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25 votes
2 answers
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What was the vis viva controversy, including its philosophical aspects?

Leibniz's concept of vis visa (literally translated as living force) was a precursor to our modern concept of kinetic energy. His formula for it was close to the modern non-relativistic one: $mv^2$, ...
Michael Weiss's user avatar
19 votes
2 answers
8k views

What was different about Planck's quantization of light compared to Einstein's?

In describing black body radiation Planck assumed that the energy that can be absorbed or emitted by charges is quantized, i.e., they can only absorb or emit certain quantities of energy. But it was ...
Quantum spaghettification's user avatar
15 votes
3 answers
2k views

Why is "Cardano's Formula" (wrongly) attributed to him?

Apparently, Cardano had learned a formula for solving cubic equations from Tartaglia, who had sworn him to secrecy, and in any event, not to publish it without giving Tartaglia due credit. Cardano ...
Tom Au's user avatar
  • 2,174
12 votes
1 answer
2k views

Is there a 'lost calculus'?

Are there any 'lost' theorems of calculus that could be used to 'simplify' it? For example, are there ways to calculate derivatives without using limits, maybe by some forgotten methods in calculus?
201044's user avatar
  • 385
11 votes
1 answer
3k views

How did Young perform his double slit experiment?

Thomas Young is famous for his double slit experiment, but I can't seem to find his experimental setup (such as how is prepared the light before it went through the apparatus. Does anyone know his ...
Quantum spaghettification's user avatar
9 votes
1 answer
1k views

When do we see for the first time the use of the Cartesian coordinates?

I want to see an exact image of the first use of the Cartesian plane. I guess it came the first time with Descartes.
copper's user avatar
  • 993
54 votes
3 answers
6k views

Which came first, the natural logarithm or the base of the natural logarithm?

The natural logarithm function ($\ln x$) and the base of the natural logarithm function ($e$) are both extremely useful. They're also both closely related: $\ln (e^x)=x$, and $e^{\ln x}=x$. But which ...
HDE 226868's user avatar
  • 8,473
13 votes
1 answer
4k views

How did Planck derive the black body radiation formula without using the Bose statistics?

It is so funny that science never develops as in the textbooks. Bose only introduced his statistics in 1924, so Planck could not possibly have used it to derive the radiation formula in 1900. So how ...
John's user avatar
  • 909
8 votes
1 answer
786 views

What 19th century developments contributed to the General theory of Relativity?

Regarding General Theory of Relativity, I'm interested to find out whether there are some contributors to this theory in 19th century or not. In fact I want to know whether there are some physicists ...
Hamid Enki's user avatar
19 votes
2 answers
1k views

Pythagoras vs. the idea of Pythagoras

Maybe we need some replies on current scholarly thinking. (Judging from some replies here, many of us are still using the myths current 100 years ago.) Is it true (as I have heard) that most, if not ...
Gerald Edgar's user avatar
  • 10.3k
13 votes
2 answers
1k views

Who was first to explain intuitively the inverse square law of gravity?

The surface area of a sphere is $4\pi r^2$ and when you increase the distance to a point charge the force diminishes like the $r^{-2}$. Who was the first person to realize this?
Ray Kay's user avatar
  • 251
9 votes
1 answer
711 views

Why is one of Maxwell's equations named after Ampère? Who first named it after Ampère?

Ampère never wrote down what is confusingly called "Ampère's circuital law," not even the form without the displacement current term, as Ampère never dealt with the field concept.* Maxwell derived $$\...
Geremia's user avatar
  • 5,339
8 votes
1 answer
2k views

What is the history of electric current and resistance?

Thomas Kuhn writes in The Structure of Scientific Revolutions Part of what the acceptance of Ohm’s Law demanded was a redefinition of both ‘current’ and ‘resistance’; if those terms had continued ...
Christian's user avatar
  • 225
24 votes
2 answers
3k views

Who first considered the $f$ in $f(x)$ as an object in itself, and who decided to call it a function?

The question is in the title, but allow me to provide some background. I’m aware that Leibniz introduced the word “function” into mathematics (around 1673) and that Johann Bernoulli or Euler ...
Michael Bächtold's user avatar
18 votes
2 answers
2k views

Was 18th century algebra more symbolic/formal than the modern conception?

I've found Lagrange's Sur la résolution des équations algébriques to be a very confusing and difficult read, and I think I'm starting to see why: it seems that Lagrange thinks of algebra in a much ...
Jack M's user avatar
  • 3,149
11 votes
2 answers
785 views

Did wave optics anticipate quantum mechanics?

