Questions tagged [mathematics]

For questions about the quantitative study of topics such as numbers, structure, space, and change, carried out by investigating patterns.

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51 views

Who was Paul Gerwien?

The famed Wallace–Bolyai–Gerwien theorem has got its name from three mathematicians who proved it independently. More precisely speaking Farkas Bolyai first formulated the question. Gerwien proved ...
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Which one goes first - Secant or Newton - in Numerical root finding technique?

In Numerical root solving technique, which comes first in history - Newton or Secant - and each one is named after whom?
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273 views

Alexander Grothendieck's “stolen” correspondence in 1985?

On the website that now displays the part of Grothendieck's archives that had been held at the University of Montpellier, it is mentioned that: Dans une lettre adressée à Monsieur Lefranc datée du 13 ...
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What are some good references elucidating the discovery/creation of Fourier Series?

I've always grappled with anything related to Fourier since my undergrad days. Recently, when revisiting why I learned what I did, I discovered how Fourier's desire to understand the flow of heat ...
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Why are étale morphisms called “étale”?

Alexander Grothendieck developed the theory of "locally trivial coverings spaces for rings/schemes" in SGAI as an analog to the theory of covering spaces in algebraic topology. He called such ...
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34 views

Aristotle's and Plato's even and odd numbers, sets and actual infinity

Plato and Aristotle both use the terms even and odd about numbers (and have a separate discussion of the number 1). From this point, it seems, there would be no great distance to the sets of even and ...
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What evidence is there that Fermat had a proof for his Last Theorem?

Aside from the fact that Fermat was a genius, is it probable that he actually did have a proof? Some specifics that I think would point one way or another: Would the mathematics of his day allow him ...
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47 views

How did Fourier determine the coefficients of Fourier series?

I was reading a chapter of Fourier's seminal work "Analytic Theory of Heat". The third chapter of this book was translated by the famous Stephen Hawking in his book "God created the ...
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1answer
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Is the story about Fermat's writing on a margin true?

Is there any evidence that Fermat wrote on the margin of a book "I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain." Everyone ...
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What was the first automated theorem prover?

From a lot of googling, it seems like the answer might be "Mizar", but I am not completely sure. What was (or is?) the first automated theorem prover (i.e. not necessarily active right now)?
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What was the notion of limit that Newton used?

I have read that the notion of limit became rigorous two centuries after the discover of calculus What Newton had in his mind regarding the notion of limit?
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278 views

Do North Koreans use Latin letters in their equations?

Do North Koreans use Latin (and Greek) letters in their equations? On the one hand, being such an isolationist country, I wouldn't be surprised if they used the Korean alphabet (조선글) in their ...
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226 views

Nobel Prize for Applied Mathematics

There is no Nobel Prize for mathematics. However, have there been any Nobel Prizes for the use of applied mathematics to model the real world?
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289 views

Did Renaissance mathematicians once consider themselves inferior to the great ancient mathematicians?

In the book "What Do You Care What Other People Think?", Feynman talks about how in the 16th century Niccolo Tartaglia discovered a solution to cubic equations. He says while this was not a major ...
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789 views

Who are the top mathematicians who were ignored due to their unconventional approach?

A perfect example would be Srinivasa Ramanujan. It is known that the conventional community throughout history have been close-minded towards great men of science and mathematics (e.g., Galileo). ...
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Who was the first person to prove the invariance of the Euler characteristic under triangulations?

Given a compact orientable surface $S$ and any triangulation where $F$ denotes the amount of triangles, $E$ denotes the amount of edges, and $V$ denotes the amount of vertices, we know that the Euler-...
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How did Dyck originally state and prove his theorem in topology about the connected sum of a torus and projective plane?

