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

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2answers
811 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 ...
20
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1answer
494 views

Who was Hermann Künneth?

Question as in the title: Who was Hermann Künneth? Where can I find some biographical information beyond what is available on Wikipedia? The well-known Künneth formula, for example in the form of ...
19
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11answers
1k views

What are some results that shook the foundations of one or more fields of mathematics? [closed]

An example would be the proof that $\sqrt{2}$ is not rational, which was a violation of some fundamental assumptions that mathematicians at the time made about numbers. Another would be Russell's ...
19
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6answers
2k views

What is the motivation for quaternions?

I know imaginary numbers solve $x^2 +1=0$, but what is the motivation for quaternions?
19
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2answers
598 views

Approximation for $\pi$

I just stumbled upon $$ \pi \approx \sqrt{ \frac{9}{5} } + \frac{9}{5} = 3.141640786 $$ which is $\delta = 0.0000481330$ different from $\pi$. Although this is a rather crude approximation I ...
19
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2answers
781 views

Who first called the Grothendieck's schéma scheme?

Grothendieck called "schemes" schémas in French. I find it strange we call them schemes. In fact, Grothendieck called them (pre-) schemas(this is an English word) in his talk(in English) at Proceeding ...
19
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4answers
704 views

Was there anybody before Cantor who conjectured existence of infinities of different sizes?

Georg Cantor is formally known as the first one who discovered existence of infinities of different sizes. But the history of thinking about the concept of "infinity" in maths and philosophy goes back ...
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2answers
1k 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 ...
19
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2answers
705 views

History of the theory of equations: John Colson

This is an EDIT version of my original question: Recently I've been interested in the history of the Theory of Equations. The thing is that I learned about this mathematician named John Colson, he ...
19
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1answer
366 views

Matsunaga's Method for solving $x^2+y^2=p$

In his history of number theory, Dickson mentions an 18th century algorithm due to Matsunago [Sic --- he means, presumably, Matsunaga Ryohitsu a.k.a. Matsunaga Yoshisuke] for finding two numbers whose ...
19
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1answer
410 views

When, and by whom, was “$\mathbb{C}$ is algebraically closed” dubbed the “fundamental theorem of algebra”?

Wikipedia has this enigmatic sentence on the page for the fundamental theorem of algebra: ...its name was given at a time when the study of algebra was mainly concerned with the solutions of ...
18
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5answers
1k views

Results that were widely believed to be false but were later shown to be true

What are some results which were widely believed to be false, but were later to be shown to be true, or vice-versa?
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 ...
18
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2answers
948 views

Motivation for/history of Jacobi's triple product identity

I'm taking a short number theory course this summer. The first topic we covered was Jacobi's triple product identity. I still have no sense of why this is important, how it arises, how it might have ...
18
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4answers
1k views

Why is the axiom of choice separated from the other axioms?

I don't know much about set theory or foundational mathematics, this question arose just out of curiosity. As far as I know, the widely accepted axioms of set theory is the Zermelo-Fraenkel axioms ...
18
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1answer
2k views

Why is the hard Lefschetz theorem “hard”?

Let $X$ be a compact Kähler manifold of complex dimension $\dim_{\mathbb C} = n$. Let $[\omega]$ be the cohomology class of a Kähler metric on $X$. Then powers of the class $[\omega]$ defines a linear ...
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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, ...
18
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4answers
3k views

Why is an image called an “image”?

Given a function $f : A \to B$, the image, denoted by $\operatorname{Im}f$ is the set of all $f(x)$ where $x \in A$. Why do we call this set the image? When was it first used, and what motivated its ...
18
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2answers
840 views

Did Zariski really define the Zariski topology on the prime spectrum of a ring?

The question is not: “Did Zariski really define the Zariski topology?” It is: “Did Zariski really define the Zariski topology on the prime spectrum of a ring?” Here is the motivation. --- On page ...
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3answers
1k 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 Arnold was 12 years old) to a Soviet classroom, most ...
18
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3answers
1k views

where does the term “integral domain” come from?

Self-explanatory title really! A student today asked me why they were called integral domains -- and I realised that the word "integral" seems to be being used in a way totally unlike any other way I ...
18
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2answers
950 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 ...
18
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1answer
771 views

Examples of falsified (or currently open) longstanding conjectures leading to large bodies of incorrect results.

In general, the way that modern mathematical research is conducted isn't the way that many would assume is the ideal method of research. That is, mathematics is not the linear progression of ...
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4answers
4k views

Difference between calculus and analysis

It's somthing I always want to figure out, when did calculus start to be extended to analysis(I reformulate the question, the previous one"where one can draw a line to distinguish calculus and ...
18
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1answer
6k views

Strange old multiplication table

Today I read an article about chalk boards from 1917 discovered in an Oklahoma school. One of the chalkboards included the following curious image: (Oklahoma City Public Schools) The article ...
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?
18
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1answer
675 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 ...
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10answers
1k views

Challenge: Demonstrate a Contradiction in Leibniz' differential notation

I want to know if the Leibniz differential notation actually leads to contradictions - I am starting to think it does not. And just to eliminate the most commonly showcased 'difficulty': For the ...
17
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1answer
836 views

What was the last mathematical paper published in Latin?