I heard in wave optics and electromagnetism that Hamilton could have discovered the Schrödinger equation, or that he was the first man who used the expression $$ \Psi(x)= \exp(i S(x)/\hbar)\,. $$ I ...
Jose Javier Garcia's user avatar
8 votes
1 answer
470 views

Viète's Relevance and his Connection to Euler

Viète's equations are used in some proofs of the Basel problem, which was allegedly solved by Euler. Viète's equations include the following: given a polynomial, $$a_0 + a_1x+a_2x^2 + ... + a_nx^n$$ ...
Antoni Parellada's user avatar
4 votes
4 answers
2k views

How were irrational numbers accepted by mathematicians?

What was behind accepting the existence of irrational numbers historically? Especially numbers that are not constructible on the real number line, say for example $\sqrt[3]{2}$. Was it a (somewhat) ...
Bassam Karzeddin's user avatar
26 votes
4 answers
5k views

Irrationality of the square root of 2

We know that Pythagoreans in Ancient Greece discovered that the square root of two is an irrational number. Why was that discovery historically significant? What value was that knowledge to the ...
Spectre's user avatar
  • 369
22 votes
2 answers
3k views

Historically, how did people define multiplication for negative numbers?

Which were the first mathematical developments to state that the product of two negative numbers is a positive number, and what was their justification for this choice? I am not interested in a modern ...
Arthur Azevedo De Amorim's user avatar
20 votes
3 answers
2k views

What was the motivation for the development of modern, intrinsic, differential geometry?

I know that tensor calculus was developed around the same time as general relativity. Tensor calculus was the prime way to deal with geometric objects, based on expliciting all coordinates and doing ...
Mark Fantini's user avatar
12 votes
3 answers
3k views

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?
veronika's user avatar
  • 265
8 votes
2 answers
1k views

Who discovered the magnetic vector potential, $\vec{A}$?

Neither Maxwell’s fundamental differential equations on electromagnetism nor Einstein’s first papers considered the magnetic vector potential A. So who discovered, formulated or used A for the first ...
Realist753's user avatar
84 votes
18 answers
27k views

Examples of when the professional scientists or mathematicians were wrong, but the nonprofessionals were right

What are the most glaring examples — if any — of when the professional scientists or mathematicians were wrong, but the nonprofessionals were right?
Seth Rich's user avatar
  • 849
40 votes
6 answers
7k views

Whose shoulders did Newton stand on?

In a letter to Robert Hooke in 1676, Newton wrote: If I have seen further it is by standing on the shoulders of giants. Do we know which giants Newton was referring to? And was he referring to a ...
TooTone's user avatar
  • 679
31 votes
4 answers
2k views

Current ways of thinking in the History of Mathematics

As a research mathematician, working in number theory, who is interested in the history of his own field, I have done some reading in the History of Mathematics, particularly that of Ancient Greek and ...
R.P.'s user avatar
  • 654
30 votes
2 answers
2k views

When and how was the geometric understanding of gauge theories developed?

In theoretical physics, the modern perspective on gauge theory is that it is most elegantly described in the 'language' of differential geometry. I am interested in the history behind these ideas. ...
Danu's user avatar
  • 3,862
27 votes
2 answers
1k views

Did Galileo's writings on infinity influence Cantor?

To what extent was Cantor motivated by Galileo's paradox? More generally, to what extent were late 19th century mathematicians motivated by, or even aware of, Galileo's paradox? This is an issue I've ...
Dave L Renfro's user avatar
24 votes
1 answer
4k views

How was Einstein led to make a contact with Differential Geometry for his theory of General Relativity?

General Relativity was developed with Differential Geometry as the tool. How was Einstein led to make a contact with Differential Geometry for his theory of General Relativity? Who suggested him to ...
Display Name's user avatar
21 votes
3 answers
2k views

How did Kepler "guess" his third law from data?

It is amazing that Kepler determined his three laws by looking at data, without a calculator and using only pen and paper. It is conceivable how he proved his laws described the data after he had ...
user avatar
21 votes
1 answer
4k views

Why is the radical symbol $\sqrt{}$ called "radical"?

This question arose in a conversation with a teacher who was introducing square roots to her students. I know from the website Earliest Uses of Symbols of Operation that the symbol $\sqrt{}$ has its ...
Joseph O'Rourke'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
18 votes
5 answers
2k views

Why don't we learn Buridan's laws of motion?

My question is why has Jean Buridan faded into obscurity while Newton is venerated as a God by scientists? Here is a description of Buridan's impetus theory: The concept of inertia was alien to the ...
Neil Meyer's user avatar
13 votes
4 answers
905 views

What resources are available for lives of recent mathematicians besides E.T. Bell's Men of Mathematics?

