4
votes
2answers
107 views

Who invented or used very first the double lined symbols $\mathbb{R},\mathbb{Q},\mathbb{N}$ etc

Who invented or used very first the double lined symbols $\mathbb{R},\mathbb{Q},\mathbb{N}$ etc. to represent the real number system, rational number system, natural number system respectively?
6
votes
6answers
208 views

Interviews of famous modern mathematicians

I was wondering, are there any good collections of interviews of famous modern mathematicians? It can be text interviews, or audio or video recordings. I am not sure what exactly I mean by "modern". ...
2
votes
1answer
53 views

The term “Homotopy” was given by whom?

I want to know the names who define the term 'Homotopy' in algebraic topology in 1907. Are they Dehn and Paul Heegaard? What is the full name of Dehn? Thank you in advance.
6
votes
1answer
173 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 ...
4
votes
2answers
76 views

How did self-similarity come into mathematics?

As far as I understand the interest in self-similarity was born outside of mathematics. The textbooks I came across give a few objects as examples (tree, broccoli, river, etc) yet it's clear that the ...
30
votes
6answers
1k views

Why are integrals called integrals?

What is the historical background for this term? I cannot quite see what is integral about an integral, even if we go back to the viewing it as the area under a curve. It seems a strange choice of ...
1
vote
1answer
85 views

Why do different countries/regions have different methods of counting large numbers?

When we start counting large quantities of $10's$, the number system varies by country/region: Europe/US: $10^3$ (thousand, million, billion are all multiples of $10^3$) Japan/China/Korea: $10^4$ ...
3
votes
3answers
95 views

Colloquialisms in Math Terminology

What are some of your favorite colloquial sounding names for mathematical objects, proofs, and so on? For example, manifolds are often described using an atlas and a neighborhood describes a small ...
3
votes
0answers
116 views

History of “Math is an Art” [closed]

For all its elegance I cannot bring myself to the conclusion that math is a form of art. As shown on the wikipedia page there is certainly math in art and art in math but what I wonder is how the ...
14
votes
2answers
637 views

Why is analysis called “analysis”?

Just as the topic says, how did the name "analysis" come to denote the specific mathematical branch dealing with limits and stuff? The term "analysis" seems very generic compared to the words for the ...
13
votes
1answer
275 views

l'Hopital's questionable premise?

Historians widely report that l'Hopital's 1696 book Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes contains a questionable premise expressed by an equation of type $x+dx=x$ ...
57
votes
23answers
10k views

Mathematicians ahead of their time?

In every field there's always that person who's just years ahead of their time. For instance, Paul Morphy (born 1837) is said to have retired from chess because he found no one to match his technique ...
7
votes
2answers
103 views

Theory vs problems in modern math

Quick background: I'm a fourth year undergraduate entering graduate school next year. I am trying to identify areas of mathematical research in which there tends to be more emphasis on developing new ...
3
votes
1answer
161 views

Errors of Euler interpretation?

To complement the recent post on Euler's errors, I would pose the following question: what common errors of Euler interpetation appear in the literature? What errors are attributed to Euler's work in ...
8
votes
1answer
275 views

Why is the permanent of interest for complexity theorists?

Studying a bit about the determinant and the permanent, I'm told that although both concepts have very similar formulas, the permanent was of not much interest historically - it was until later that ...
3
votes
1answer
60 views

Enlightening books giving a guided tour of mathematics, in a style that Gian-Carlo Rota would not mind?

I am currently reading Gian-Carlo Rota's Indiscrete Thoughts. What more can I say apart from "the man can write"? (In other words, you should really read it if you are interested in mathematics.) I ...
6
votes
1answer
341 views

Did Albert Einstein contribute to math?

