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9 votes
1 answer
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History of the inverse matrix

I know the definition and the procedure to calculate the inverse of a matrix, but I want to know the history of starting the idea of an inverse matrix. mathematicians must have faced a real life ...
user 31466's user avatar
7 votes
2 answers
3k views

Was Richard Feynman a double major?

I know this might be a silly question, but I think it's worth asking. For his undergraduate degree at MIT, did he do a double major with math, or did he really just get that good at mathematics by ...
Arturo don Juan's user avatar
10 votes
1 answer
453 views

What were the initial applications of finite fields?

Finite fields, I believe, were introduced by Galois in his paper "Sur la théorie des nombres", found on page 398 of his Oeuvres. In this paper Galois introduces the idea of taking a polynomial ...
Jack M's user avatar
  • 3,149
9 votes
1 answer
765 views

Did Galileo bet money on the ship experiment?

Galileo's writings describe two experiments involving ships. These are summarized in the Wikipedia article Galileo's ship. (A lot of the text in the article is mine, and if there are things I'm ...
user avatar
4 votes
1 answer
417 views

A reason for why Leucippus isn't credited the original "atomist" in the norm?

His exact contributions are difficult to disentangle from those of his mentor Leucippus, as they are often mentioned together in texts. Their speculation on atoms, taken from Leucippus, bears a ...
M.A.R.'s user avatar
  • 345
5 votes
0 answers
105 views

How did the discovery of the platypus affect Linneaus' taxonomy?

I heard there was a lot of controversy in the royal scientific societies when the first specimens of platypus were shown. How did this affect the taxonomy of animals used at the time, if at all? Has ...
Teusz's user avatar
  • 231
6 votes
2 answers
191 views

Did Schiaparelli comment on the martian canals debate?

It s well known that in 1888, Italian Giovanni Schiaparelli announced finding a network of narrow lines on Mars, which he described as "canali," which a lot of English speakers including American ...
Colin McLarty's user avatar
6 votes
1 answer
2k views

First use of Bernoulli's inequality and its name

The Wikipedia article “Bernoulli's inequality” says, that this inequality is called after the mathematician Jacob Bernoulli. Was he the first one using the inequality? Why is this inequality named ...
Stephan Kulla's user avatar
20 votes
2 answers
13k views

Origin of 360 degrees?

This is by far one of the most challenging and popular HSM questions on the Net. Proofs are, countless discussions about it in math forums. The answers only led to two theories, which Wikipedia does a ...
M.A.R.'s user avatar
  • 345
7 votes
2 answers
2k views

Discovery and Development of Coordinate Systems

I'm very interested to know how coordinate systems were discovered and why mathematicians discovered them? Actually I want to know what things motivated mathematicians to discover and develop ...
Shahed al mamun's user avatar
2 votes
0 answers
908 views

Was Kepler aware of the following golden relationship between the planets?

Was Kepler aware that Venus and Mars have a golden section relationship other than that he attributed to them in his 5 perfect solids model of the Solar System? The dodecahedron and the icosahedron, ...
John Shanahan's user avatar
5 votes
3 answers
4k views

How long did it take to prove that the Earth revolves around the Sun?

I get that Galileo Galilei was a major contributor in proving the helio-centric theory, and same goes to Sir Isaac Newton. The battle for the theory to become law took centuries to prove. People ...
Anthony Pham's user avatar
3 votes
1 answer
277 views

Origin of "world-line?"

The term "world-line" is a little odd in English. Google n-grams shows the English term going back to 1915 in the books google has scanned. Is its origin in Minkowski, Raum und Zeit (1909), ...
user avatar
5 votes
0 answers
642 views

How did Einstein know tensors would be needed in the EFEs?

I'd really never studied tensors until I started studying the Einstein Field Equations. Since then, I have realized they are fairly common tool in physics and pretty basic to understanding many areas. ...
Stan Shunpike's user avatar
17 votes
4 answers
5k views

Who was the first to calculate $\pi$?

I am very interested in the history of $\pi$. I am first trying to find out who calculated it. Many sources have different answers, from the ancient Egyptians, to Archimedes, to the Babylonians. I ...
Anthony Pham's user avatar
18 votes
2 answers
10k views

Who calculated for the first time the volume (and surface area) of the sphere exactly?

As we know, even Archimedes did soon some experimental calculations. My question were, who calculated first time the exact formulas ($V=\frac{4\pi}{3}r^3$, $A=4\pi r^2$)? As I know, these formulas ...
peterh's user avatar
  • 919
7 votes
2 answers
270 views

What are the early examples of taxonomies in the history of science?

When you think of taxonomies, the first thing that comes to mind is Linneaus. But taxonomies were and continue to be used for all kinds of classification, from biology to astronomy and even ...
Teusz's user avatar
  • 231
1 vote
1 answer
247 views

Did Turing ideas make any impact on Psychology or Brain Science? Why?