Dyck's theorem in topology is sometimes stated as follows: the connected sum of a torus and projective plane is homeomorphic to the connected sum of three projective planes. Certainly, this is the ...
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34 views

Old Indian and Chinese references

It is been some years since I completed my graduate studies in mathematics at a Spanish university. I remember one of the most pleasant and enriching moments I experienced was when reading Euclid´s ...
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688 views

Who was the first to show that this quintic equation has five radical roots?

Despite this is being a very trivial question, I would like to know who was the first (with reference evidence) to show that the following quintic equation has five radical roots: $$x^5 + x + 1 = 0$$ ...
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452 views

Were ancient Romans so bad at computations before Arab numerals?

It is often said that Romans (see below) had a terrible number system, which made computations a mess. I do believe this, but I'm suspicious of the claim that nobody had better ways to do computations ...
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193 views

Why do we call it a “positive definite matrix” rather than a “positively definite matrix”?

The term positive definite matrix is a standard one used in mathematics, especially in linear algebra. Are there grammatical, linguistic, or historical reasons why it was not called a positively ...
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1answer
114 views

Why positive definite matrix rather than positively definite matrix? [duplicate]

"Positive definite matrix" is a standard term in mathematics, espeically linear algebra. Are there grammatical, linguistic, or historical reasons why it was not called "positively definite matrix"?
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129 views

Have orthogonal complex matrices appeared in the literature?

According to https://en.wikipedia.org/wiki/Orthogonal_matrix, https://en.wikipedia.org/wiki/Unitary_matrix, and Friedberg et al.'s Linear Algebra (4th edition), a matrix $A\in F^{n\times n}$ is ...
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Are there widely accepted math symbols using non-Latin alphabets or characters other than Greek and Hebrew?

We have $\pi$ and $\aleph_0$ borrowed from Greek and Hebrew alphabets. Are there widely accepted math symbols using non-Latin alphabets or characters other than Greek and Hebrew? A related question ...
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63 views

Any idea on how Lagrange came up with similar functions concept in (proto)group theory?

Lagrange defines "similar functions" as functions of the roots of an equation where they change values only at the same kind of permutations of the roots. What's a possible predecessor of the idea of ...
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1answer
64 views

When was the Laguerre's method first used to approximate roots?

Is there a specific date when Laguerre published his root finding method? I found his 1880 note Résolution des équations numériques, but I am not sure if this is the source because I can not read ...
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1answer
160 views

When is the first use of Newton's method for root finding?

I saw this from Wikipedia. The name "Newton's method" is derived from Isaac Newton's description of a special case of the method in De analysi per aequationes numero terminorum infinitas (written in ...
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70 views

How was mathematics used in World War II to “act on the right amount of intelligence”?

In the movie "The Imitation Game", Alan Turing along with his team crack the German encryption machine Enigma but advises his superiors to not act on all decrypted intelligence, as that might lead to ...
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256 views

What problem was solved by introducing the dimension of a vector space?

In linear algebra, we care a lot about dimensions. I get why it’s useful but not why it’s such a big deal. So I wondered what problem was solved historically by introducing a rigorous definition of ...
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79 views

What is the history of these prime counting function approximations?

I am reading several sources and there seems to be a lack of clarity, and some contradiction, about the origins of the most recognised prime counting function approximations: $\pi(n) \sim \frac{n}{\...
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251 views

Who first identified $\frac{n}{\ln(n)}$ as an approximation of a prime counting function?

Gauss, in his 1849 letter to Encke, mentions that he noticed the primes have a density approx $\frac{1}{\ln(n)}$. In that letter, he also mentions an integral function for approximating the prime ...
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1answer
141 views

Could a “field” have non-commutative multiplication originally?

Today, when the term "field" is defined in algebra, it is almost always stipulated that all fields are commutative. However, the author of these lectures says that this has not always been the case: ...
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79 views

When and where was Legendre's Conjecture first published?

When and where did Legendre first publish or write about his conjecture that there is a prime between consecutive square numbers? $$n^2 < p < (n+1)^2$$ I have looked through edition 1 and 2 of ...
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191 views

Why was the original typesetting of Number Fields by Marcus so horrible?

