Use this tag for questions concerning history of mathematics, historical primacies of results, and evolution of terminology, symbols, and notations.

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18
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1answer
3k views

Where did the word “logarithm” come from?

Where did the word logarithm come from? Any relation to the word algorithm?
5
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1answer
929 views

Who was the mathematician who thought “god” was out to get him?

Wasn't there a mathematician who was convinced that "god" was out to get him? When he was travelling by sea he would write a friend a letter claiming that he had finally proved a difficult theorem ...
16
votes
2answers
2k views

History of dot product and cosine

The fact that the dot product and the cosine of the angle between two vectors are mutually computable is easy to show (see the two sides in the two answers at Dot product in coordinates). But looking ...
13
votes
2answers
1k views

Etymology of $\arccos$, $\arcsin$ & $\arctan$?

Does anyone know the origin of the words $\arccos$, $\arcsin$ & $\arctan$? That is to say, why are they named like this? What connects "arc" with inverse? Can't seem to find out via Google. ...
5
votes
1answer
582 views

Why is Harish-Chandra's last name never used?

This is only barely a math question but I don't know where else to ask. I've always wondered about Harish-Chandra's name. The Wikipedia article seems to mention "Mehrotra" as a last name but only in ...
2
votes
1answer
591 views

How to “grok all the major pieces” of math

To start really getting somewhere with attacking hard problems in the wild, I would guess we need to have a cursory understanding of a wide variety of math topics, and how they link together. How ...
25
votes
1answer
2k views

What concept does an open set axiomatise?

In the context of metric (and in general first-countable) topologies, it's reasonably clear what a closed set is: a set $F$ is closed if and only if every convergent sequence of points in $F$ ...
11
votes
3answers
2k views

Why has the Perfect cuboid problem not been solved yet?

Why hasn't Perfect Cuboid Problem been solved yet, whereas (possibly) more nontrivial ones such as FLT and Sphere packing have been solved? I understand that calling some problems more nontrivial ...
34
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7answers
7k views

Good books on Math History

I'm trying to find good books on the history of mathematics, dating as far back as possible. There was a similar question here Good books on Philosophy of Mathematics, but mostly pertaining to ...
24
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11answers
6k views

Good books on Philosophy of Mathematics

Where can I learn more about the implications, meta discussions, history and the foundations of mathematics? Is Russell's Introduction to Mathematical Philosophy a good start?
3
votes
1answer
979 views

What does matrix multiplication have to do with scalar multiplication?

Why are matrix and scalar multiplication denoted the same way and treated as the same operation in standard mathematical notation? This is always a source of confusion for me because they have ...
53
votes
17answers
15k views

Anecdotes about famous mathematicians or physicists

I'm not sure whether this question suits this website, however, I don't know where else I could ask it. It is no mathematical problem or something similar, still I hope it won't be closed. A few ...
5
votes
2answers
568 views

Reference request: Riemann's paper on abelian functions

I don't know if this is the right kind of question for here. But, can someone help me find an english translation (a link to a pdf would be nice) of: B. Riemann, "Theorie der Abelschen Funktionen", ...
8
votes
4answers
884 views

Uses of the 'Golden Ratio'

I have heard much about the numerous appearances of the ratio found in nature: 1.6180339887. Are there any actual mathematical uses that have been found of this number? What are its advantages? Just ...
78
votes
16answers
8k views

Why did mathematicians take Russell's paradox seriously?

Though I've understood the logic behind's Russell's paradox for long enough, I have to admit I've never really understood why mathematicians and mathematical historians thought it so important. Most ...
158
votes
22answers
9k views

Why do mathematicians use single-letter variables?

I have much more experience programming than I do with advanced mathematics, so perhaps this is just a comfort thing with me, but I often get frustrated trying to follow mathematical notation. ...
33
votes
4answers
2k views

Understanding the intuition behind math

I'm currently a Calculus III student. I enjoy math a lot, but only when I understand its beauty and meaning. However, so many times I have no idea what it is I am learning about, althought I am still ...
16
votes
1answer
1k views

Did the Appel/Haken graph colouring (four colour map) proof really not contribute to understanding?

