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Biographical details of Isador M. Sheffer

The Sheffer sequence of polynomials satisfies conditions that are related to the umbral calculus. They are named after the American mathematician Isador M. Sheffer. He obtained his PhD degree at ...
Max Muller's user avatar
-1 votes
0 answers
39 views

If can list all the think breakthrugh events in the science? [closed]

I want to understand the relationship between scientific development and intellectual development: Can the history of science be regarded as the history of the development of human thinking? At what ...
aircraft's user avatar
0 votes
0 answers
23 views

What is the difference between Bragg scattering coefficient and Fresnel's reflectivity coeffficient? [closed]

So I would like to know the fundamental difference between the Bragg scattering coefficient and Fresnel's reflectivity coefficient. Also why are they both the same for horizontal polarization? Does ...
Ashmitha Nihar's user avatar
12 votes
4 answers
2k views

Why are the categories of category theory called "category"?

The category-theoretical concept called "category" seems quite dissimilar to what we consider a "category" in everyday life or colloquial speech and even other fields of science, ...
das-g's user avatar
  • 221
1 vote
1 answer
75 views

In Newton's time, were observations accurate enough to corroborate that the Sun orbits the common center of mass of Sun-Jupiter?

The context of the question: In Newton's time the distances between the celestial bodies of the Solar system were known. On the assumption that the inverse square law of gravity holds good: From the ...
Cleonis's user avatar
  • 814
3 votes
2 answers
102 views

Historically, when were the terrestrial planets first called terrestrial planets?

I asked this on the Astronomy Stack Exchange, but it's probably better suited here—When did we start using the phrase "terrestrial planets" to refer to the inner planets in English ...
oaklight37's user avatar
5 votes
1 answer
295 views

What's a Heine reference for the "Andréief-Heine identity"

The "Andréief identity" or "Andréief-Heine identity", which can be interpreted as a continuous analogue of the Cauchy-Binet formula, comes up a lot in the context of random matrix ...
kimchi lover's user avatar
  • 2,647
3 votes
0 answers
69 views

Why did Vandermonde become interested in algebraic problems?

I recently became interested in a person named Vandermonde when I posted a question on this site about the history of determinants and read the answers and comments. He was a person who loved music ...
user1274233's user avatar
4 votes
1 answer
70 views

Boole's use of supplementary classes

Boole could have represented "$x$ is a subclass of $y$" via the formula $x=xy$ (where $xy$ signifies the intersection of the class $x$ and the class $y$), but according to Daniel Bonevac and ...
James Propp's user avatar
2 votes
6 answers
1k views

A Comprehensive Masterpiece on History of Science

I am looking for books that are very technical on History of Science as a whole. It should be encyclopedia-typed, and written by prominent historians. It should also include philosophy of science type ...
Yinuo An's user avatar
  • 121
3 votes
2 answers
135 views

Origins of the use of matrices for the calculus of binary relations

Nowadays it's common to represent a binary relation $r$ (a subset of the Cartesian product of two sets $A$ and $B$) as a 0,1-matrix whose rows correspond to elements of $A$, whose columns correspond ...
James Propp's user avatar
2 votes
0 answers
76 views

How was Laplace able to propose the Laplace expansion?

I read Sylvester's 1850 paper, which is on file here. If you look at page 147 of this file, you will see the following sentence: Imagine any determinant set out under the form of a square array of ...
user1274233's user avatar
4 votes
1 answer
146 views

What were the details of Brahmagupta's theory of gravitation?

When talking of our evolving idea of Gravitation we usually talk about Aristotle's theory of falling things, Newton's universal gravitation and Einstein's general relativity. However, I want to ask of ...
Prasoon Jha's user avatar
3 votes
1 answer
478 views

Source for a story about algebraic number theory?

I once read that Hilbert and Hurwitz (I think it was them) once discussed the theorem about unique factorization of ideals/divisors in algebraic number fields in one of their walks. They, the story ...
Fernando's user avatar
  • 148
0 votes
0 answers
49 views

History of Invertible linear transformations

Who studied invertible linear transformations for the first time? I would guess these linear transformations weren't studied for the sake of studying invertible linear transformations, they probably ...
user926356's user avatar
2 votes
2 answers
129 views

Infinity as a truth value

I seem to recall that Claude Shannon, in developing his symbolic theory of electrical networks, remarked in a footnote that for some purposes it would make more sense to represent truth by infinity ...
James Propp's user avatar
3 votes
2 answers
181 views

Where does this quotation attributed to Turing actually originate from?

Many sources (e.g. Wikiquote, referencing a 2012 Guardian article) attribute the following quote to Alan Turing: A computer would deserve to be called intelligent if it could deceive a human into ...
ACuriousMind's user avatar
1 vote
0 answers
79 views

Who first proved the "Fundamental Theorem of Well-Ordered Sets"

This theorem is also known as the "Comparability theorem for well-orderings", https://proofwiki.org/wiki/Fundamental_Theorem_of_Well-Ordering. It states that two well-ordered sets are either ...
Porky's user avatar
  • 111
4 votes
1 answer
136 views

Regula Pigri: How far does it date back?

