category theory

I'm looking to understand the conceptual process that brought Eilenberg and Mac Lane in developing the basic concepts of category theory. I quote Mac Lane's book "Category theory for working ...
14
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2answers
2k views

Why is “h” used for entropy?

Why is the letter "h" (or "H") used to denote entropy in information theory, ergodic theory, and physics (and possibly other places)? Edit: I'm looking for an explanation of the original use of "H". ...
5
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4answers
3k views

On the Origin and Precise Definition of the Term 'Surd'

So, in the course of last week's class work, I ran across the Maple function surd() that takes the real part of an nth root. However, conversation with my professor ...
16
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1answer
579 views

History of Commutative Algebra

There are books on the history of Algebraic Geometry, there are also papers about it (all had done by J. Dieudonné). But I could not find any book or paper about the history of Commutative Algebra. ...
5
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1answer
1k views

What applications of the Residue Theorem to real integration have had the biggest impact outside of pure math?

A typical undergraduate student (at least in North America) learns about integration of real-valued functions of one real variable, and learns some of its applications to science and probability, e.g. ...
12
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3answers
468 views

Is there any difference between a math invention and a math discovery? [closed]

From wikipekia: The calculus controversy was an argument between 17th-century mathematicians Isaac Newton and Gottfried Leibniz (begun or fomented in part by their disciples and associates – ...
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2answers
3k views

Development of the Idea of the Determinant

While I basically understand what a determinant is, I wonder how this idea was developed? What was the principal idea behind its origination? I would like to know this so that I can have a better ...
18
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2answers
1k views

Who are some forgotten mathematicians? [closed]

In Thomas' Calculus, he presents ''Nicole Oresme's Theorem'': $$ \sum_{n=1}^\infty {n\over 2^{n-1}}=4. $$ My first reaction was "who is this person?''. As it turns out, he was a Frenchman from the $...
28
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3answers
2k views

When did Fubini's name get applied to the theorem without measures?

Fubini's theorem, from 1907, expresses integration with respect to a product measure in terms of iterated integrals. The simpler version of this theorem for multiple Riemann integrals was used long ...
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0answers
184 views

A full math history encyclopedia. Is there one?

Is there a book or a site or a periodic or a encyclopedia or something like this that's a complete reference in math history, talking about all known mathematicians and their achievements, not ...
11
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4answers
1k views

What was the notation for functions before Euler?

According to the Wikipedia article, [Euler] introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical ...
15
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1answer
601 views

Polarization: etymology question

The polarization identity expresses a symmetric bilinear form on a vector space in terms of its associated quadratic form: $$ \langle v,w\rangle = \frac{1}{2}(Q(v+w) - Q(v) - Q(w)), $$ where $Q(v) ...
0
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1answer
206 views

Where does the % symbol originate from? [duplicate]

Possible Duplicate: What is mathematical basis for the percent symbol (%)? Where does the % symbol originate from?
7
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3answers
294 views

The Hopfian property for groups

Let $G$ be a group, which for my purposes would be abelian. To say that $G$ has the Hopf property is to say that every epimorphism of $G$ is an automorphism. Does anyone happen to recall the context ...
10
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3answers
914 views

Who introduced the notation $x^2$?

In the book 'Problem Solving and Number Theory' I read The law of quadratic reciprocity was discovered for the first time, in a complex form, by L. Euler who published it in his paper ...
10
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1answer
386 views

Is Hilbert's second problem about the real numbers or the natural numbers?

In his famous "23 problems" speech, Hilbert gave his second problem as follows: The axioms of arithmetic are essentially nothing else than the known rules of calculation, with the addition of the ...
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0answers
1k views

History of mathematical symbols, especially the symbol for right angle

Yesterday a child asked me, why (historically) a right angle is denoted by an arc and a dot like in this picture: I dont't know it, but I am interested in it too, so I post this question to this ...
0
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1answer
1k views

History of solving linear equations with matrices

I'm solving linear equations with matrices right now and I wonder, how did it start. Who, how, why came to idea that such kind of equations could be solved with matrices? What was first: matrix or ...
13
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2answers
3k views

Curious about math and Soviet Union

Why so many very good books were written by authors with Russian surnames?
11
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1answer
724 views

Why is $i$ called “imaginary”?

I was reading this question, and, after reading the responses, I felt like I had a much better understanding about how they're just another type of number definition. Why, then, are they called ...
18
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1answer
688 views

Did Leonardo of Pisa prove $n=4$ case of FLT?

Reputable on-line sources agree that Leonard 'Fibonacci' proved the nonexistence of positive-integer solutions to $c^4 - b^4 = a^2$ . Yet my change to Wikipedia to reflect this was reverted. I hope ...
7
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2answers
222 views

Which is the primary source of the Conway base 13 function?

I have been looking for the first appearance of the Conway base 13 function in the literature, but the only thing I have found is the wikipedia article whose unique element in the bibliography I ...
4
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2answers
275 views

Rota's “lure of the algorithm”?

Quoting Gian-Carlo Rota (from the Foreword to Richard Stanley's Enumerative Combinatorics Volume I), "In mathematics, however, the burden of choice faced by the writer is so heavy as to turn off all ...
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2answers
2k views

Origins of the modern definition of topology

The modern definition of topology is 'a family of subsets of a set $X$ containing the empty set and $X$, closed under unions and finite intersections'. In Grundzüge der Mengenlehre (1914) Hausdorff ...
3
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1answer
1k views

Why are variables lowercased?

While contemplating the existence of math, I came across an interesting problem: Why are variables often lowercased? There may not be a reason, but if there is, I would like to find out. Maybe it's ...
0
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1answer
185 views

When - during the study and development of- - and how were complex numbers introduced in the study of [real-valued] power series (expansions)?

Follow-up to: Mathematical reason for the validity of the equation: $S=1+x^2S$ and General question on relation between infinite series and complex numbers (This question seems broad at this stage, ...
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2answers
384 views

What is the origin of the prefix logic notation used in WFF 'N PROOF?

The classic "modern logic" game of WFF 'N PROOF uses a set of symbols to represent logical relations that I've seen used nowhere else: $C$ for then; $A$ for or; $K$ for and; $E$ for if and only if; ...
1
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1answer
392 views

Why is the zero factorial one i.e ($0!=1$)? [duplicate]

Possible Duplicate: Prove $0! = 1$ from first principles Why does 0! = 1? I was wondering why, $0! = 1$ Can anyone please help me understand it. Thanks.
3
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0answers
251 views

What's the origin of the terminology “Normalization” in commutative algebra?

Since the terminology "normal", "normalized", etc has different meanings in mathematics (some geometric in flavor, like when referring to perpendicularity) and I just read in Eisenbud's book on ...
18
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2answers
1k views

Once and for all - “Rational numbers” - because of ratio, or because they make sense?

This is a question I'm sure was asked before but I can't find it. There are many sources claiming that the term "rational number" for the elements of $\mathbb{Q}$ comes from the word "ratio", since a ...
8
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2answers
806 views

Historical basis and mathematical significance of Riemann surfaces

It is written in Riemann Surfaces (Oxford Graduate Texts in Mathematics) by Simon Donaldson, that: "[t]he theory of Riemann surfaces occupies a very special place in mathematics. It is a culmination ...
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2answers
185 views

History of the vocabulary for group extensions

In regular everyday English if you say something like "A was extended by B to get C", to me it means that A was in existence, B was added onto it, and now there is a larger object C. For example, "...