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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The history and motivation of eigenvectors
I want to understand more about the history of eigenvectors. Was the discovery of eigenvectors inspired from an application to achieve a result in a historical context, was there a phenomenon which ...
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What was the role of Schmidt in derivation of the Gram-Schmidt process?
When reading the section related to Gram-Schmidt process in the book Linear Algebra and Its Applications by Gilbert Strang, I found a foot note that says:
If Gram thought of it first, what was left ...
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Are adjoint operators historically related to integrating factors?
Birkhoff and Rota, in their book Ordinary Differential Equations (4e), claim on p.55 that:
The concept of the adjoint of a linear operator, which originated historically in the search for integrating ...
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Writing Mathematical Symbols in 20th century
As I was reading some papers written by Schrödinger and Heisenberg back in 1920s, I noticed that the symbols they use such as the integral or summation sign or calligraphic letters are as if printed ...
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Did John von Neumann hate pure mathematics that became too abstract?
John von Neumann wrote the following in his essay The Mathematician:
As a mathematical discipline travels far from its empirical source, or still more, if it is a second and third generation only ...
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Who first stated the "uncertainty principle" for Fourier transforms?
My question is clearly related to this one, but my interest is not specifically in Heisenberg's result. To quote from Wikipedia.
A nonzero function and its Fourier transform cannot both be sharply ...
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How do we explain the lack of activity in the study of Latin mathematics?
A full professor teaching the history of mathematics at Masters level recently told a friend of mine that there was nothing of interest left to explore in the mathematics written in Latin over the ...
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Different models for the development of mathematics: Latin versus butterfly
Ian Hacking's 2014 book *Why is there philosophy of mathematics at all?", see here, contains many interesting ideas. One of the ideas is the dichotomy of two distinct models for the development ...
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What is Cardano trying to say in this passage of his Ars Magna Arithmeticæ?
It is well known that Cardano considered the problem of "dividing 10
into two parts the product of which is 40" in his Ars Magna. This problems leads to the complex solutions $5+ \sqrt{-15}$ ...
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Is there existing footage of Stanislaw Mazur giving Per Enflo a live goose for solving the approximation problem?
There is a famous incident in the history of mathematics involving the mathematician Per Enflo being awarded a live goose by Stanislaw Mazur for solving problem 153 in the Scottish Book by ...
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Seeking Comprehensive References on the History of Scientific Notation
I am on a quest to uncover the rich tapestry of history surrounding scientific notation as a way of expressing numbers. Specifically, I'm interested in scholarly books, peer-reviewed articles, and ...
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How did someone discover LCM?
How did someone came up with an idea that if we do prime factorization of two numbers and then multiply all the prime factors but including common ones only once, we will get a number that is the ...
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Origin of exact and closed differential expressions
In differential geometry and other fields, an expression involving differentials can be closed or exact. In $\mathbb R^2\setminus\{0\}$ for example, $dr$ is exact whereas $d\theta$ is closed but not ...
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Whence Whitehead's essence?
In the article Quine’s New Foundations of The Stanford Encyclopedia of Philosophy (Summer 2019 Edition), Thomas Forster writes:
In [1944] Hailperin gave the first of a number of finite ...
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Was "potency set" used for power set?
Cross posted at Math Overflow
For historical reasons, the English term "power set" in set theory is a translation of the German "Potenzmenge", which is still in use in German ...
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Reference request: What were the problems of accepting zero, negative numbers, and complex numbers? And how were they solved?
I asked this question on MSE and comments suggested I should ask it here
I am currently reading Baby Rudin as my second analysis book (after Introduction to Real Analysis by Robert G. Bartle and ...
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Examples of mathematicians who applied to patent their work
MIT's RSA encryption was granted a patent although it was not enforced for non-commercial applications. Similarly for Stanford's PGP encryption algorithm. However, these are institutions rather than ...
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Did anyone apply for a patent based on sphere packing?
Some while ago we had a question about mathematicians patenting their work Examples of mathematicians who applied to patent their work I was about to answer when I realised I needed to find a ...
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Where does the term elasticity (of a function) come from?
Elasticity of a function is a mathematical concept that is widely used in economics. In particular, price elasticity of demand or supply. But generally elasticity in economics is the measurement of ...
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Etymology of "power" (math.)
Having done some searches on the internet, seems like the term "power" is a mistranslation. The Wikipedia article links to an article in the MacTutor History of Mathematics archive where it is written
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Why did systems theory never gain popularity?
Briefly from wikipedia,
Systems theory is the interdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or human-made. Every system has ...
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Did Fibonacci not grasp the idea of zero?
Indian mathematicians (e.g., Brahmagupta in the 6th century) developed the idea of 0 as more than a placeholder.
In 1202, Fibonacci wrote "These are the nine figures of the Indians: 9 8 7 6 5 4 3 ...
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Who proposed terminating decimals as a major set and why are them important in France?
After looking at some school sources in French, it is common to provide the various number sets in the following order
$$\mathbb{N}\subset \mathbb{Z}\subset\mathbb{D}\subset\mathbb{Q}\subset\mathbb{R}\...
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Group theory in non-European/subaltern cultures?
I'm doing undergraduate research on the history of abstract algebra (specifically permutation groups) and the notion of symmetric groups in indigenous artwork has come up several times. Is anyone ...
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Did J. W. Gibbs “invent” Hilbert spaces before Hilbert formulated the notion of such spaces?
I was surprised to see a reply to a comment on his answer to a Quora question by a research mathematician claiming that Hilbert spaces were actually due to J. W. Gibbs rather than to D. Hilbert. The ...
