All Questions

Filter by
Sorted by
Tagged with
5 votes
1 answer
627 views

Who first derived $a =v^2/r$

This is a basic formula in mechanics, which determines the acceleration of a particle performing uniform circular motion. By who first derived it? In Newton's Principa, what one can find is that $$...
poisson's user avatar
  • 417
5 votes
1 answer
404 views

When was the inverse relationship between tangents and quadrature/area first identified?

Problems concerning tangents and quadrature have a long history predating the Newton/Leibniz formulation of calculus; indeed, they are amongst the oldest problems in mathematics. It seems reasonable ...
nwr's user avatar
  • 6,909
5 votes
1 answer
1k views

What are Philolaos' “even-odd” numbers?

Number, indeed, has two proper kinds (ιδια ειδη), odd and even, and a third mixed together from both, the even-odd(αρτιοπέριττον). Of each of the two kinds there are many shapes, of which each ...
sand1's user avatar
  • 2,422
5 votes
2 answers
882 views

Riemann's Contribution to Integration

What did Riemann do for the theory of integration? I am asking because I hear his name a lot in relation to integration and it is often implied that he made large contributions, but I do not know ...
user109871's user avatar
4 votes
3 answers
3k views

Why is one meter as long as it is?

The metre is defined as the length of the path travelled by light in a vacuum in 1/299 792 458 of a second Why is this so? Who decided that 1/299,792,458 of a ...
Dylan Kerler's user avatar
4 votes
1 answer
312 views

Was it suspected that the speed of electricity was equal to the speed of light?

Was it believed early on that signals sent via wire moved at exactly the speed of light or simply very fast? Who was the first to estimate the speed? EDIT: Given that they move at less than the ...
releseabe's user avatar
  • 1,173
4 votes
1 answer
374 views

Was there any atomic model(s) that came between Bohr's and the actual beginning of Quantum Mechanics in early 20s?

Well, the question arose in the physics chat when slereah mentioned about it. So, was there any prominent model that came to light after Bohr and before the actual beginning of Quantum Mechanics in ...
user avatar
4 votes
2 answers
466 views

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 ...
pie's user avatar
  • 263
1 vote
3 answers
5k views

How the law of inertia got discovered?

In the Feynman lectures, it is mentioned that [Vol 1; Gravitation]: Galileo discovered a very remarkable fact about motion, which was essential for understanding these laws. That is the principle ...
user avatar
49 votes
6 answers
9k views

How did German become the language of science?

Recently, I read an interesting article about how English replaced German as the language in which scientists communicate. But how did German become the leading language in the first place? In the ...
Ondřej Černotík's user avatar
48 votes
3 answers
4k views

What led to the fall of Göttingen?

Göttingen was the place in which many important mathematicians such as Riemann worked. It was also one of the main locations for the development of quantum theory in the twenties (e.g. Heisenberg, ...
tox123's user avatar
  • 1,094
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
  • 77.6k
41 votes
1 answer
4k views

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 ...
Michael Weiss's user avatar
41 votes
3 answers
3k views

What motivated Cantor to invent set theory?

I can't imagine mathematics without sets, but the question "what was mathematics like before there were sets" is not answerable, I think. Instead, a good answer to the title question should cover a ...
Ben's user avatar
  • 802
28 votes
2 answers
4k views

Roman engineers

It is a common opinion that Romans did not contribute anything to exact sciences, but did contribute much to engineering. (How can it be otherwise, anyone who has been on the territory of the former ...
Alexandre Eremenko's user avatar
27 votes
2 answers
2k views

What attracted Einstein to the anomalous precession of Mercury?

The story is usually told starting with Einstein's 1915 paper Explanation of the Perihelion Motion of Mercury from General Relativity Theory, or at least its drafts from 1913-14. It was the first ...
Conifold's user avatar
  • 77.6k
26 votes
2 answers
2k views

How did scientists plot complicated graphs in the 19th century?

I am wondering how did Maxwell in the 19th century draw such figures as the one shown? What tools or procedures did he need? Is it all compass and ruler drawing?
hat's user avatar
  • 363
25 votes
2 answers
3k views

Who discovered the covering homomorphism between SU(2) and SO(3)?

Who discovered this? It is quite nontrivial and very important in quantum mechanics.
John's user avatar
  • 909
25 votes
2 answers
4k views

What did Einstein contribute to Special Relativity that hadn't already been done by Lorentz in 1904 and Poincaré in 1905?

