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

learn more… | top users | synonyms (1)

2
votes
0answers
19 views

history of holomorphic implies analytic and goursat theorem

I'm studing complex analysis and am curious about its history. Did Cauchy know that holomorphic functions (to have derivative in every point of an open set) are infinitely derivable? and that they ...
-2
votes
1answer
130 views

How values of the constants are derived mathematically? [closed]

As said by Jan regarding constant value $\pi$ ,Imagine you have a circle and you are able to measure its circumference "c". Then, you can also find out what its diameter "d" is. When you divide ...
2
votes
1answer
97 views

Why is the nuclear norm called so?

A simple question. Why is the sum of the singular values of a matrix called its nuclear norm? What is the origin of, and motivation for, this term? Apparently the term nucleus is sometimes used to ...
12
votes
5answers
489 views

When can ZFC be said to have been “born”?

The "History" section of the Wikipedia article on ZFC isn't particularly helpful. The only thing I have understood from it is that ZFC had appeared after 1922. In what book or paper was ZFC first ...
1
vote
1answer
40 views

How to graph in hyperbolic geometry?

I was given the following question regarding hyperbolic geometry: In the hyperbolic geometry in the upper half plane, construct two lines through the point $(3,1)$ that are parallel to the line ...
0
votes
2answers
56 views

why soh cah toa is right?

i am confused by the sine of an angle, (it might appear evident for some of you but please i am not an expert ). sine of an angle is says to be the half of the magnitude of the chord of 2 time the ...
19
votes
3answers
2k views

What is the origin of the expression “Yoneda Lemma”?

Thank you very much in advance for telling where the expression “Yoneda Lemma” comes from. EDIT 1. On page -14 of Reprints in Theory and Applications of Categories, No. 3, 2003. Abelian Categories, ...
2
votes
1answer
69 views

How old is the distinction of right homotopy from left homotopy?

Going into the 1960s it seems to me that topologists saw path spaces as an advanced idea, useful in come contexts but not fundamental. So they took homotopy of maps as basically what is now called ...
0
votes
1answer
30 views

What is the example called, where someone was wrongly convinced of a sequence function because of naive induction.

I remember I have seen a classical example of a mistake, where someone was convinced that a sequence defined somehow had a close form, which did in turn work until some very high $n$. I think the ...
13
votes
2answers
346 views

Before Abel's proof, what did they used for trying to find the general solution for quintics?

Whenever I read about the history of algebra, I end up with the same conclusion: They solved the general cubic, then the general quartic and then spent lots of years trying to solve the general ...
-6
votes
0answers
53 views

Why was Ramanujan compared to Jacobi? [on hold]

Both Hardy compare him only with Euler or Jacobi and Littlewood I can believe that he's at least a Jacobi compared Ramanujan to Jacobi to indicate his mathematicial ability. Of course ...
15
votes
9answers
2k views

Why are the Trig functions defined by the counterclockwise path of a circle?

My understanding is that $\cos$ is defined by the value of $x$ as you trace the graph of a circle counterclockwise, starting at the point $(1, 0)$. Similarly, $\sin$ traces the $y$ value. I understand ...
0
votes
1answer
42 views

How are gigantic primes actually defined in the 1992 article by Samuel Yates?

The Prime Glossary states: In a 1992 article, Samuel Yates coined the name gigantic prime for any prime with 10,000 or more decimal digits (he had also coined the term titanic primes a decade ...
3
votes
0answers
46 views

Reference request for Grothendieck's work on “Integration with values in a topological group”

Recently I was reading the available part of the second part of W. Scharlau's book on Alexandre Grothendieck (see here). There I found, An anecdote survives about Grothendieck's arrival in Nancy: ...
1
vote
1answer
245 views

Why must there be an infinite number of lines in an absolute geometry?

Why must there be an infinite number of lines in an absolute geometry? I see that there must be an infinite number of points pretty trivially due to the protractor postulate, and there are an infinite ...
23
votes
2answers
4k views

How was the normal distribution derived?

Abraham de Moivre, when he came up with this formula, had to assure that the points of inflection were exactly one standard deviation away from the center, and so that it was bell-shaped, as well as ...
-5
votes
0answers
37 views

Would any experts be interested in helping me accumulate a knowledge database, for mathematical concepts? [closed]

I'm building a free learning service with crowd sourced information for mathematical concepts. The topics can be widely varying, as I believe users will be looking up an infinite number of topics. All ...
2
votes
4answers
204 views

Why do we use degrees? [closed]

I see a lot of people who ask why we use radians instead of degrees. But why do we use degrees instead of radians. In the cases we use degrees instead of radians, what convenience does it bring? The ...
3
votes
2answers
75 views

Mathematic books with historical and original view

I am looking for books along the lines of history of mathematics but I have some conditions; History must not be the main aim of the book, the main aim of using historical context should be ...
1
vote
0answers
23 views

Weak convergence in probability and functional analysis

Let $X$ be a metric space. By definition, the sequence of Borel measures $\mu_n$ on $X$ converges weakly to a measure $\mu$, if for all bounded continuous functions $f:X\to\mathbb{R}$ we have ...
0
votes
1answer
59 views

What is the first absolutely normal number to be discovered?