Many great scientists have made important contributations to many related fields. Gauss, Euler and Newton each made many contributions to both math and physic. One of the great scientists of last ...
2
votes
1answer
94 views

Definition of the $\sec$ function

I am a postgraduate student of mathematics from Slovenia (central Europe) with quite some experience in mathematics. While answering questions on this site, I often encounter the function $\sec(x)$ ...
7
votes
4answers
203 views

“important” math concepts to pass on to next generation of creatures at some cataclysm [closed]

This may be somewhat silly to ask, but I couldn't resist the temptation. The idiosyncratic physicist Richard Feynman was once asked If, in some cataclysm, all of scientific knowledge were to be ...
0
votes
0answers
18 views

Lebesgue - differentiation of monotone functions

I was wondering how Lebesgue himself proved the continuous case. Since my French is not good enough to read his own book, I was wondering if someone knows if there exists a translation ? (at least of ...
2
votes
2answers
221 views

Are there still undiscovered simple/fundamental theorems? [closed]

Well, if it is undiscovered, then actually we cannot know whether it exists or not. But i am wondering if theorems/equalities like $Pythagorean$ $Theorem$ or maybe $Fermat's$ $Last$ $Theorem$ have ...
3
votes
4answers
142 views

Soft question: Examples where implications derived from mathematical models failed to describe reality

I have always been fascinated by how well conclusions drawn from mathematical models could fit reality, so I wondered if there are any counter examples. In "Gödel, Escher, Bach" I could already find ...
2
votes
1answer
47 views

The Jacobi nome $q$

Does anyone know why $q = e^{-\pi K'/K} = e^{\pi i \tau}$ is called the nome? Is there a historical reason? Does the word nome mean something in Latin or German?
0
votes
1answer
62 views

Reference on Infinite Dimensional Manifold

I am studying manifold. For comprehension, I read the site http://en.wikipedia.org/wiki/Manifold, and there is some information about infinite dimensional manifold. Now I have two questions or ...
2
votes
1answer
163 views

Famous deaf mathematicians?

There are some really inspiring examples of blind mathematicians. However in my experience I also think problems inside my head using words. So I was wondering if there are some examples of deaf ...
5
votes
1answer
142 views

More unknown / underappreciated results of Euler

What are some of the more unknown and/or underappreciated things that Euler discovered? The man has done so much that there's bound to be notable results that most people aren't aware of. This could ...
81
votes
30answers
16k 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 ...
4
votes
0answers
71 views

Was the Weierstrass function constructed or discovered?

Reading Halmos' I want to be a mathematician, he mentions a continuous function without a tangent. Naturally, I was curious to see how such a function could possibly exist, and I imagined it to be ...
3
votes
0answers
28 views

History of Moment Generating Functions

I am beginning to appreciate how important Moment Generating Functions (MGFs) are regarding various common probability distributions and the ways their expectations/variances are calculated. My ...
1
vote
1answer
143 views

Have any definitions in mathematics been redefined

Based on certain intuitions and motivations we make certain definitions and then proceed to use these concepts in further developing our intuition. For example, we have an intuition that a line has ...
4
votes
0answers
93 views

Earliest precursor to category theory

In the Historical notes section of the Wikipedia article on category theory, it is mentioned that in 1942-1945, Samuel Eilenberg and Saunders Mac Lane, in the course of their work in algebraic ...
5
votes
2answers
456 views

What fields (and operators acting on those fields) might form the basis of alien mathematics?

Addition and multiplication, according to most histories, arose in human civilizations out of a need to count a finite number of objects, and then later on especially, to measure land. What might be ...
2
votes
2answers
154 views

Which small area of mathematics had fully developed already and thus no more research in this area?

Which small area of mathematics had fully developed already and thus no more research in this area? For example, no more PHD research in Euclidean Geometry anymore.
2
votes
3answers
140 views

Mathematician's names in structures.

