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

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What cubic problems did Tartaglia and Fior pose to each other?

I have been researching the history of finding roots to general polynomials and the story of solving for the roots of cubic polynomials ($ax^3+bx^2+cx+d=0$) lead me to find several sources describing ...
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The correct pronunciation of Whaples?

What is the correct the family name of the mathematician George Whaples? Feel free to migrate my question to a another forum if you think here is not the right place.
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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 ...
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The Historical Importance of Keynes' A Treatise on Probability

A visiting speaker in Economics recently happened to mention that John Maynard Keynes' A Treatise on Probability revolutionized probability theory. I have not heard any such claim before and it struck ...
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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?
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In Whitehead and Russell's PM, are overlapping ranges of significance necessarily identical?

In Principia Mathematica summary of ✳63 In virtue of ✳20.8, we have $\vdash : \phi a ∨ \sim\phi a . ⊃ . \hat{x}(\phi x \vee \sim \phi x ) =t‘a$ i.e. if "$\phi a$" is significant, then ...
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What is the “Principle of permanence”?

While reading the book "The Number-System of Algebra (2nd edition)." term "Principle of permanence" occurred to me. I remember I had read this in the book "Beginning algebra for college students.". I ...
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History of five lemma

I am interested in the history of five lemma. Who was first to prove it and What was the purpose of proving it ? http://en.wikipedia.org/wiki/Five_lemma
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Why the name “umbilic”?

Umbilic points are points on a surface at which the principle curvatures of the surface are equal. "Umbilic(al)" refers to the navel/belly button. But why do we call these points so? What about the ...
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Concept of a function and Idea of a formula as a function; History of

Enderton Elements of Set Theory, p. 43 (1977, Academic Press), writes: There was a reluctance to separate the concept of a function itself from the idea of a written formula defining the function. ...
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How did Newton and Leibniz actually do calculus?

How did Leibniz know to write derivatives as $$\frac{dy}{dx}$$ so that everything would work out? For example, the chain rule: $$\frac{dy}{dz}=\frac{dy}{dx}\frac{dx}{dz}$$ Integration by Parts: ...
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158 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 ...
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72 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 $\sec(x)$ ...
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2answers
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Why the $\log$ is so special?

When I first learn about the logarithm function $\log$ or $\ln$. My professor said that $\log x$ is a function that when we derive we get the inverse function $1/x$. This $\log$ becomes very popular ...
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Reason behind standard names of coefficients in long Weierstrass equation

A long Weierstrass equation is an equation of the form $$y^2+a_1xy+a_3y=x^3+a_2x^2+a_4x+a_6$$ Why are the coefficients named $a_1, a_2, a_3, a_4$ and $a_6$ in this manner, corresponding to $xy, x^2, ...
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What is the definition of a positive integer?

I am reading the book "The Number-System of Algebra (2nd edition)". At the starting of page-4 the author writes: A positive integer is a symbol for the number of things in a group of distinct ...
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“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 ...
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History of Morse theory.

How can I get good references which give many information about history of Morse theory? Now I am interested in how and who found that Hessian have a lot of data. Thank you for your helping!!
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Works on Calculus by Newton and Leibniz (primary sources)

I'm trying to find PDFs or hard copies of the following works from the dawn of calculus. Does anyone know where I could find English translations of them? Newton - De analysi per aequationes numero ...
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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 ...
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1answer
54 views

History of the Enneper Surface

I was just wondering whether anyone could tell me more about the Enneper surface and its history (why it is important historically in the development of mathematics), or where to go in order to learn ...
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1answer
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Soft Question: Algorithms: Will We (One Day) No Longer Need to Study Algorithms? [closed]

I'm just now getting into the study of algorithms and it seems like as computers get faster and faster the need to study algorithms may begin to diminish. How likely is it that in 50 years there ...
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1answer
54 views

Need help locating a paper

One of the references of the paper Paulo Régis C. Ruffino, A Criticism on "A Mathematician's Apology" by G. H. Hardy (arXiv:1112.4499 [math.HO]) is: Vershik, A. M. – A Dangerous Joke, The ...
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Did the world experience a “mathematical drought” at any time in history?

Mathematics history goes back pretty far: the Greeks were studying it in 600BC, the Babylonians and Egyptians all the way back beyond 2000BC, and there's even some evidence of prehistoric mathematics. ...
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2answers
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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 ...
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5answers
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Can mathematics be traced back to a fundamental system of truths?

