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

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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 ...
15
votes
1answer
990 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
335 views

Weierstrass M-Test

What does "M" stand for in Weierstrass M-Test? Just asking...
6
votes
1answer
489 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
224 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
763 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
500 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
189 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
votes
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
285 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? ...
13
votes
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.
64
votes
12answers
10k 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
425 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 ...
38
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
836 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
votes
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
683 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
550 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
1k 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
644 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
613 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
277 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
votes
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 ...
32
votes
19answers
2k views

Which mathematicians have influenced you the most?

This question is lifted from Mathoverflow.. I feel it belongs here too. There are mathematicians whose creativity, insight and taste have the power of driving anyone into a world of beautiful ideas, ...
40
votes
3answers
2k views

History of the Concept of a Ring

I am vaguely familiar with the broad strokes of the development of group theory, first when ideas of geometric symmetries were studied in concrete settings without the abstract notion of a group ...