All Questions
4,412
questions
91
votes
14
answers
17k
views
What famous theorems or results were proven by female mathematicians?
We know that there were/are many famous female mathematicians who influenced the mathematics as we know it today, but their numbers are few compared to male mathematicians. While we have numerous ...
- 2,520
83
votes
16
answers
26k
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?
- 839
74
votes
3
answers
14k
views
What evidence is there that Fermat had a proof for his Last Theorem?
Aside from the fact that Fermat was a genius, is it probable that he actually did have a proof?
Some specifics that I think would point one way or another:
Would the mathematics of his day allow him ...
- 1,295
74
votes
5
answers
14k
views
Why was Évariste Galois killed?
It is well known that Évariste Galois died a young man. I have heard that he died in a duel. What was the duel about? More rather what is the back story behind his death and did he really write down ...
- 1,556
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
58
votes
3
answers
2k
views
What is Ptolemy holding in this picture?
I would like to know the name of the device Ptolemy is holding in the following picture.
[Image Source]
- 647
57
votes
3
answers
14k
views
Why are $X$ and $Y$ commonly used as mathematical placeholders?
I realize that $X$ and $Y$ are relatively popular terms when wanting to use a placeholder for an unknown English or math term. What is the origin of this term, and why was it $X$ and $Y$; why not the ...
- 673
56
votes
2
answers
6k
views
Timeline of measurements of the electron's charge
Where can I find a paper or reference that describes the timeline of measurements of the magnitude of the electron's electric charge.
For context, Millikan's oil drop experiment in 1908 determined the ...
- 1,125
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
49
votes
5
answers
5k
views
Was Occam’s razor ever wrong?
In brief, I am looking for an example where Occam’s razor favoured a theory A over another theory B, but theory B turned out to be a better description of reality later. But let me formulate some ...
- 1,014
49
votes
2
answers
16k
views
Did Gauss find the formula for $1+2+3+\ldots+(n-2)+(n-1)+n$ in elementary school?
I heard Gauss's primary school teacher gave some busy-work to his class: to add all the numbers between 1 and 100 up. Gauss immediately wrote 5050. His teacher was shocked, so she told him to add up ...
- 5,229
47
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, ...
- 1,084
46
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 ...
- 829
45
votes
3
answers
5k
views
When exactly (and why) did matrices become a part of the undergraduate curriculum?
Let me tell what I know about this. It is well-known that Heisenberg invented matrix multiplication himself, in his great paper that is considered part of the foundation of quantum mechanics. This was ...
- 47.4k
44
votes
44
answers
15k
views
Which mathematicians died very young or in a tragic way?
When I first thought of this question, I wanted to ask: If you could give one mathematician his remaining life until an average age for the time he lived in, who would you choose? However, this ...
- 2,962
44
votes
4
answers
7k
views
Writing Mathematical Symbols in 20th century
As I was reading some papers written by Schrödinger and Heisenberg back in 1920s, I noticed that the symbols they use such as the integral or summation sign or calligraphic letters are as if printed ...
- 775
44
votes
1
answer
9k
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 ...
- 73.1k
44
votes
3
answers
62k
views
Why is price on the vertical axis and quantity on the horizontal axis?
In most of science, it is typical to have the independent variable on the horizontal axis and the dependent variable on the vertical axis.
But in economics, this is often (traditionally?) flipped ...
user67
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 ...
- 4,774
40
votes
1
answer
6k
views
Why volt instead of volta?
Why is the volt not identical to the full name Volta, unlike the other electrical units ohm, ampere, coulomb, tesla, weber and henry? Is there a historical explanation, was the volt introduced at a ...
- 411
40
votes
6
answers
17k
views
What is the difference between Calculus of Newton and that of Leibniz?
Are there any differences between the study of Calculus done by Newton as compared to that done by Leibniz? If yes, please mention point by point.
- 503
39
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 ...
- 782
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
39
votes
2
answers
6k
views
Why do we call Tycho Brahe by his first name?
Why do we use the fist name in Tychonic system or Tycho's comet of 1577, instead of using the last name of Tycho Brahe?