I would like to know how it is that mathematical objects come to receive the name of a mathematician. Do these mostly happen through the author's proposal, or is it a process that takes more time? ...
6
votes
2answers
166 views

Popular Topics in mathematical analysis(Functional analysis)

I am writing a text(as a duty by my mentor) dealing with the recently popular topics(including open problems) in mathematical analysis. At first part, I briefly introduced the mathematical ...
14
votes
2answers
687 views

Are infinitesimals dangerous?

Amir Alexander is a historian of mathematics. His new book is entitled "Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World". See here. Two questions: (1) In what sense are ...
15
votes
1answer
617 views

Why are there so few Euclidean geometry problems that remain unsolved?

Stillwell mentions in his book Mathematics and its History that: Most of the really old unsolved problems in mathematics, in fact, are simple questions about the natural numbers... What is it ...
25
votes
4answers
5k views

Why are so many of the oldest unsolved problems in mathematics about number theory?

Stillwell mentions in his book, Mathematics and its History that: Most of the really old unsolved problems in mathematics, in fact, are simple questions about the natural numbers... Have ...
3
votes
1answer
98 views

Important results of calculus before Newton and Leibniz?

We have all come to know that calculus was invented by Newton and Leibniz, right? But many calculus results were already proven by the time. I have read that Fermat already found how to calculate ...
2
votes
0answers
216 views

Is there any English version of Récoltes et Semailles?

I felt like my question isn't appropriate for MO, so I though maybe I should post it here. I want to read Alexander Grothendieck's "Récoltes et Semailles", but I don't know any French. I can easily ...
5
votes
5answers
571 views

Why are second-order 'things' studied so much in mathematics?

In many areas of math, I've been surprised at how much research, past and present, focuses on second order 'things'. Examples: Number theory: quadratic reciprocity, quadratic number fields Analysis: ...
13
votes
2answers
257 views

Motivation for introducing algebraic topology?

What kind of topological questions does algebraic topology answer where point set topology is not enough? Phrased differently: Where is the line (or maybe intersection) between point set topology ...
3
votes
0answers
68 views

Is there a link between level of abstraction and use of numbers?

One of my friend who stopped studying maths in high school told me once You study maths, can you help me fill my tax forms? In her mind, advancing in maths studies implied manipulating an ...
7
votes
3answers
566 views

Why are compact sets called “compact” in topology?

Given a topological space $X$ and a subset of it $S$, $S$ is compact iff for every open cover of $S$, there is a finite subcover of $S$. Just curiosity: I've done some search in Internet why compact ...
13
votes
2answers
568 views

A problem V.I. Arnold solved as a primary school student

According to a 1995 interview that Vladimir I. Arnold gave to the Notices of the AMS, his primary school teacher I.V. Morozkin gave in 1949 (when Vladimir I. Arnold was 12 years old) to a Soviet ...
18
votes
1answer
491 views

The most active fields of mathematics?

Which fields of mathematics are the most active at this time -- by number of papers published, grant money, people working in them or by any other measure? Any trends in this regard?
20
votes
3answers
749 views

Who came up with the $\varepsilon$-$\delta$ definitions and the axioms in Real Analysis?

I've seen a lot of definitions of things like boundary points, accumulation points, continuity, etc, and axioms of the real numbers. But I have a hard time accepting these as "true" definitions or ...
2
votes
2answers
90 views

why function argument is on right side $f(x)$ rather than on left side as $xf$

Is there an advantage for writing function arguments on the right side as $f(x)$ rather than on the left side as $xf$? The latter looks more natural if we think about it in diagram as $domain ...
1
vote
1answer
77 views

From $\mathsf{O}$ to $\mathsf{I}$ via $\infty$

The following is not true mathematics, but a little imaginary story about mathematical symbols. I wonder if there is - in parts - a true (etymological) story behind it. Once there was a symbol ...
1
vote
2answers
148 views

Is there any surprising elementary probability problem that result in surprising solution like the Monty Hall problem?

For recreational purpose, i haven't seen a interesting elemetary probability question quite a while. Is there any surprising elementary probability problem that result in surprising solution like the ...