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

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1answer
955 views

What did Gauss think about infinity?

I have someone who is begging for a conversation with me about infinity. He thinks that Cantor got it wrong, and suggested to me that Gauss did not really believe in infinity, and would not have ...
15
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10answers
993 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 ...
15
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1answer
806 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 ...
15
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4answers
837 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 ...
15
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7answers
4k 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 ...
15
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3answers
1k 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, ...
15
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3answers
319 views

Ultrafilters - when did it start?

I am writing a paper on some of the applications of ultrafilters, especially the ones on $\mathbb{N}$. I thought that it would be interesting to include some information about how the concept got ...
15
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2answers
657 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 ...
15
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1answer
874 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 ...
15
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2answers
504 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} - ...
15
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3answers
665 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 ...
15
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2answers
890 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 ...
15
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1answer
393 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 ...
15
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4answers
400 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 ...
15
votes
1answer
614 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 ...
15
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1answer
289 views

Motivation for the study of amoebas.

What was the primary motivation for the study of the amoebas?
14
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7answers
1k views

Reference request: is mathematics discovered or created?

I have to write a short monograph as an assignment for a course on the philosophy of science. Being a math student, of course I want to opt for something math-related. After some initial ideas which ...
14
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2answers
190 views

Was there some prior idea that inspired both Fermat & Descartes to invent coordinates?

It seems incredible to me that both Descartes & Fermat could have both simultaneously discovered such a novel & significant idea, without there being some single prior idea that they both ...
14
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2answers
634 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 ...
14
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5answers
561 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 ...
14
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1answer
396 views

Hilbert's Original Proof of the Nullstellensatz

Does anyone have a link to Hilbert's Original Proof of the Nullstellensatz, or know a book where it's printed? I'd be interested to see what it was like. I only really know the Noether normalisation ...
14
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4answers
2k 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 ...
14
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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 ...
14
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2answers
660 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 ...
14
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4answers
490 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 ...
14
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1answer
364 views

Mendelson's $\mathit{Mathematical\ Logic}$ and the missing Appendix on the consistency of PA

In the first edition of Elliott Mendelson's classic Introduction to Mathematical Logic (1964) there is an appendix, giving a version of Schütte's (1951) variation on Gentzen's proof of the consistency ...
14
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2answers
370 views

Who was the first to use dual space?

Who was the first person who used the dual space? In which paper / book did he or she use the dual space? Who was the first who called it dual space and in which paper / book?
14
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0answers
349 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 ...
13
votes
2answers
675 views

How to evaluate trigonometric functions by pen and paper?

How did people determined the values of trigonometric functions before calculators, like e.g. $\sin 37^\circ$ up to five decimal places? Was that possible to find before series were invented?
13
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7answers
1k views

Films about math: a question about math education and motivation for learning math

I'm interested in movies about or related with mathematics or physics, I mean not documentaries which I also consider movies, but artistic or mainstream films about math. Now I have the following in ...
13
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4answers
671 views

How do mathematicians think about the existence of numbers?

Question: How do mathematicians think about the existence of numbers? And how did Newton, Euler, and other famous mathematicians thought about this concept? I know that existence of numbers is a ...
13
votes
2answers
138 views

Identity of a Mathematician Mentioned in Euler

I and several others are in the process of translating one of Euler's papers from Latin to English, in particular the one that the Euler Archive lists as E36. In it Euler proves the Chinese Remainder ...
13
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2answers
873 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. ...
13
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2answers
564 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 ...
13
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2answers
255 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 ...
13
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3answers
437 views

Who gave you the epsilon?

Who gave you the epsilon? is the title of an article by J. Grabiner on Cauchy from the 1980s, and the implied answer is "Cauchy". On the other hand, historian I. Grattan-Guinness points out in his ...
13
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2answers
597 views

Who is a Math Historian?

In the context of classes, it is very often that discussion on the history of mathematics arises, whether it'd be on who should a lemma be attributed to or a certain event that occurred during the ...
13
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1answer
186 views

Why are proofs written in first person plural? Were they ever written differently?

It's probably a silly question but it interests me when was the convention of writing proofs in first person plural introduced? Is there any historical examples of a different POV for proof writing?
13
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4answers
667 views

Documentary of mathematics. [duplicate]

Possible Duplicate: List of Interesting Math Videos/ Documentaries I just watched a documentary of Fermat's last theorem. It is so good. I can feel how mathematician think and get excited. ...
13
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1answer
274 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 $x+dx=x$ ...
13
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0answers
94 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 ...
12
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2answers
1k views

Hardy / Wright's intro to number theory is highly praised but has no exercises

"An introduction to the theory of numbers, G.H Hardy, E.M. Wright, revised by D.R. Heath-Brown, J.H. Silverman. Originally published 1938. Sixth edition 2008 with a foreword by Andrew Wiles" is AFAIK ...
12
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2answers
614 views

What is the mathematical intuition behind àl-jàbrà?

The term algebra comes from the arabic term àl-jàbrà that means "to force", "to restore". Over centuries mathematicians, in east and west, celebrate by this term mathematical disciplines. What is ...
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2answers
1k views

“L'Hôpital's rule” vs. “L'Hospital's rule”?

I know this is not strictly a mathematical question, and I considered putting it on Linguistics SE, but I decided that seeing as this is most probably a mathematical history question, it would be ...
12
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6answers
973 views

Motivation of the Gaussian Integral

I read on Wikipedia that Laplace was the first to evaluate $$\int_{-\infty}^\infty e^{-x^2} \, \mathrm dx$$ Does anybody know what he was doing that lead him to that integral? Even better, can ...
12
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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 ...
12
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2answers
277 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 ...
12
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2answers
681 views

Famous black mathematicians

Are there any famous black mathematicians? By famous, I mean in the sense of having a theorem or well-known result named after them.
12
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3answers
2k views

How was the Fourier Transform created?

The Fourier Transform is a very useful and ingenious thing. But how was it initiated? How did Joseph Fourier composed the Fourier Transform formula and the idea of a transformation between periodic ...
12
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1answer
2k views

Proof of Euler's Theorem without abstract algebra?

Every proof I've seen of Euler's Theorem (that $\gcd(a,m) = 1 \implies a^{\phi(m)} \equiv 1 \pmod m$) involves the fact that the units of $\mathbb{Z}/m\mathbb{Z}$ form a group of order $\phi(m)$. ...