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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24 views

How did Gaussian and Eisenstein integers get their names?

I can separate this into two questions at some point if necessary, but it's possible that sources for the answer to one will provide the answer to the other at the same time. I learned about ...
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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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Why was the Vietnam Day Committee, begun by Stephen Smale and Jerry Rubin, named as it was?

Stephen Smale, an American mathematician and Jerry Rubin, who was at Berkeley before dropping out to organise around left wing causes, set up the Vietnam Day Committee in 1965 during a 35 hour anti-...
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How did Von Neumann come up with his Merge sort algorithm?

Since merge sort was the first $O(nlogn)$ general purpose sorting algorithm I find it rather surprising that it was discovered without having any obvious conceptual predecessors. Are there any ...
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Why did the existential and universal quantifiers in logic took so long to become formalized into symbols after the invention of boolean algebra?

Was there a specific reason that prevented researchers in boolean algebra to invent such quantifiers in the flexible format that are known today earlier? Since the compact symbols for multiplication ...
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Finding sources for “computers will become so powerful that special functions will become obsolete” as a zeitgeist

In Why are special functions special [Physics Today 54, 11 (2007); eprint], Michael Berry makes the following observations: This continuing and indeed increasing reliance on special functions is a ...
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Advantages of numbers growing to the left (ordered Arabic numbers)? [closed]

I was just thinking how the BOM in files makes a lot of sense. I mean the fact that by default numbers grow to the right. And then I started wondering why our numbers grow to the left, if columns of ...
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History of Mathematical Biology - Resource Recommendations

Biology nowadays is filled with mathematics. Indeed, the field of mathematical biology is huge, and shows no sign of decay. But the mathematisation of biology is, to my knowledge, a recent phenomenon -...
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Is there any book or site where Gauss' collected philosophical writings are presented?

From the questions on some of Gauss' philosophical ideas here at HSM stackexchange it's clear that Gauss had some major philosophical ideas that despite their profundity don't seem to have had much ...
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Where does the name “geometric theory” come from?

In mathematical logic, where does the adjective "geometric" comes from, in terms like "geometric theories" and "geometric logic"? These terms come up in fields like topos ...
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Origin of notation “R with a stroke on the leg” for the square-root (℞)

The following text from Ars magna (1545) by Girolamo Cardano is known as the inception of complex numbers: "imaginaberis ℞ m 15" (You will imagine the square root of minus 15): The "R&...
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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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Has anyone explored Ptolemy's epicycles as an early form of Fourier analysis?

Whilst researching science in the ancient world, I came across an observation, which unfortunately I did not make a note of, and so cannot credit, that Ptolemy's epicycles were an early form of ...
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Did Fourier use heated metal rings as experimental evidence to justify his mathematical discoveries?

In his answer to a previous question Alexandre Eremenko pointed out that Joseph Fourier in his book Analytic Theory of Heat gave all kinds of arguments in favor of the following mathematical ...
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How was Fourier analysis important to the development of set theory?

I recently read the following quote (unfortunately, I copied it down without attribution): You may be surprised to know that Fourier analysis played a role in the early development of set theory. In ...
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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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An English translation of Simon Stevin's De Thiende

I enjoy reading manuscripts written by mathematicians of old, and I would love to read the famous De Thiende by Simon Steven. I've done some research online here and there, but I have not found any ...
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Origin of Tensor Product

When and why did Mathematicians saw a need to define Tensor Products? I want to know the historical development of the idea "Tensor Product"?
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149 views

Differences between modern and old mathematical notations

Note: I didn't write the word "ancient" in the title because I want to see the notation from 1400 A.D. to 1700 A.D. Mathematical notation has changed very much from the past millennium, and ...
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Photo of Wilhelm Ackermann

I am writing a text on the Theory of Computation. I am looking for a photo of the mathematician Wilhelm Ackermann. He is well-known in the field, was a student of one of the most famous ...
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Lagrange's Theorem as he stated it

In Wikipedia, I found that Lagrange did not state Lagrange's Theorem in its general form. He stated "If a Polynomial in $n$ variables has its variables permuted in all $n!$ ways, the number of ...
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Did physicists correct an error of mathematicians in counting twisted cubics in the quintic?

One problem in enumerative geometry consists in counting the number of rational curves of degree $d$ in the plane going through $n$ general points. If $n = 3d-1$, this number, denoted $N_d$, is finite ...
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Who first used the Completeness Axiom for real numbers?

I was studying calculus and the following question came to my mind: Who was the first person to use or suggest the use of the Completeness Axiom of the Real Numbers?
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The origins of differential homological algebra

Differential homological algebra in its initial formulation is due to Eilenberg and Moore, who first published the homological version of the Eilenberg–Moore spectral sequence in 1965 (and the ...
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What's the history of the heuristics on doing science efficiently and effectively?

I recently read a paper by Taleb about doing science efficiently and effectively and I was wondering if there other predecessors to his work which more or less express the same things(since Taleb ...
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Research about Stafford Beer's claim about a method for solving simultaneous equations unknowingly via a game by kids?