What did Einstein contribute to what is now called Special Relativity theory that hadn't already been done by Lorentz in his 1904 "Electromagnetic Phenomena in a System Moving with any Velocity ...
Geremia's user avatar
  • 5,371
24 votes
4 answers
11k views

Ancient Chinese numbering system

It has been said that the invention of zero was a great leap forward, not only in abstract understanding, but in the ability to introduce place value notation and do computations; computing using ...
rogerl's user avatar
  • 673
23 votes
3 answers
6k views

Hypothesis testing: Fisher vs. Popper vs. Bayes

I try to make my question short. I am familiar with Popper’s philosophy as well as with statistical hypothesis testing after Fisher and Neyman-Pearson. I am not so familiar with the Bayesian approach ...
Stefan's user avatar
  • 333
23 votes
3 answers
6k views

What was the relationship between Einstein and Minkowski?

I read many Einstein's Biographies, but Minkowski was never mentioned, though his discovery of the union of space and time created the basis for GR. Minkowski was Einstein's teacher of mathematics ...
Realist753's user avatar
22 votes
3 answers
16k views

Why were 20th Century German scientists so impressive?

German (and Austrian) scientists of the late 19th - early 20th centuries seem to have been the backbone of most of modern physics - namely quantum theory/mechanics. The following are a few predominant ...
galois's user avatar
  • 724
22 votes
4 answers
2k views

Is there any historical "evidence" maintaining that Euclid was a single person?

Bourbaki, for example, was the name of a set of mathematicians, rather than a single person, under which several books were published. Out of curiosity, I wonder if there is any historical evidence ...
Yes's user avatar
  • 403
21 votes
1 answer
8k views

Why did angular momentum get the letter L

Note - this question was inspired by this questions on physics.SE. Many (most) physical quantities are denoted with a single letter - latin or greek. For many, the letter chosen makes sense: $t$ for ...
Floris's user avatar
  • 758
20 votes
2 answers
557 views

What data did Kepler work out his laws from?

It's well known that Kepler worked out his laws by fitting curves to Tycho Brahe's data on the trajectories of planets through the sky. What was this data? How does one record the trajectory of a ...
Jack M's user avatar
  • 3,149
19 votes
1 answer
3k views

How did Ptolemy know that days were unequal lengths?

Apparently Ptolemy was aware of the fact that the duration of time from noon to noon varied by many seconds throughout the course of a year. In modern times this fluctuation in length of day leads to ...
Jagerber48's user avatar
19 votes
3 answers
4k views

When and on what basis was it decided that an hour have 60 minutes and a minute have 60 seconds?

There were always some or he other means of measuring(estimating) the time. But I always wonder that when and how the present time system (1 Hr. = 60 Min., 1 Min. = 60 Sec.) evolved ?
Amit Tyagi's user avatar
  • 1,478
18 votes
1 answer
1k views

Did Guinness Book of Records screw up on the "longest-standing maths problem (ever)"?

Did they screw this up? It says that Fermat's Last Theorem was the longest open problem - with only 365 years. See Guinness Book of Records. However, there are Greek problems that were longer open: ...
wythagoras's user avatar
  • 3,112
18 votes
1 answer
583 views

Did Archimedes use epicycles in his planetarium?

Archimedes constructed a planetarium where as described by Cicero "he had thought out a way to represent accurately by a single device for turning the globe those various and divergent movements with ...
Conifold's user avatar
  • 77.6k
18 votes
1 answer
4k views

Was Kolmogorov enraged after learning about the Karatsuba multiplication algorithm?

Some years ago, I read that Kolmogorov was so enraged that Karatsuba disproved one of his conjectures that he terminated his seminar shortly thereafter. This Wikipedia page claims that Kolmogorov was ...
GEP's user avatar
  • 1,525
17 votes
5 answers
2k views

What was the motivation for Minkowski spacetime before special relativity?

If I understand correctly, the concept of a Minkowski space/metric was already known before Einstein's paper on special relativity. Was there any physical motivation for studying this type of metric ...
Prastt's user avatar
  • 271
17 votes
1 answer
2k views

How did mathematicians notate the empty set before $\varnothing$?

Recently, I learned that $\emptyset$ or $\varnothing$ is a relatively new notation for the empty set and was created in 1939. I know $\{\}$ is also used along with $\{\cdot\}$ to denote empty sets. ...
quiet's user avatar
  • 273
17 votes
1 answer
1k views

How did the publication feat of Einstein's four 1905 Annus Mirabilis papers get through peer review?