I hope this isn't off topic - sorry if I'm wrong. In 1976, Kenneth Appel and Wolfgang Haken proved the claim (conjecture) that a map can always be coloured with four colours, with no adjacent regions ...
6
votes
1answer
339 views

Weierstrass M-Test

What does "M" stand for in Weierstrass M-Test? Just asking...
6
votes
1answer
492 views

Best place to find open questions / latest research

Is there a central wiki or something where open questions (and relevant research on them) takes place?
4
votes
1answer
225 views

Origin of mathematical use of “orbit”

If $G$ is a group acting on a set $S$, then the "orbit" of a point $x$ in $S$ is defined as the set of all elements of the form $gx$ where $g \in G$. My question: why was the word "orbit" chosen for ...
20
votes
2answers
769 views

A place to learn about math etymology?

I was recently wondering where the word `kernel' comes from in mathematics. I am sure the internet must know. I did manage to find http://www.pballew.net/etyindex.html#k which contains the origin ...
7
votes
3answers
502 views

Why are they called “Isothermal” Coordinates?

If I understand correctly, Gauss proved that given any oriented Riemannian surface, one can find a complex structure on the surface so that the metric on the charts is just $f|dz|$, where $f>0$. ...
31
votes
1answer
1k views

History of “Show that $44\dots 88 \dots 9$ is a perfect square”

The problem Show that the sequence, $49, 4489, 444889, \dots$, gotten by inserting the digits $48$ in the middle of the previous number (all in base $10$), consists only of perfect squares. ...
6
votes
1answer
191 views

Where can I find a time scale (or anything similar) listing the main discoveries and achievments in mathematics?

I am currently preparing my next physics exam, and I got courious if there may be on the Net some sort of time scale of mathematical discoveries, so that I could compare discoveries and achievements ...
10
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6answers
1k views

Historical textbook on group theory/algebra

Recently I have started reading about some of the history of mathematics in order to better understand things. A lot of ideas in algebra come from trying to understand the problem of finding ...
6
votes
1answer
288 views

What is the origin of the term “Differentiable”?

I was wondering today about why the word differentiable is used for describing functions that have a derivative or are differentiable. Perhaps because originally one considered finite differences? ...
14
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3answers
5k views

How did the square root get its shape?

I was wondering when in history did people start use the $\sqrt{}$ sign for square root, what did they use before, and why this curious nomenclature is adopted.
65
votes
12answers
11k views

Is zero odd or even?

Some books say even numbers start from two but if you consider the number line concept, I think zero should be even because it is in between -1 and +1 (i.e in between 2 odd numbers). What is the real ...
4
votes
2answers
426 views

Politics of the Adelics

The adelics seem counter-intuitive. I wonder how they came up originally, and what was the immediate reward for introducing them. What was the politics of introducing the adelics into mathematical ...
39
votes
6answers
4k views

How hard is the proof of $\pi$ or $e$ being transcendental?

I understand that $\pi$ and $e$ are transcendental and that these are not simple facts. I mean, I have been told that these results are deep and difficult, and I am happy to believe them. I am curious ...
11
votes
7answers
840 views

What's the hard part of zero?

A lot of textbooks said it was hard for human to accept zero when it was first introduced. How could it be? It seems to me as natural as positive integer which represent there is no elements at all.
31
votes
2answers
1k views

Image of a math problem that was stated in Cuneiform, Arabic, Latin and Finally in modern math notation

Many years ago a lecturer of mine had a photocopy of a page from a book containing a math problem ( I think it was a simple quadradic equation ) that was stated/solved in Cuneiform, Arabic, Latin ...
8
votes
2answers
1k views

Khayyam's work on cubic equations

Omar Khayyam is known for his significant progress in solving cubic polynomial equations. For example, his biography on www-history.mcs.st-andrews.ac.uk says (...) This problem in turn led Khayyam ...
3
votes
2answers
253 views

Why do our number start over at million, billion, etc

In English (I think this is universal anyway) we use the 1s, 10s, and 100s in a cycle. One, one thousand, one million; twenty two, twenty two thousand, twenty two million; one hundred and forty six, ...
10
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6answers
6k views

Why do we need vectors and who invented it?