I found this claim in the book "How many grapes went into the wine", in the Artorga section: In 1956 I devised a game for solving simultaneous linear equations in two variables. The theory ...
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Were pictorial notations like Feynman diagrams for integrals used before Feynman?

In the book Mathews, Walker: Mathematical Methods of Physics, Addison-Wesley(1969), there is a pictorial notation of the solution found by Fredholm about an integral equation.p.304, p.305This circle ...
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What are some of Euler's mistakes?

[Note: This is the same question on MSE, but it has only five answers, one of which doesn't give an exact answer (it tells that a conjecture of Euler was wrong, but a conjecture isn't a mistake) and ...
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What was Heawood's proof of maximal planar graph 3-colorable implies its dual is bipartite?

In graph theory, it is a well-known (I guess folklore) result that the following three conditions are equivalent for a maximal planar graph $G$ (definitions are given at the end). Every vertex in $G$ ...
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Was Lebesgue differentiation theorem the motivation for Vitali's, Riesz's and Hardy-Littlewood's results used to prove it?

I have been reading about the Lebesgue differentiation theorem from Terence Tao's book and came across a bunch of things. In his book, Tao uses the Vitali Covering lemma (finite), Hardy-Littlewood ...
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Which mathematician traveled to and moved in with each collaborator?

I remember a video, perhaps a Numberphile episode where a mathematician was described who would simply move in to the home of a collaborator with which they were engaged to so that they could work ...
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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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“Family tree” of mathematicians and their PhD advisors and students

Whilst looking at the Wikipedia pages for some well known mathematicians I was surprised at how many of them were advised by other recognisable mathematicians. In some cases I could back track 5 or ...
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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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Where does the word root comes from?

Where comes the word root when talking about the points when a polynomial gets the value $0$?
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Complete list of publications of Rebecca Barlow

Rebecca Barlow is the discoverer of an interesting surface in algebraic geometry. Is anybody aware of a full list of her contributions? Has she continued working in mathematics in the 21st century?
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Does Blum's speedup theorem have any conceptual predecessors?

Blum's speedup theorem seems to me that bears at least some superficial resemblance to Godels research on the length of proofs under certain axiomatic systems. Does Blum's speedup theorem has any ...
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How did Peano come up with his space filling curve?

Wikipedia cites an earlier result of Cantor as an inspiration but I wonder if there are any previous results of some kind of recursive curve constructions that may have also "inspired" him ...
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What are some historical examples in physics of heuristic proofs of mathematical results?

In the proceedings of the XIth International Congress of Mathematical Physics Edward Witten wrote (p. 704) [$\dots$] when a mathematical result is really relevant to a physics problem it often ...
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164 views

Are there any mathematicians who expressed non-obvious sets of rules on how to do research?

I recently saw a paper where there are presented some rules on how to learn mathematics (and do research) which were firstly articulated by Lagrange. Are there any similar rules that were expressed ...
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What were Riemann's “semi-physical” methods?

In John Von Neumann's The Mathematician one can read that [$\dots$] even after the reign of rigour was essentially re-established with Cauchy, a very peculiar relapse into semi-physical methods took ...
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Was Morse code the first practical application of binary encoding of information?

As I understand schemes for sending different symbols over different wires were implemented but the simplicity of Morse's dot or dash made it the easiest to read and/or implement. It seems similar to ...
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Was Giuseppe Peano one of the greatest mathematicians of his era? [closed]

Besides the Peano axioms which perhaps brought him fame but which are considered a refinement of similar previous axioms Peano seems to have done relatively little original work. Does the rest of his ...
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When did mathematicians suspect that $\pi$ is irrational?

The title says it all. The irrationality of $\pi$ was proved by Lambert in the 18th century, but the Greeks at the time of Pythagoras already knew that $\sqrt2$ and the golden ratio were irrational. ...
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247 views

How did ZFC become the standard foundations of mathematics?

I would like to hear about the historical and technical reasons for why Zermelo-Fraenkel set theory with the axiom of Choice became the dominant standard for the foundations of mathematics. The system ...
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Why didn't the ancient Greeks consider 1 to be odd?

The Wikipedia page on parity currently says: The ancient Greeks considered 1, the monad, to be neither fully odd nor fully even Why didn't they consider 1 as odd? (I am assuming they already had the ...
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Who coined the Hawaiian Earrings?

I hope to know who first used the name "Hawaiian Earrings." Barratt, Milnor(1962) says "This example was suggested by Steenrod" in its Introduction: https://www.ams.org/journals/...
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Where did Leibniz explore the product rule of differential calculus?

In what book/letter did Gottfried Wilhelm Leibniz explore the product rule as part of differential calculus?
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How did the Vietnamese manage set up the Vietnamese Mathematical Society during the Vietnam War?

The Vietnamese Mathematical Society was set up in 1965 by Le Van Thiem and Hoang Tuy. Both had studied in Europe, the former in Paris and Germany and the latter in Moscow. By 1965, the Vietnam War, ...
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Why isn't the history of mechanics dated from Archimedes time?

It's often said - and more often written - and perhaps, even more spoken of - that modern physics began with Galileo due to his application of mathematics to motion. This is the position taken by ...

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