What is the first absolutely normal number to be discovered? Is it the Chaitin's constant? $$\Omega_F = \sum_{p \in P_F} 2^{-|p|}$$
0
votes
0answers
13 views

Oka's coherence theorem and Cartan's theorem A and B

So reading up on some articles I've found that whilst attempting to characterize Oka's coherence theorem in sheaf-theoretic language, Cartan was ultimately led to formulating his theorem A and B in ...
10
votes
7answers
351 views

On a definition of manifold

In the book Mathematical Masterpiece, on page 160, the authors wrote that A manifold, in Riemann's words, is a continuous transition of an instance I know a manifold is something glued by ...
4
votes
2answers
126 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 ...
4
votes
2answers
380 views
3
votes
1answer
126 views

Who proved Fundamental Theorem of algebra using Liouville's theorem?

One of the most famous proofs of the Fundamental Theorem of Algebra involves Liouville's theorom stating that a bounded entire function in constant. Who first came up to the idea of deriving FToA ...
103
votes
34answers
17k views

Examples of mathematical results discovered “late”

What are examples of mathematical results that were discovered surprisingly late in history? Maybe the result is a straightforward corollary of an established theorem, or maybe it's just so simple ...
0
votes
3answers
80 views

History and early development of Mathematics

Please provide references (books, articles, websites links, video links) that describe the conceptual development of calculus, complex numbers, group theory, matrix and linear algebra. I am curious to ...
3
votes
1answer
58 views

Gauss: The study of Euler's works…

I keep coming across this quote by Gauss but I haven't actually been able to locate the original source: “The Study of Euler’s works will remain the best school for the various fields of mathematics ...
6
votes
1answer
131 views

Personal notebooks of a Fields medalist

I once read that some Fields medalist published all of his personal handwritten notebooks, and that they are freely available somewhere on the net. I can't remember whose mathematician it was, so I ...
4
votes
1answer
82 views

Why isn't '&' used for logical conjunction?

There is a beautiful and well-established logogram for "and" that is known to virtually every more or less educated person in the world - it's the ampersand '&'. It's completely unambiguous, as ...
16
votes
1answer
542 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. ...
3
votes
4answers
313 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 ...
45
votes
3answers
3k 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 ...
12
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
434 views

Chinese estimate for $\pi$. Were they lucky?

The famous chinese estimate $\pi\approx\frac{355}{113}$ is good. I think that is too good. As a continued fraction: $$\pi=[3:7,15,1,292,\ldots]$$ That $292$ is a bit too big. Is there a reason for a ...
3
votes
1answer
37 views

Why can we identify complex numbers as points on a plane?

Modern mathematicians seem to define the complex number $a+bi$ as the ordered pair $(a,b)$, with the usual rules for complex addition and multiplication. I'm reading a book on the history of the ...
0
votes
2answers
73 views

Cauchy's contribution

Sometime, I believe perhaps 2 years, ago I asked a question about breakthroughs, such as those within mathematics and physics which may lead a whole discipline forwards in many ways. One example from ...
10
votes
0answers
131 views

Did Landau prove that there is a prime on $\bigl(x,\frac65x\bigr)$?

Was Landau the first to prove that there is a prime on $\bigl(x,\frac65x\bigr)$? In his Handbuch $\!^1$ discussing the limit $$\lim_{n\to\infty} ...
3
votes
1answer
94 views

why can't quintics be solved by radicals and the relevance of permutations of roots of polynomials

I am seeking to learn about the motivation in the development of group theory. It has been a few years since algebra, and we got as far as rings and fields. I am aware that there were several ...
33
votes
4answers
2k views

Why weren't continuous functions defined as Darboux functions?

When we were in primary school, teachers showed us graphs of 'continuous' functions and said something like "Continuous functions are those you can draw without lifting your pen" With this in ...
9
votes
1answer
404 views

Bourbaki and the symbol for set inclusion

Which notation ($\subset$ or $\subseteq$) was preferred by Bourbaki for set inclusion (not proper)? A side question: Was the notation for subset one of the many notations invented by Bourbaki?
6
votes
2answers
676 views

What is “Bourbaki's style in mathematics”?

I know Nicolas Bourbaki "is the pseudonym of a group of (mainly) French mathematicians who publish an authoritative account of contemporary mathematics." But what characterizes "Bourbaki's style in ...
6
votes
0answers
140 views

Is Bourbaki unique?

So my understanding is that a while back a group of mostly French mathematicians, under the pseudonym Bourbaki, wrote a somewhat austerely written series titled "Elements of Mathematic(s)" covering a ...
2
votes
1answer
183 views

What is the legacy of Bourbaki?

As I was preparing a short lecture (for amateurs) on the mathematics of the '900, I realized that this year marks the 70-th anniversary of the founding of the Bourbaki group. I remember that Bourbaki ...
1
vote
1answer
91 views

"Problems worthy of attack prove their worth by fighting back.”

That is quote has been attributed to Piet Hein, inventor of the Soma cube, which is how I know of him. Q. Is the attribution correct? I wonder because the quote has a nice ring in English that ...
3
votes
0answers
32 views

Historical use of k in proof by induction

Does anybody know the history of why the symbol k is used in proof by induction? As an example, in physics the symbol p is used for momentum because Newton called it impetus, and the letters i and m ...
42
votes
20answers
3k views

Which mathematicians have influenced you the most? [closed]

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, ...
-1
votes
2answers
176 views

Andrew Wiles' Abel Prize for FLT - delayed or not? [closed]

Andrew Wiles was recently awarded the Abel Prize for his work proving Fermat's Last Theorem (FLT). The Abel Prize has existed for 14 years. From my layperson's perspective, it would seem that he ...
-3
votes
1answer
56 views

Mersenne numbers fail primality test at 2047 itself. How could we believe Mersennes are primes?

M$_{11}=2047$ is a composite number. How could one, not check the primaility of such a small number and believe that all Mersenne numbers are primes?