Some authors, namely Daniel Dennett and Douglas Hofstadter, argue that anything capable of passing the Turing test is necessarily conscious (Hofstadter, D. R., & Dennett, D. C. (2006). The Mind's ...
Lucas Soares's user avatar
6 votes
4 answers
1k views

What year was Euler's paper on the Konigsberg bridge problem first published?

All the sources I've read say that Leonhard Euler presented his paper on the Konigsberg bridge problem to the St. Petersburg Academy on August 26, 1735. However, they don't seem to agree on what year ...
JRN's user avatar
  • 846
13 votes
7 answers
827 views

Apparently different objects discovered to be the same

To make it more formal, I am looking for striking historical examples of objects or concepts that were well known in a field and perceived as different, but later discovered to be the same. I am ...
Conifold's user avatar
  • 77.9k
2 votes
1 answer
408 views

How did Archimedes complete this impossible task? [closed]

I am reading this book on Archimedes, famous mathematician of his days and now, and it was found that he caculated the amount of sand in the known Universe at his days, which is from Mercury to ...
Anthony Pham's user avatar
6 votes
1 answer
468 views

Modern critiques of, alternatives to Kuhn's paradigm shifts?

Kuhn's theory of paradigm shifts dates back over 50 years. Are there modern critiques of or alternatives to his theory? It seems to have been controversial from the start, with some people apparently ...
user avatar
5 votes
3 answers
278 views

Any book on the timeline of progress of mathematical concepts and applications?

I was wondering if there is any book that chronicles the progress of Math over the centuries and also mentions about how/when applications of various theories were discovered/invented. I have been ...
square_one's user avatar
7 votes
2 answers
2k views

How were vector quantities developed?

I'm very interested to know how the concept of vectors came in mathematics and physics. How were vector quantities discovered in physics, and how and by whom were they developed?
Shahed al mamun's user avatar
2 votes
1 answer
773 views

Who really was the first inventor of the laser?

I am reading these articles and books about science and I find that there are debates on who was the real (and first) inventor of the laser. Who is the real inventor of the laser? Please include ...
Anthony Pham's user avatar
10 votes
2 answers
2k views

Einstein's assistants

Some previous questions on Einstein bring the following question: is a complete (or incomplete) list of Einstein assistants available somewhere? A quick search on the Internet brings several familiar ...
Alexandre Eremenko's user avatar
7 votes
3 answers
544 views

When were fictitious forces introduced

Some problems in mechanics are simplified by considering the action of "fictitious forces". These appear in accelerated frames, such as circular movements. When were these first considered so? Did ...
Mark Fantini's user avatar
5 votes
3 answers
889 views

Knowledge of Einstein during obtaining his graduation

I'm interested to know what mathematical and physics topics Einstein learnt during his graduation.Did he know about advanced mathematical topics such as Hamiltonian mechanics ,Lagrangian mechanics, ...
Shahed al mamun's user avatar
11 votes
11 answers
19k views

Was Aristotle really wrong about gravity?

When I was in 9th grade, I learned that Aristotle was responsible for holding back physics for centuries because he said that heavier objects fall faster than lighter objects. Finally, in the 16th ...
Craig Feinstein's user avatar
45 votes
1 answer
10k views

Why did algebraic geometry need Alexander Grothendieck?

Grothendieck is arguably the most brilliant mathematician of the 20th century, with his influence felt the most in algebraic geometry, which he transformed. Some time ago the story used to be told was ...
Conifold's user avatar
  • 77.9k
13 votes
1 answer
338 views

Who blocked publication of "Mathematics in USSR. 1958-1967"?

A while ago, in USSR there were published two very voluminous collections entitled "Mathematics in USSR for 30 years. 1917-1947" and "Mathematics in USSR for 40 years. 1917-1957". These collections ...
Pasha Zusmanovich's user avatar
2 votes
2 answers
348 views

Origin of Perron-Frobenius Operator

The Frobenius Perron Operator $P: L^1 \to L^1$ is defined by the integral equation $$ \int_A Pf(x) \mu(dx) = \int_{S^{-1}(A)} f(x) \mu(dx)$$ for some $\mu$-non singular map $S$. I found it in the book ...
Adam's user avatar
  • 387
12 votes
3 answers
3k views

Who first distinguished planets from the stars?

This is a pretty straightforward question, when the first observations of the night sky were being made, who was the first person to suggest that a planet, say Mars, was not a star, in the sense that ...
L.R.'s user avatar
  • 261
7 votes
1 answer
793 views

Why were hot-air balloons invented so late?

