Use this tag for questions concerning history of mathematics, historical primacies of results, and evolution of terminology, symbols, and notations.
16
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1answer
994 views
What concept does an open set axiomatise?
In the context of metric (and in general first-countable) topologies, it's reasonably clear what a closed set is: a set $F$ is closed if and only if every convergent sequence of points in $F$ ...
16
votes
1answer
1k views
Where did the word “logarithm” come from?
Where did the word logarithm come from? Any relation to the word algorithm?
16
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1answer
543 views
Where can I find the old papers of the Math Tripos?
Is there a repository on the Internet which has the old question papers of the tripos? I am specifically interested in the papers during the 1890-1910 era, which was the era before the reforms, ...
16
votes
1answer
605 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
votes
7answers
2k 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 disapprove of this ...
15
votes
3answers
942 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
votes
4answers
627 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}
...
15
votes
2answers
509 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
votes
2answers
333 views
History of Modern Mathematics Available on the Internet
I have been meaning to ask this question for some time, and have been spurred to do so by Georges Elencwajg's fantastic answer to this question and the link contained therein.
In my free time I ...
15
votes
4answers
304 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
243 views
Does there exist a copy of Euclid's Elements with modern notation and no figures?
I am working through Euclid's Elements for fun, but I find the propositions difficult to understand without referencing the provided figures. Unfortunately, the figures usually give away the proofs, ...
14
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5answers
773 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?
14
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4answers
483 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 ...
14
votes
1answer
601 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 ...
14
votes
2answers
663 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 ...
14
votes
1answer
368 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 ...
14
votes
2answers
802 views
De Moivre's Theorem. Motivation and origins.
I've purchased "A Source Book in Mathematics" some time ago and I'm still baffled by De Moivre's paper on his formula. We all know the famous
$$\{\cos(x) + i \sin(x)\}^n = \cos(nx)+i \sin(nx)$$
but ...
14
votes
0answers
107 views
Hilbert's original proof of basis theorem
Does anyone know Hilbert's original proof of his basis theorem--the non-constructive version that caused all the controversy? I know this was circa 1890, and he would have proved it for ...
14
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0answers
268 views
Definitive source about Dirichlet finally proving the Unit Theorem in the Sistine Chapel
There is a remark one can find in various books or survey articles (e.g., page 49 of Helmut Koch's "Number Theory: Algebraic Numbers and Algebraic Functions") saying Dirichlet figured out a proof of ...
13
votes
1answer
552 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 ...
13
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6answers
2k 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 ...
13
votes
1answer
627 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 ...
13
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3answers
1k views
Where did mathematicians learn how to do truth tables?
I'm trying to find out who invented truth-tables. Here is what I have so far.
Leibniz 'invented' binary arithmetic, or at least is the first one recognized to have codified and explained a base 2 ...
13
votes
1answer
259 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 ...
13
votes
2answers
352 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
votes
4answers
473 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.
...
12
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7answers
896 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 ...
12
votes
2answers
714 views
Why is lambda calculus named after that specific Greek letter? Why not “rho calculus”, for example?
Where does the choice of the Greek letter $\lambda$ in the name of “lambda calculus” come from? Why isn't it, for example, “rho calculus”?
12
votes
2answers
943 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
votes
7answers
677 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 ...
12
votes
4answers
1k views
Origin of the dot and cross product?
Most questions usually just relate to what these can be used for, that's fairly obvious to me since I've been programming 3D games/simulations for a while, but I've never really understood the inner ...
12
votes
1answer
540 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.
...
12
votes
3answers
288 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
votes
4answers
862 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 ...
12
votes
3answers
292 views
Is there any difference between a math invention and a math discovery? [closed]
From wikipekia:
The calculus controversy was an argument between 17th-century
mathematicians Isaac Newton and Gottfried Leibniz (begun or fomented
in part by their disciples and associates – ...
12
votes
1answer
231 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 ...
12
votes
2answers
198 views
Lie and Weierstrass' visualization of complex functions
I am reading Whittaker and Watson's A Course of Modern Analysis. In the third chapter where they discuss different ways to visualize functions that map the complex plane to the complex plane, they ...
12
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1answer
399 views
successful absurd formalities
Has anyone published in print or on a web site or elsewhere a compilation of successful illogical formal arguments? By those I mean arguments that follow a form in disregard of the legality of its ...
12
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0answers
102 views
Is Dover publishing Moore's book on the Axiom of Choice? [closed]
Dover is publishing a paperback edition of Gregory H. Moore's Zermelo's Axiom of Choice: Its Origins, Development, and Influence. It's supposed to come out March 20th and is available for pre-order at ...
11
votes
6answers
590 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 ...
11
votes
3answers
873 views
how exactly did calculus change our understanding of the world?
I am taking calculus course and I keep wondering if this is really necessary. I know it is the cornerstone of modern science but what I don't understand is why and how.
Was it impossible to pursue ...
11
votes
5answers
293 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 ...
11
votes
1answer
134 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 ...
11
votes
1answer
221 views
History of Commutative Algebra
There are books of 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. ...
11
votes
1answer
360 views
Polarization: etymology question
The polarization identity expresses a symmetric bilinear form on a vector space in terms of its associated quadratic form:
$$
\langle v,w\rangle = \frac{1}{2}(Q(v+w) - Q(v) - Q(w)),
$$
where $Q(v) ...
11
votes
2answers
242 views
What do Greek Mathematicians use when they use our equivalent Greek letters in formulas and equations?
Like for example, it's common to use the Greek letter $\theta$ to represent an angle right? So what would a Greek person doing math use to represent an angle? Would they also use $\theta$? Or is there ...
11
votes
2answers
312 views
Why are Darboux integrals called Riemann integrals?
As far as I have seen, the majority of modern introductory real analysis texts introduce Darboux integrals, not Riemann integrals. Indeed, many do not even mention Riemann integrals as they are ...
11
votes
1answer
91 views
Original Formulation of Hilbert's 14th Problem
I have a problem seeing how the original formulation of Hilbert's 14th Problem is "the same" as the one found on wikipedia. Hopefully someone in here can help me with that. Let me quote Hilbert first:
...
10
votes
7answers
602 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.
10
votes
2answers
1k 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.