Einstein's early career is well-known for the lack of success he had applying for assistant lecturer positions with universities; he could not get a position, and he ended up working in a Bern patent ...
DBS's user avatar
  • 273
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
16 votes
2 answers
2k views

History of various definitions of topology

I have been reading Point Set Topology for a while, and turns out that there are various possible ways to define a topology. Most popular one is using open set axioms. Another one is using closure ...
Anirban's user avatar
  • 261
16 votes
1 answer
972 views

Hidden agenda of the Galileo trial?

Redondi argued that Galileo's trial on heliocentrism was merely a show trial concealing the real objection against Galileo among the catholic establishment, which was his atomism thought to be at ...
Mikhail Katz's user avatar
  • 6,161
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
16 votes
4 answers
2k views

Is Kline right that Cauchy believed that continuous functions must be differentiable?

Morris Kline, in Mathematical Thought from Ancient to Modern Time, writes in chapter 40 (The Installation of Rigor in Analysis), "Though Bolzano and Cauchy had rigorized (somewhat) the notions of ...
Mikhail Katz's user avatar
  • 6,161
15 votes
1 answer
739 views

Did du Bois-Reymond invent the diagonal argument before Cantor?

The Wiki article on Cantor's diagonal argument mentions that the first use of a diagonal argument was in the work of Paul du Bois-Reymond in 1875. This would be one year after Cantor's first proof of ...
user4894's user avatar
  • 1,345
14 votes
0 answers
660 views

Did Kronecker say that set theory is not mathematics?

I have frequently come across Kronecker's statement about set theory: I don't know what predominates in Cantor's theory - philosophy or theology, but I am sure that there is no mathematics there. It ...
Franz Kurz's user avatar
14 votes
1 answer
1k views

Notation for Christoffel symbols

In Christoffel's 1869 paper in which he introduced the Christoffel symbols on the 3rd and 4th pages, they are written as $\left[\substack{ij \\ k}\right]$ and $\{\substack{ij \\ k}\}$. The notation $...
KCd's user avatar
  • 5,689
14 votes
4 answers
3k views

What was Einstein's motivation for relativity theory?

I'm a high school student who never studied any relativity before, but I'm just wondering what was the question that Einstein asked himself before going into this field. I knew he has done lots of ...
user avatar
14 votes
5 answers
708 views

Which school of philosophy motivated thinking about spaces of higher dimension?

I'm trying to make a link between important mathematical breakthroughs in history and the important philosophical schools at the time. I realize that this topic is awfully broad and could be the ...
hjhjhj57's user avatar
  • 1,142
13 votes
2 answers
2k views

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 ...
მამუკა ჯიბლაძე's user avatar
13 votes
3 answers
5k views

Why are quaternions more popular than tessarines despite being non-commutative?

Is this simply because of marketing, hype, etc? The bicomplex numbers (especially tessarines) look just great being commutative and all. Images source:https://citeseerx.ist.psu.edu/viewdoc/download?...
Anixx's user avatar
  • 662
13 votes
2 answers
560 views

What examples led to the modern definition of a topological space?

Today the language of topological spaces via open sets is fundamental in many different areas of mathematics, and it is a bit mysterious that the same formalism successfully captures such a wide ...
Paul Siegel's user avatar
  • 1,041
13 votes
5 answers
589 views

How did prisoners of war discover scientific breakthroughs while interned?

Reading the excellent thread What are some scientific breakthroughs that have been done during jail time?, it stands to reason to ask what are some scientific breakthroughs made by interned prisoners ...
user avatar
12 votes
1 answer
14k views

Euler's first proof of $e^{ix}=\cos(x)+i\sin(x)$

What was Euler's first proof of his famous formula? In Euler's book on complex functions he used the following proof. But was this his first proof? Euler starts with writing down De Moivre's Formula (...
MrYouMath's user avatar
  • 610
12 votes
1 answer
673 views

How certain is it that Lucas invented the Towers of Hanoi puzzle?

Wikipedia is unequivocal: The puzzle was invented by the French mathematician Édouard Lucas in 1883. I have no reason to doubt this, but given the many legends surrounding the topic, I wonder if ...
Joseph O'Rourke's user avatar

15 30 50 per page
1 2
3
4 5
14