Regula pigri, or rule of the lazy, is a method of multiplication of single-digit numbers. If one is to multiply 6 by 8, one would start by bending one's fingers like so: B B B B S        B B S S S ...
Shacharit's user avatar
0 votes
0 answers
83 views

How and when did the set brackets disappear from standard accounts of classical set theory?

On page 287 of the article On the Axiom of Extensionality, Part II, The Journal of Symbolic Logic, Vol. 24, No. 4 (Dec., 1959), pp. 287- 300, the author R. O. Gandy writes: "But, in the absence ...
Frode Alfson Bjørdal's user avatar
3 votes
1 answer
115 views

Origin of decomposition theorem

There are many different types of decomposition theorem in linear algebra. For example, there are primary decomposition theorem, cyclic decomposition theorem, etc. But I became curious about the ...
user1274233's user avatar
-2 votes
1 answer
106 views

Did Grothendieck have any thoughts on foundations of mathematics? [closed]

I remember reading that Grothendieck didn't care much about foundational issues and didn't want to be 'stuck all the way down there'. Does anybody know if he ever actually said this? Did he have any ...
junior56's user avatar
3 votes
1 answer
127 views

From where did the term "context-free" originate?

In Greibach's survey Formal Languages: Origins and Directions, she writes the following paragraph on page 19 about the term "context-free": The theory of context-free languages was being ...
user319109's user avatar
0 votes
0 answers
20 views

Equator on astrolabe - how to determine location

I am reading "The Light Ages" by Sebastian Falk. I have a grasp of the main markings on an astrolabe but I am having difficulty understanding how the equator marking was determined on the ...
Clive Long's user avatar
5 votes
4 answers
874 views

Books using the axiomatic method

Apart from works on geometry (such as Euclid's Elements and its various translations) and Spinoza's Ethics, has the axiomatic method been used as a means of exploring a certain field or exposing one's ...
Holland's user avatar
  • 51
2 votes
1 answer
177 views

Given that the ancient Greeks had a rough idea of the great distance, did any of them suggest the sun was not just a big fire?

I believe that the ancient Greeks' measurement of the sun's distance showed great sophistication. Given that fire was something everyone was familiar with and they knew how rapidly heat diminished as ...
releseabe's user avatar
  • 1,213
1 vote
0 answers
63 views

When were Peano axioms formulated purely in first-order logic?

It is mentioned on the Wikipedia article about Peano axioms that: The ninth, final axiom is a second-order statement of the principle of mathematical induction over the natural numbers, which makes ...
Weier's user avatar
  • 399
1 vote
0 answers
74 views

Who are some famous statisticians from the 20th and 21st centuries, who didn't have a formal training in statistics?

I'm looking for examples of people who made some important contributions to the field of statistics, yet their original training was not in statistics and they may have learned it 'on the job', while ...
Coris's user avatar
  • 11
2 votes
0 answers
63 views

Does Henry Rice's doctoral dissertation exist online?

Henry Gordon Rice is perhaps best known for Rice's theorem, which states that any non-trivial semantic property of Turing machines is undecidable. In a footnote to his Trans. Amer. Math. Soc. article (...
user319109's user avatar
1 vote
1 answer
133 views

Origin of Multi-linear map

Multi-linear map is used to define the determinant. However, since the multi-linear map itself does not have linearity, I feel a sense of heterogeneity when I compare this concept with the contents ...
user1274233's user avatar
15 votes
10 answers
3k views

Folk stories and notions in mathematics that are likely false, inaccurate, apocryphal, or poorly founded?

There are numerous popular folklore stories in mathematics, and it is an interesting question to understand the accuracy of these folk stories. Folklore stories, and urban legends are subborn things, ...
Georg Essl's user avatar
  • 1,201
0 votes
1 answer
82 views

Universal logicians

Henri Poincaré is often considered to be the last universal mathematician, meaning the last individual who made contributions across all areas of mathematics of his time. Today, even a prodigious ...
B. Peterson's user avatar
5 votes
1 answer
1k views

Historically are there any documented attempts at finding algorithms that are asymptotically faster than the FFT for the Discrete Fourier Transform?

I found out some bounds on the Discrete Fourier Transform calculation on certain models of computation but nothing on attempts at finding algorithms asymptotically faster than the Cooley-Tukey FFT on ...
Nicolaus 's user avatar
3 votes
0 answers
123 views

Who first introduced trigonometric substitutions in integral calculus?