From an answer to a previous question I learned that Peano published in Latin as long as 1889. What was the last mathematical paper/book of recognized importance published in Latin?
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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 ...
17
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6answers
1k views

Is the theory of dual numbers strong enough to develop real analysis, and does it resemble Newton's historical method for doing calculus?

I've been interested in non-standard analysis recently. I was reading up on it and noticed the following interesting comment on the Wikipedia page about hyperreal numbers, right after giving an ...
17
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1answer
289 views

Why would I define Alexander–Spanier cohomology?

I think I can motivate the definitions of simplicial, singular, de Rham, Čech, and sheaf (co)homology, more or less. I might want to understand bordism, and start by trying to understand ...
17
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1answer
1k views

What is magical about Cartan's magic formula?

Why is Cartan's magic formula $$\mathscr{L}_X\omega = i_Xd\omega + d(i_X\omega)$$ called "magic"? Should it be considered a highly surprising result? Does it "magically" prove several other ...
16
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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 ...
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7answers
5k views

History of zero?

I learn't as a kid from my teachers that zero was discovered/invented in india and if you ask anybody here in india, the answer is simple yes it was invented in india. Now we have something to say ...
16
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4answers
835 views

How did the ancients view *infinitesimals*?

With some category/topos theory we can now put infinitesimals on a rigorous ground, as in Bell's A Primer of Infinitesimal Analysis, where the author introduces $\epsilon$ satisfying \begin{equation} ...
16
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5answers
723 views

What are reasons why some symbols in mathematical logic are not standardized?

Why is so hard to find a standardisation regarding symbolism and/or terminology in Mathematical Logic ? We see again and again students asking if e.g. $\rightarrow$ and $\implies$ means the same ...
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1answer
1k views

About a paper of Zermelo

This about the famous article Zermelo, E., Beweis, daß jede Menge wohlgeordnet werden kann, Math. Ann. 59 (4), 514–516 (1904), available here. Edit: Springer link to the ...
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2answers
817 views

Adriaan van Roomen's 45th degree equation in 1593

Adriaan van Roomen proposed a 45th degree equation in 1593(see this book, picture reference as follows): $$ \begin{gathered} f(x) = x^{45} - 45x^{43} + 945x^{41} - 12300x^{39} + 111150x^{37} - ...
16
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3answers
1k views

Did Gauss ever make a mistake?

I have read a bit about Gauss, who was well known for being careful in only publishing work he had perfected (or in his own words "few, but ripe"). What is interesting to me about Gauss though is that ...
16
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2answers
779 views

History of Algebraic Geometry: Motivation behind definition of schemes

I am trying to read an article by Jean Dieudonne which talks about development of Algebraic Geometry. The article was being published in the journal "Advances in Mathematics" Volume 3, Issue 3, Pages ...
16
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5answers
738 views

history of the double root solution of $ay''+by'+cy=0$

Motivation: It is a well-known fact that $ay''+by'+cy=0$ has solutions which are found from substituting the ansatz $y=e^{\lambda t}$ into the DEqn. It turns out that we replace the calculus problem ...
16
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1answer
297 views

Who is buried in Weierstrass' tomb?

The tangent half-angle substitution often used to anti-differentiate rational functions of sine and cosine, and also sometimes used to find closed-form solutions of some differential equations, is ...
16
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2answers
3k 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 ...
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5answers
789 views

Reflections on math education

Why is there such a big difference in math education between The Americas and (Europe and Asia) ? except for a few privileged who have the opportunity to access to math much earlier than the ordinary ...
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4answers
445 views

When was $\pi$ first suggested to be irrational?

When was $\pi$ first suggested to be irrational? According to Wikipedia, this was proved in the 18th century. Who first claimed / suggested (but not necessarily proved) that $\pi$ is irrational? I ...
16
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1answer
578 views

A curious theorem by Peano

Let $f$ be defined on $[a,b]$ and there differentiable. Show that for every $ \epsilon>0 $ there exists a partition $\, a=a_0<a_1<...<a_n=b \,$ of $ \,[a,b] \,$ so that $$\left|\frac ...
16
votes
1answer
279 views

How and why did Weierstrass $\wp$ get its special symbol?

I kind of always hated drawing the Weierstrass $\wp$ symbol by hand, and it struck me as odd how and why it achieved its special status in the first place. After all, there are tons of other important ...
16
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0answers
260 views

Why is $J$ often used to denote $\mathbb{N}$ or $\mathbb{Z}$ in older texts?

In older books, I've noticed that authors tended to use $J$ to denote (usually) the natural numbers and (less commonly) the integers. Does anyone have any idea why that might've been? A few examples ...
15
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7answers
597 views