All Questions
625
questions
24
votes
2
answers
4k
views
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: $mv^2$, ...
- 4,774
18
votes
2
answers
7k
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 ...
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 ...
- 2,154
11
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?
- 365
11
votes
1
answer
2k
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 ...
8
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.
- 945
53
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 ...
- 8,393
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 ...
- 909
8
votes
1
answer
761
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 ...
- 99
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 ...
- 10.1k
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?
- 251
9
votes
1
answer
673
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
$$\...
- 5,229
8
votes
1
answer
2k
views
What is the history of electric current and resistance?
Thomas Kuhn writes in The Structure of Scientific Revolutions
Part of what the acceptance of Ohm’s Law demanded was a redefinition of both ‘current’ and ‘resistance’; if those terms had continued ...
- 225
18
votes
2
answers
1k
views
Was 18th century algebra more symbolic/formal than the modern conception?
I've found Lagrange's Sur la résolution des équations algébriques to be a very confusing and difficult read, and I think I'm starting to see why: it seems that Lagrange thinks of algebra in a much ...
- 3,109
7
votes
1
answer
444
views
Viète's Relevance and his Connection to Euler
Viète's equations are used in some proofs of the Basel problem, which was allegedly solved by Euler.
Viète's equations include the following: given a polynomial,
$$a_0 + a_1x+a_2x^2 + ... + a_nx^n$$ ...
- 211
4
votes
4
answers
2k
views
How were irrational numbers accepted by mathematicians?
What was behind accepting the existence of irrational numbers historically? Especially numbers that are not constructible on the real number line, say for example $\sqrt[3]{2}$. Was it a (somewhat) ...
- 181
25
votes
4
answers
5k
views
Irrationality of the square root of 2
We know that Pythagoreans in Ancient Greece discovered that the square root of two is an irrational number. Why was that discovery historically significant? What value was that knowledge to the ...
- 359
22
votes
2
answers
3k
views
Historically, how did people define multiplication for negative numbers?
Which were the first mathematical developments to state that the product of two negative numbers is a positive number, and what was their justification for this choice? I am not interested in a modern ...
20
votes
3
answers
2k
views
What was the motivation for the development of modern, intrinsic, differential geometry?
I know that tensor calculus was developed around the same time as general relativity. Tensor calculus was the prime way to deal with geometric objects, based on expliciting all coordinates and doing ...
- 561
11
votes
3
answers
3k
views
What was the notion of limit that Newton used?
I have read that the notion of limit became rigorous two centuries after the discover of calculus
What Newton had in his mind regarding the notion of limit?
- 255
9
votes
2
answers
739
views
Did wave optics anticipate quantum mechanics?
I heard in wave optics and electromagnetism that Hamilton could have discovered the Schrödinger equation, or that he was the first man who used the expression
$$ \Psi(x)= \exp(i S(x)/\hbar)\,. $$
I ...
6
votes
2
answers
938
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 ...
- 491
39
votes
4
answers
6k
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 ...
- 661
30
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 ...
- 644
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 ...
- 2,947
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 ...
- 435
23
votes
2
answers
2k
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 ...
- 1,715
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 ...
- 345
20
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 ...
Joshua Benabou
17
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 ...
- 397
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,...
- 121
11
votes
2
answers
644
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 ...
user2114
10
votes
2
answers
1k
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 ...
- 183
9
votes
2
answers
1k
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?
- 915
8
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. ...
- 181
6
votes
1
answer
4k
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 ...
- 171
3
votes
2
answers
616
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. ...
- 1,163
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 ...
- 143
65
votes
1
answer
8k
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 ...
- 1,295
32
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 ...
- 423
29
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♦
- 3,812
24
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....
- 654
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 ...
- 565
23
votes
2
answers
15k
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?
user4795
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 ...
- 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 ...
- 1,478
20
votes
1
answer
9k
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 ...
- 209
19
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 ...
- 1,397
18
votes
1
answer
4k
views
Examples of Kuhn loss?
A Kuhn loss is:
a success, empirical or theoretical, of a prior theory – or paradigm as Kuhn would have preferred – that does not carry over to the theory or paradigm that replaced it. [Midwinter ...
- 4,774
16
votes
2
answers
852
views
Did Newton develop the concept of gravity first for falling objects or for celestial motion?
A benefit of Newton's concept of gravity as a force--despite the fact that it involved what was considered mysterious action at a distance--was that it explained objects falling to earth, and the ...
- 367