I've been researching the history of integral calculus, specifically focusing on the use of trigonometric substitutions. Despite my efforts, it remains unclear who first introduced this technique. ...
Emmanuel José García's user avatar
2 votes
1 answer
261 views

Was Freud a scientist? If so, does this mean psychoanalysis is a scientific method? [closed]

Freud was a dominant thinker in 20th c intellectual history, testimony to which is given by the sheer volume of articles, papers and books written by and about him and the psychoanalytic method. ...
DJohnson's user avatar
  • 382
2 votes
0 answers
68 views

History of Leibniz' notation

Does anybody have an idea what manuscript this page (with Leibniz's differential notation) comes from?
Dmitri Starostin's user avatar
0 votes
0 answers
55 views

Does the paper "W.F. Eberlein, Axiomatic charge conjugation, J. Math. Phys. (to appear)" exist?

I found the reference Axiomatic charge conjugation, J. Math. Phys. (to appear) in W. F. Eberlein, Models of space-time, Bull. Amer. Math. Soc. 71 (1965), 731-736, (pdf) however, I don't find the ...
mma's user avatar
  • 139
1 vote
1 answer
699 views

Who first documented the smell of hydrogen sulfide to be "the smell of rotten eggs"?

Hydrogen sulfide is known for its characteristic "rotten eggs" smell. And it is well known to everybody having discovered in 18th century. But who first documented it of having the "...
Nilay Ghosh's user avatar
1 vote
1 answer
121 views

Role of Alessandro Padoa in the development of modern mathematics

Here is an excerpt from ESSAI D’UNE THÉORIE ALGÉBRIQUE DES NOMBRES ENTIERS, PRÉCÉDÉ D’UNE INTRODUCTION LOGIQUE A UNE THÉORIE DÉDUCTIVE QUELCONQUE from Alessandro Padoa (as can be found here): nous ...
Weier's user avatar
  • 399
1 vote
0 answers
108 views

Was there experimental data underlying Einstein's $E=mc^2$?

It is customary to provide formulas to describe experimental data, namely in regression. So, when Einstein proposed the formula $E = mc^2$ (I reckon the original formulation was not like this, but I ...
Gigiux's user avatar
  • 111
0 votes
0 answers
115 views

Is Navier-Stokes equations first time derived in work "Sur les lois des mouvements des fluides, en ayant égard à l’adhésion des molecules"?

Quote from this article, page 114 : "Navier provided this equation in a memoir that was read on 18 March 1822 at the Academy of Sciences and published in summary form in the Annales de Chimie et ...
22flower's user avatar
  • 185
2 votes
2 answers
220 views

Origin of the concept of "impulse"

Question: So, I recently looked back into my physics textbook and found the concept of "impulse" there. Now, upon reading the explanation in the textbook and several definitions online, I ...
Bhavya Jain's user avatar
2 votes
0 answers
70 views

When was extreme longevity of some species first suspected?

Although myths of extreme age in heroes and even ordinary humans seemed to have been common, it is only fairly recently that lifespans of centuries for Greenland sharks and Bowhead whales has been ...
releseabe's user avatar
  • 1,213
2 votes
0 answers
57 views

Körner-Contardi reaction: Lost to history?

When we talk about synthesizing aryl halides, the more famous reaction is Friedel-Crafts halogenation which is still used commercially to produce chlorobenzene. If we consider synthesis through ...
Nilay Ghosh's user avatar
0 votes
1 answer
167 views

When did Claude Navier write the work "Sur Les Lois du Mouvement des Fluides"?

When did Claude Navier write the work "Sur Les Lois du Mouvement des Fluides"? I can’t find this information on the internet. "Sur Les Lois du Mouvement des Fluides" read at 1822
22flower's user avatar
  • 185
2 votes
1 answer
88 views

How does the daguerrotype give directly a positive image?

I have already asked this question in the Chemistry community, but since daguerrotype is an old, obsolete technique, I hope this question can be considered as on-topic also here, to increase my ...
Alfred's user avatar
  • 202
12 votes
11 answers
6k views

Are there any well-known mathematicians who were marxists?

Inspired by this post I would like to ask whether there were any well-known (deceased) mathematicians who were marxists? In the early 1930s, Ernst Kolman approved the publication of the Russian ...
Mikhail Katz's user avatar
  • 6,331
10 votes
1 answer
302 views

Did Ulam discover category theory?

(The following query by Noam Zeilberger has recently appeared on the Categories mailing list; I am taking the liberty of asking it here.) In Ulam's autobiography Adventures of a Mathematician, there ...
Todd Trimble's user avatar
3 votes
2 answers
189 views

Were there any criticisms of his first FTA proof during Gauss's lifetime?

According to several papers related to Gauss' FTA proof, in the first proof he said, “It seems to be well demonstrated that an algebraic curve neither ends abruptly (as it happens in the ...
Leonhard's user avatar
2 votes
1 answer
65 views

Why coin "Apophänie" for delusional revelations of a schizophrenic?

In 1958, Klaus Conrad published a monograph entitled Die beginnende Schizophrenie. Versuch einer Gestaltanalyse des Wahns, in which he described in groundbreaking detail the prodromal mood and ...
user95921's user avatar

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