I am about halfway through reading E.T. Bell's Men of Mathematics, and I absolutely love it. I'm a mathematician, and I enjoy learning about the lives behind the names that I know and use so often. (I ...
davidlowryduda's user avatar
12 votes
1 answer
3k views

The origin of quadratic equation in actual practice

I read that in ancient times the quadratic equation of this kind $$x^2+10x=39$$ had been solved long ago. I read that this kind of equation originated in the geometric question of "Given an area of 39,...
user2921's user avatar
  • 121
11 votes
2 answers
693 views

What came first? The kernel from vector spaces or from group theory?

In studying vector spaces we learn about linear transformations from one vector space to another and in particular the kernel of such a transformation. When learning about group theory we also learn ...
user avatar
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
9 votes
2 answers
2k views

When did people start viewing a matrix as a linear transformation between two vector spaces?

The notion of a matrix appeared far ahead of that of a vector space. So when did people start considering a matrix as a linear transformation between two vector spaces?
wdlang's user avatar
  • 915
9 votes
2 answers
9k views

Why did Einstein oppose quantum uncertainity?

Einstein always believed that everything is certain, and we can calculate everything. That's why he rejected quantum mechanics, due to its factor of uncertainty. But still quantum physics was right. ...
Creepy Creature's user avatar
6 votes
2 answers
5k views

What are the major flaws of the “caloric” theory of heat?

I was reading about the history of thermodynamics and came across Lavoisier's idea of heat. He proposed that heat was a fluid. I am curious to know what are the major drawbacks of this theory. I know ...
Student's user avatar
  • 171
3 votes
2 answers
679 views

Introduction of $\imath$ and $\jmath$ notations for the imaginary unit

The imaginary unit is generally denoted $i$ or $\imath$. I have learned that the term imaginary ("imaginaires") was coined by R. Descartes in 1637, and the "i" notation was introduced by L. Euler (cf. ...
Laurent Duval's user avatar
3 votes
1 answer
1k views

How was geometry historically used to solve polynomial equations?

I'm researching historical use of geometry to find solutions to polynomial equations. I'd like to ask for those familiar with this topic, could you describe the use of geometry by early mathematicians ...
user975's user avatar
  • 143
67 votes
1 answer
9k views

What's the famous story about a mathematician who gave a talk without saying a word?

Years ago, I read a story about a mathematician who found a numerical counterexample to some conjecture long believed to be true. He gave a talk during which he didn't utter a single word but simply ...
user4894's user avatar
  • 1,345
31 votes
4 answers
4k views

Is the Scientific Method uniquely Western?

I'm studying High School Science teaching in Australia. In our Science curriculum there are "cross-curriculum" priorities "Aboriginal and Torres Strait Islander histories and cultures" and "Asia and ...
pdmclean's user avatar
  • 413
25 votes
3 answers
5k views

Is Millikan's famous oil drop experiment a fraud?

I read in my mechanics textbook written by Goodstein that Robert Millikan cherry-picked his data in his famous oil drop experiment, and now I'm left wondering about the scientific value of his results....
Shing's user avatar
  • 664
23 votes
2 answers
18k views

What is the etymology behind sine, cosine, tangent, etc.?

I heard somewhere that it was actually a mistake in translation. What's the correct story?
user avatar
23 votes
2 answers
2k views

When did it become understood that irrational numbers have non-repeating decimal representations?

I know that the notion of irrational number (in one form or another) goes back to the Pythagoreans, and therefore far predates the decimal system, and certainly the representation of non-integer ...
mweiss's user avatar
  • 567
23 votes
2 answers
6k views

When did it become possible to predict the time and place of solar eclipses?

That is, when did astronomy figure out how to predict when and where a solar eclipse will be visible? It seems people noticed fairly early on that the Sun, Moon and Earth return to the same ...
Semaphore's user avatar
  • 605
22 votes
3 answers
5k views

When was zero actually introduced in mathematics?

Children learn counting things, naturally like, 1, 2, 3, ... and so on. Because it seems obvious to them. But, zero is something we need to teach them about. As far as my understanding goes zero was ...
Amit Tyagi's user avatar
  • 1,478
20 votes
1 answer
10k views

What was the historical context of the development of Taylor series?

I knew about linear approximations, quadratic approximations and the use of Taylor polynomials to approximate a function. Furthermore, I was aware of other applications of Taylor polynomials and the ...
shahed al mamun's user avatar

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