I'm not sure exactly how to state this question, or even if it belongs here. Still, I hope you will consider it, as I find it very interesting: Most of the results I've seen in mathematics come from ...
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Historical study of dynamical system

I am currently doing a historical study on my school project 'study of ODE' which slowly shift to the study of dynamical system as I am interested in pursuing my study of ode from linear system, phase ...
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C. Neumann passage in Latin from *Annali di Matematica Pura ed Applicata*

Neumann, Carl. “Theoria nova phaenomenis electricis applicanda.” Annali di Matematica Pura ed Applicata 2, no. 1 (August 1868): 120–128. doi:10.1007/BF02419606. p. 121: Nova introducitur ...
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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 ...
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How to interprete ✳43.3 and ✳43.31 in Whitehead and Russell's PM?

Take ✳43.3 for example, I presume $ P = R |Q $ where R is fixed. $ R| $ is the relation between $R|Q$ and $Q$, ie. $ R| = \hat{P} \hat{Q} \{ P = R|Q \} $ $Ɑ‘R|= \hat{Q}\{ E! R|‘Q \}$ Given that ...
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How did the Symmetric group and Alternating group come to be named as such?

The Dihedral group makes sense, "Di" means two, and "hedral" means.. shape I think (I've just realised how much of what I think words mean are guesses based on experience) like a "polygon" is a 2d ...
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Grothendieck's manuscript on differential manifolds

I have a Japanese book on Grothendieck's life and his mathematical works. The author writes that Grothendieck wrote manuscripts(over 250 pages) on "the category of manifolds" and "differential ...
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1answer
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A Concept Which Has Been 'Specialized' In the Course of History

There are so many concepts which have been generalized during history of mathematics - the concept of "number" may be the best examples. On the other hand, a concept may have been specialized ; the ...
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History Of Algebra

Did the Indians invent algebra which was taken by Arabs and introduced by them to Europe as their own invention? Or did the Arabs invent algebra?
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Borel's result on transcendence measure

In "Sur la nature arithmétique du nombre e" (Comptes rendus de l'Académie des Sciences 128 (1899), 596-9) Borel presented his result on transcendence measure for e. This can be restated as follows: ...
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What is the importance of Hilbert and Birkhoff in mathematics in the twentieth century? [closed]

someone could help me find the most important tools that contributed Hilbert and Birkhoff in twentieth century mathematics Thanks for your help
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115 views

Sources on Hamilton's Discovery of Quaternions

This is a strange question and I'm not sure where to put it; I'm currently writing an essay for a history of maths course, and I've chosen the topic of Hamilton's discovery of the quaternions. I ...
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Exactly who popularized the modern definition of domain and codomain of functions?

In Whitehead and Russell's Principia, domain is the referents of relation; converse domain is the relata. Modern function in mathematics is just one special case of relation whose referent is unique ...
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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?
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Who discovered this number-guessing paradox?

In this math.se post I described in some detail a certain paradox, which I will summarize: $A$ writes two distinct numbers on slips of paper. $B$ selects one of the slips at random (equiprobably), ...
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How did Fourier find the formula for the fourier series coefficients?

The modern proof use the dot product but did he use that ?
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Reference for Hilbert numbers

I've been studying a little bit of number theory, and during such studies I came across this interesting reference to Hilbert numbers, that is, numbers of the form $4n +1$. My question is a purely ...
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1answer
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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 ...
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Cauchy gave 1st example of a Lie algebra in 1847 & exterior product in 1853‽

I read in PDF pg. 5 of this that Cauchy gave the first example of a Lie algebra in 1847: It also claims that he invented the exterior product in 1853. Does anyone have references for this?
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Not pi - What if I used 3? Teaching pi discovery to K-6th grade

So, in ancient Mesopotamia they knew that they didn't really have the correct number (pi) to determine attributes of a circle. They rounded to 3. If you acted as though pi = 3, what shape would you ...
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Who was the first person to construct the real numbers by Cauchy sequences in $\mathbb{Q}$

Who was the first person to construct the real numbers by Cauchy sequences in $\mathbb{Q}$? Was it Cauchy himself?
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132 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 ...
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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 ...
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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 ...
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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 ...