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

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17
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1answer
927 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?
17
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2answers
937 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 ...
17
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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 ...
17
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1answer
293 views

Errors in math research papers [duplicate]

Have there been cases of errors in math papers, that were undetected for so long, that they caused subsequent errors in research, citing those papers. ie: errors getting propagated along. My ...
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 ...
16
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4answers
865 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
814 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 ...
16
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5answers
957 views

Purpose of the Peano Axioms

Wikipedia says the Peano Axioms are a set of axioms for the natural numbers. Is the purpose of the axioms to create a base on which we can build the rest of mathematicas formally? If this is true ...
16
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2answers
1k 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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2answers
1k 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.
16
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1answer
710 views

Any branch of math can be expressed within set theory, is the reverse true?

Set theory seems to have the property of being "universal", in the sense that any branch of math can be expressed on its language. Is there any other branch of math with this property? I am asking ...
16
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1answer
311 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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1answer
546 views

History of Commutative Algebra

There are books on 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. ...
16
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5answers
898 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 ...
16
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4answers
467 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
356 views

Motivation for the study of amoebas.

What was the primary motivation for the study of the amoebas?
16
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1answer
310 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 ...
15
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7answers
643 views
15
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9answers
2k views

Why are the Trig functions defined by the counterclockwise path of a circle?

My understanding is that $\cos$ is defined by the value of $x$ as you trace the graph of a circle counterclockwise, starting at the point $(1, 0)$. Similarly, $\sin$ traces the $y$ value. I understand ...
15
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3answers
618 views

Why is the word associative used to represent the concept of the associative property?

For the commutative property ... According to wikipedia: The word "commutative" is a combination of the French word commuter meaning "to substitute or switch" and the suffix -ative meaning ...
15
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6answers
2k views

Motivation of the Gaussian Integral

I read on Wikipedia that Laplace was the first to evaluate $$\int\nolimits_{-\infty}^\infty e^{-x^2} \, \mathrm dx$$ Does anybody know what he was doing that lead him to that integral? Even better, ...
15
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3answers
489 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
2k 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 the name "Law of Inertia" fit with the statement of the theorem? I guess it's from ...
15
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5answers
969 views

In what ways has physics spurred the invention of new mathematical tools?

I came across this comment: Mathematical rigor is not a criterion that physicists have for evaluating their theories. From a mathematical perspective, the non-rigorous theories are far more ...
15
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7answers
2k views

Films about math: a question about math education and motivation for learning math [closed]

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 ...
15
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2answers
1k views

Who is the “father of number theory”?

I noticed that some sources state Fermat as the father of modern number theory while others say Gauss. I am trying to start a paper on the history of number theory for a presentation, but I cannot ...
15
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3answers
2k views

When the trig functions moved from the right triangle to the unit circle?

I have to write a paper about the unit circle and I'm trying to uncover some of its origins. Also, when the trig functions were expanded to angles greater than 90° and what was the rationale behind ...
15
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3answers
2k views

History of elliptic curves

In one sense elliptic curves are a rather modern object as some of its properties have been studied only in the last century or so. But in another sense there are a very classical object for studying ...
15
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1answer
8k views

Dantzig's unsolved homework problems

From Wikipedia: An event in George Dantzig's life became the origin of a famous story in 1939 while he was a graduate student at UC Berkeley. Near the beginning of a class for which Dantzig ...
15
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1answer
618 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 ...
15
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4answers
679 views

What did Whitehead and Russell's “Principia Mathematica” achieve?

In philosophical contexts, the Principia Mathematica is sometimes held in high regard as a demonstration of a logical system. But what did Whitehead and Russell's Principia Mathematica achieve for ...
15
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2answers
2k 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
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1answer
441 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?
15
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1answer
595 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) ...
15
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1answer
490 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 ...
15
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1answer
982 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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2answers
419 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?
15
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1answer
580 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 ...
14
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8answers
523 views

Serendipitous mathematical discoveries in recent times

As of today, most important results in mathematics are conjectured long before they are proven. Are there any examples of (important) mathematical discoveries that were proven by chance rather than ...
14
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8answers
2k 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
3k 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 ...
14
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2answers
2k views

Has any error ever been found in Euclid's elements?

Has any error ever been found in Euclid's elements since its publication? Or it is still perfect from the view point of modern mathematics.
14
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3answers
7k 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.
14
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4answers
6k 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 ...
14
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2answers
2k views

Why is “h” used for entropy?

Why is the letter "h" (or "H") used to denote entropy in information theory, ergodic theory, and physics (and possibly other places)? Edit: I'm looking for an explanation of the original use of "H". ...
14
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2answers
231 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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3answers
856 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 ...
14
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1answer
4k 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 ...
14
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1answer
657 views

What is “inner” about the inner product?

The inner product I am asking about is the one that generalizes the dot product for an arbitrary inner product space. Why is it called an "inner" product? Is there an outer product? Who named it ...
14
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1answer
1k views

History of Lagrange Multipliers

How did Lagrange discover Lagrange multipliers? Also, was it related to his work on the calculus of variations? And how did he originally understand/implement the technique?