It is natural to understand the need for scalars (numbers), but why did we invent vectors? Who invented it and for what? EDIT: As George Lowther pointed out, the problem is too broad; I added the ...
2
votes
1answer
189 views

Is the above statement true for maths?

In maths, you can use something as simple as statistical analysis to intuit the theory, and in comp-science you can use simulators. Is the above statement true for maths ?
3
votes
1answer
278 views

Inconsistent naming of elliptic integrals

This may be a question whose answer is lost in the mists of time, but why is the elliptical integral of the first kind denoted as $F(\pi/2,m)=K(m)$ when that of the second kind has $E(\pi/2,m)=E(m)$? ...
0
votes
1answer
160 views

Alternative, consistent frameworks of mathematics with isomorphic mappings to physical phenomenon

A friend of mine who is quite an aggressive Nominalist told me the other day: "Mathematics and numbers are arbitrary; they can accurately predict physical systems in real life only because they are ...
13
votes
2answers
1k views

Why is it called Sylvester's Law of Inertia?

By "Sylvester's Law of Inertia," I mean: http://en.wikipedia.org/wiki/Sylvester%27s_law_of_inertia How does "Law of Inertia" with the statement of the theorem? I guess it's from physics, but... I ...
7
votes
4answers
690 views

Can Leibniz Notation Be Treated As a Quotient?

Why is saying $\frac{dy}{dx}\frac{dy}{dx}=y\frac{d^2y}{(dx)^2 }$ not valid? Does Leibniz notation (and thinking of it as an infinitesimal quotient) not work for higher-order derivatives?
1
vote
3answers
561 views

Book recommendation on the history of PDE/ODE?

I would like to know something like what's the first PDE etc. Could you recommend book on the history of PDE/ODE? thanks.
12
votes
2answers
2k views

Why the name 'FACTORIAL'?

Factorial is defined as $n! = n(n-1)(n-2)\cdots 1$ But why mathematicians named this thing as FACTORIAL? Has it got something to do with factors?
4
votes
3answers
2k views

What is Modern Mathematics? Is this an exact concept with a clear meaning? [closed]

Motivated by this question I would like to know whether there is an exact definition of modern mathematics. In which point in time (century, decade) does one think, when speaking about modern ...
2
votes
4answers
647 views

What is your favorite isomorphism? [closed]

By "isomorphism" I mean any structure-preserving map with a structure-preserving inverse. (Please accept my advance apology if this question is out of bounds. I sense that it's borderline, but I'm ...
7
votes
2answers
617 views

When did the term “tuple” get its current meaning?

In a recent discussion, someone told me tuples in the modern meaning (in particular, tuples are heterogeneous: that is, different elements of a tuple can belong to different sets/have different ...
6
votes
4answers
5k views

Why are x and y such common variables in today's equations? How did their use originate?

I can understand how the Greek alphabet came to be prominent in mathematics as the Greeks had a huge influence in the math of today. Certain letters came to have certain implications about their ...
3
votes
4answers
278 views

Definition of an Algebraic Objects

How did the definition of Algebraic objects like group, ring and field come up? When groups were first introduced, were they given the 4 axioms as we give now. And what made Mathematicians to think of ...
18
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8answers
4k views

How did the notation “ln” for “log base e” become so pervasive?

Wikipedia sez: The natural logarithm of $x$ is often written "$\ln(x)$", instead of $\log_e(x)$ especially in disciplines where it isn't written "$\log(x)$". However, some mathematicians ...
10
votes
8answers
3k views

Why are derivatives specified as d/dx?

Is the purpose of the derivative notation d/dx strictly for symbolic manipulation purposes? I remember being confused when I first saw the notation for derivatives - it looks vaguely like there's ...