Does anyone here know what technology or instrument was used to typeset the first edition of the well-received textbook Number Fields by Daniel A. Marcus? I ask because the original edition looked ...
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274 views

Why are complex numbers called 'complex'?

I'm a high school teacher, and I was just wondering why complex numbers are called 'complex'. I have read that Gauss coined the term. But I couldn't find any reference where it was explained. I also ...
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102 views

The Roman numeral system continues to lack a zero digit today. Would zero ever get its own Roman numeral digit in the future? [duplicate]

This question is a follow-up to: Why didn't the number zero (0) have a Roman numeral of its own? The number zero did not have an official Roman numeral symbol in the first place, and it still ...
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143 views

Has any large group of people used a base other than 10, 20 and 60 for ordinary purposes?

Wikipedia's list of numeral systems lists only $10,20,60$ as having been used in history. There are about twenty-five sets of symbols there used by different groups of people, but only three different ...
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94 views

How did Ruffini manage to extend the methods of Lagrange in order to “prove” the insolvability of the general quintic equation?

Since Lagrange published his Reflections papers during the early 1770s — around 30 years before Ruffini took up and extended the subject — I was wondering if there were any results that were ...
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70 views

What's the history of experimentation by simulation? [closed]

How did the essemtial general purpose algorithms for simulations evolve over the past 50-100 years?
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239 views

What does an 100 year old calculus exam look like?

I wonder whether the questions on a calculus exam at university were easier or harder 100 years ago. Nowadays we have all these aids and different learning methods. I would love to see an old exam.
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78 views

What are the Peirce's axioms of arithmetic and how do they relate to the Peano axioms?

I will be glad if someone who has seen Peirce's paper could summarily describe here Peirce's axioms and describe their relation to Peano's.
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93 views

What is the name of the “largest complete history” of physics?

Somewhere in the world is housed what is thought to be the largest complete history of physics. I recall it being of some ridiculous length, something like hundreds or thousands of volumes. I cannot, ...
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162 views

Who introduced the divisibility symbol $a\vert b$ (“$a$ divides $b$”) and when?

I have just stumbled across this post and became curious about the same question, namely the part regarding the origin/history of the vertical bar symbol $a\vert b$ that we use to denote "a ...
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84 views

How were number symbols derived/shaped up?

This question was sitting on my to do list for sometime. So, as I was reading a book on history of science, I came across of a paragraph where the author attempted to give a historical development ...
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1answer
2k views

Story of a student who solves an open problem

A number of years ago, I read a (non-fiction) story about a young mathematician whose professor wrote an open problem on the board and the student went ahead and wrote down a solution after a moment ...
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86 views

What is the origin of the “Japanese bracket”?

In discussions of Sobolev spaces one often sees the Japanese bracket, $$\langle x \rangle = (1+|x|^2)^{1/2},$$ as useful shorthand. I was not easily able to find information about this term. (1) What ...
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71 views

What is the difference between Einstein's and Boltzmann's definitions of probability?

In the Einstein's 1905 paper on light quanta, he wrote the following about Boltzmann's notion of probability: The word probability is used in a sense that does not confirm to its definition as it ...
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416 views

Who discovered the difference between the infinities?

As we know, there is a difference between the (infinite) size (or cardinality) of the integer numbers and the size of the reals ($\aleph_0$ and $\mathfrak c=2^{\aleph_0}$). Who discovered it first?
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Are there theorems that have been truly lost?

Related: Are there any theorems that become "lost" and discarded over time? Is there a 'lost calculus'? The questions above use the term 'lost' to refer to theorems that exist in ...
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What are the earliest known proofs that planimeters 'work'?

The dates of various physical implementations of planimeters are pretty well known. I'm interested in discovering when formal mathematical proofs were published that any given design does calculate ...

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