The first (documented) hot-air balloon was made in the late 18th century. The materials necessary (wood to burn, sheets for balloon) were around for thousands of years. Why didn't anyone think of ...
weeeeeeeeeeeeeeeeeeeee's user avatar
6 votes
4 answers
665 views

First use of zero as a number

The first know use of $0$ as it's own number was in India, but what was the equation in which it was used? Also, what was the tablet/scroll/whatever about?
tox123's user avatar
  • 1,094
21 votes
3 answers
15k views

Who first measured the distance to the Moon? How was it done?

Who first measured the distance to the Moon? How was it done? I think it had to happen after Newton, but I am not sure.
Milkman's user avatar
  • 321
2 votes
0 answers
93 views

Motivation behind Euler Theorem in differential geometry [duplicate]

I am teaching a class on elementary differential geometry and I would like to know, for myself and for my students, something more about the history of Euler Theorem and Euler equation: the curvature ...
Giuseppe's user avatar
  • 183
6 votes
0 answers
42 views

Motivation behind Euler Theorem in differential geometry [duplicate]

I am teaching a class on elementary differential geometry and I would like to know, for myself and for my students, something more about the history of Euler Theorem and Euler equation: the curvature ...
Giuseppe's user avatar
  • 183
7 votes
0 answers
148 views

Who first discussed the Lorentz force with respect to special relativity?

The fact that a Lorentz force in a reference frame 1 can become a Coulomb force in another reference frame 2 has always astonished me, especially because the velocities involved are really small. I ...
Gerard's user avatar
  • 171
10 votes
2 answers
2k views

Was Euler's theorem in differential geometry motivated by matrices and eigenvalues?

I am teaching a class on elementary differential geometry and I would like to know, for myself and for my students, something more about the history of Euler Theorem and Euler equation: the curvature ...
Giuseppe's user avatar
  • 183
2 votes
1 answer
151 views

Invention of modular inverse

A question arose in my mind about modular inverse. We know that there is no division operator in modular arithmetic, so we figure out the modular inverse of the denominator. For example, if we want to ...
Shahed al mamun's user avatar
4 votes
3 answers
229 views

When in the history of physics did 'laws of nature' become the primary form of explanation?

Aristotle's natural philosophy was an inquiry into the causal principles of nature. He famously proposed the notions of formal, material, efficient and final causes. At the dawn of modernity, figures ...
kristof2014's user avatar
5 votes
1 answer
310 views

How did the notion of "time" come in the world of physics?

I was trying to figure out how people came to know about time then I realized that people started keeping track of time to know about sunset and sunrise. But I can't figure out how did time came into ...
Soham's user avatar
  • 175
20 votes
1 answer
4k views

How did Babylonians figure out that the evening star is the morning star?

Hesperus (Roman Vesper) is the name ancient Greeks gave to the evening star that appears in the sky for an hour after the Sun sets. Phosphorus (Roman Lucifer, sic!), was the name of the morning star ...
Conifold's user avatar
  • 77.9k
14 votes
3 answers
1k views

3 Poles and 3 Texans who had read "Principia Mathematica"

To quote Bertrand Russell, "My Philosophical Development", Simon and Schuster, N.Y., 1959, p. 86: I used to know of only six people who had read the later parts of the book [Principia Mathematica]...
Pasha Zusmanovich's user avatar
7 votes
1 answer
392 views

When was the term 'elementary function' first coined and who did it?

The definition of what an elementary function is is quite arbitrary (see what math.SE has to say about it) and it makes me wonder why hasn't the mathematical community added other rather natural ...
hjhjhj57's user avatar
  • 1,142
16 votes
3 answers
1k views

Why did mathematicians not see that $f_n(x)=x^n$ is a counterexample to Cauchy's "theorem" about limits of continuous functions?

In 1821 Cauchy claimed that the limit of a sequence of continuous functions is continuous. In 1826 Abel gave a complicated trigonometric counterexample. When we teach analysis courses, we usually give ...
Helmer.Aslaksen's user avatar
15 votes
1 answer
2k views

When was the vector notation in physics and other sciences first introduced?

The vector notation in physics is a very compact and easy way to write things down, and according to Feynman it also saves print. When exactly did scientists realize that they were summarizing things ...
Gonenc's user avatar
  • 785
38 votes
6 answers
4k views

What is so mysterious about Archimedes' approximation of $\sqrt 3$?

In his famous estimation of $\pi$ by inscribed and circumscribed polygons, Archimedes uses several rational approximations of irrational values; a typical example is that he states, without ...
Mark Dominus's user avatar
9 votes
1 answer
2k views

When and by whom was the term 'momentum' introduced?

We know that up to 1726, when the third edition of the Principia was published, the name for $m\vec v$ was: quantitas motus. Do you know who substituted that with another Latin word: 'momentum'?
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