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Why was the cubic specifically so hard to solve?
I'm a huge fan of the history of Algebra and, recently, I've noticed a bit of an oddity. Degree one equations have been known (and solved) for as long as human history. For degree two equations, we ...
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How did the obelus ÷ come to stand for division?
The obelus ÷ represents division on calculator keyboards, and sometimes in elementary education.
It has a long non-mathematical history starting before 200 BC. Its ...
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Question about Leibniz's "characteristic numbers" and propositional logic
The Wikipedia article on Gottfried Wilhelm Leibniz mentions, in the chapter on symbolic thought, that:
Leibniz saw that the uniqueness of prime factorization suggests a central role for prime numbers ...
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What was Euler's motivation for introducing $i$ for $\sqrt{-1}$?
[Mauro Allegranza has answered the question of who introduced the notation $i$ (Euler, followed later by Gauss), so I have changed the title. I have also edited the question in other ways to make it ...
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History of Algebraic Geometry: Morphisms and Birational Geometry
Good people, I'm trying to get my head around the history of algebraic geometry, and while Dieudonné's tome is a very good source (very often the only source), it can from time to time be very ...
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Source of a Poincaré quote: "Logic sometimes makes monsters..."
There's a quote by Poincare on the "new functions", such as continuous functions without derivatives, that were appearing during the second half of the 19th century. The fullest version I've ...
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Was there an intentional purge of all audio recordings of Alan Turing?
The YouTube video Alan Turing's lost radio broadcast rerecorded contains a re-enactment of Alan Turing's lecture broadcast by the BBC.
In the introduction, the narrator (James Grimes, also of the ...
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Etymology of "discrete" in mathematics
People sometimes make a distinction between continuous mathematics and discrete mathematics.
Continuous mathematics study objects that abstract the notion of a continuum and typical examples are the ...
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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 Gödel's research on the length of proofs under certain axiomatic systems.
Does Blum's speedup theorem have any ...
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Who introduced the terminology “nondecreasing” for weakly increasing (i.e. x≤y ⇒ f(x)≤f(y)), and when/why?
Arguably one of the most hated parts of English mathematical terminology is the word “nondecreasing”, referring to a function such that $x\leq y \;\Rightarrow\; f(x)\leq f(y)$ (what other conventions ...
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Can I find the number e in the tables of Napier?
As Napier calculated the logarithms of numbers in the base $\left(1-\frac{1}{10^7}\right)^{10^7}$, I expected to find the number $e$ in the tables of his Mirifici Logarithmorum Canonis Descriptio. ...
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What is the history of moment generating functions, and the more general characteristic functions?
Moment generating functions provide an alternative specification for a probability distribution function (pdf), often making it very convenient to calculate expectations, variances, etc. of said pdf.
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When did mathematicians realize that theory of algebraically closed fields admits quantifier elimination?
A nice property of algebraically closed fields is that the theory that describes them ($ACF$) admits quantifier elimination: any statement can be shown equivalent (in the theory) to another statement ...
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Foundational crises in non-Western historical mathematical communities
In Foundations of Set Theory by Fraenkel, Bar-Hillel, and Levy (1973), the authors argue that there have been three distinct periods of crisis in the foundations of mathematics. The first was ...
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History of right hand rule
I am curious to know when the right-hand-rule for vector product was established and used consistently in mathematics.
I read here
Who gave right hand thumb rule for circular loop of current ...
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List of textbooks on Abstract Algebra in the order of time
I am knowing Abstract Algebra things; I am searching aims of Abstract Algebra and origins of parts of Abstract Algebra. I thought original initial textbooks have explicit links to aims and origins of ...
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Any notable large proof that took a long time before anyone checked it?
Have there been any examples in the past where a large proof is claimed but nobody takes the time to check and that has been proved/disproved after a long time? I am not interested in proofs that were ...
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Who first referred to the number of nonzero entries of a vector as its $\ell_0$ norm?
It is common in the compressed sensing literature to refer to the number of nonzero entries of a vector as its $\ell_0$ "norm." The scare quotes are there because strictly speaking, the $\...
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Did Gauss formulate, or at least know of, the full essence of the Gauss-Bonnet Theorem?
I know that a special case of the Bonnet theorem, called the Theorema Elegantissimum, was proved by Gauss in his 1827 treatise on differential geometry. This was a theorem that dealt with the ...
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When did Zermelo and Fraenkel publish their axioms?
I have googled the heck out of this but cannot find a reference to the year Z&F published their axioms. I'd expected to see an article reference but none that I could find.
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How to find the first appearance of a theorem?
I often have questions of the "who predicted and proved this theorem when and in what context?" kind.
There are two ways I can think of.
Read books on the history of mathematics.
Find ...
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Pefsu problem explanation
Problem no. 12 from Moscow Mathematical Papyrus:
Example of calculation of $13$ heqats of grain
If someone says to you: Take $13$ heqats of grain to make them into $18$ jugs of beer
Note that the ...
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Did the Romans really use the binomial formula to calculate products?
I'm not quite sure if this is the right place to ask this question (in fact, I was redirected to this SE from the Math Stackexchange), but it's probably more fitting than the original posting place.
I ...
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When was the first time/s that sheaves entered algebra and algebraic geometry?
I'm interested in knowing about the first published texts in which sheaf-theoretic methods were used in algebra and/or in algebraic geometry.
The oldest instance I am aware of is J.-P. Serre, ...
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Why is Robinson arithmetic "Q"?
I see Peano arithmetic so often abbreviated as "P" or "PA". Why is Robinson Arithmetic "Q"? Following the obvious pattern, I would have expected R" or "RA".
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