For comparison, we have the Ptolemaic system and the Copernican system.
I am ...
- 699
39
votes
4
answers
2k
views
What new mathematics was inspired by biology and chemistry?
While physics and astronomy sported mathematical models for centuries mathematical chemistry and biology appeared relatively recently. Most of the interaction seems to go one way, established ...
- 73.1k
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 ...
- 748
36
votes
5
answers
3k
views
When did Mathematics stop being one of "the Sciences"?
If you ask a mathematician today, many will tell you that mathematics is not a science. Many physicists, chemists, and scientists in other disciplines would say something similar. Mathematicians will ...
- 2,802
35
votes
6
answers
10k
views
Who introduced the Principle of Mathematical Induction for the first time?
Can you tell me the name of the mathematician, who introduced the Principle of Mathematical Induction for the first time? (with reliable source).
Please don't say De Morgan because I have read the ...
- 965
34
votes
8
answers
7k
views
Is there any example of a long-standing mathematical conjecture whose resolution did not require advanced knowledge?
Famous conjectures whose solutions took decades or centuries were usually resolved with the help of sophisticated theories and techniques unknown at the time the conjecture was first claimed. Is there ...
- 1,289
33
votes
8
answers
4k
views
What are some scientific breakthroughs that have been done during jail time?
I am looking for examples of scientific breakthroughs that have been made within the confines of a prison cell.
- 3,263
33
votes
3
answers
4k
views
Why did the ancient Greeks originally become interested in conic sections?
How much is known, or can be conjectured, about why the Greeks originally became interested in the somewhat arbitrary construction of intersecting a plane with a cone? The folklore that I've heard is ...
- 3,109
33
votes
3
answers
1k
views
Are there written (19th century) sources expressing the belief that the intermediate value property is equivalent to continuity?
As asked in the title:
Are there any written sources (from the 19th century) explicitly stating the belief that any function satisfying the intermediate value property is continuous?
(I do not ...
- 1,023
32
votes
11
answers
8k
views
Has physics ever given a physical significance to a mathematically abstract idea?
Consider a fundamental concept in maths that was created to 'solve' a problem that simply couldn't be solved by any other approach (or maybe for some other reason). Now let's assume that this concept ...
- 453
32
votes
10
answers
14k
views
How did people make things perfectly straight?
Constructing houses, telescopes, and most other important projects requires shaping pieces to precise size, at perfect right angles, or to have flat surfaces. People today have all kinds of ways of ...
- 491
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
32
votes
1
answer
4k
views
Why is American and French notation different for open intervals (x, y) vs. ]x, y[?
The Americans and the French use a different notation for open intervals: The Americans use (x, y) while the French use ]x, y[. How did this notational divergence appear?
- 3,263
31
votes
4
answers
14k
views
What did the Soviets do with German scientists after WWII?
The U.S. picked up a whole bunch of German scientists after World War II in Operation Paperclip. One of the most notable was Wernher von Braun, who jump-started the American space program.
The ...
- 8,393
31
votes
2
answers
37k
views
Story of Grothendieck's Prime Number
There is a story about Alexander Grothendieck and the "Grothendieck Prime" 57, which goes roughly as follows (cf. this wikipedia article):
In a mathematical conversation, someone suggested to ...
- 1,697
31
votes
1
answer
3k
views
Was object oriented programming influenced by the mathematical category theory?
Object oriented programming (OOP) is a programming model where code and data are encapsulated into units called objects that behave semi-autonomously. Interaction between objects is arranged through ...
- 73.1k
31
votes
1
answer
50k
views
Who first defined the "equal-delta" or "delta over equal" ($\triangleq$) symbol?
The symbol $\triangleq$ is sometimes used in mathematics (and physics) for a definition. It is instantiated for instance in the Unicode Character 'DELTA EQUAL TO' (U+225C).
The notation $t \triangleq ...
- 1,163
30
votes
3
answers
5k
views
How did Napier come to invent logarithms?
What was Napier's original logic, leading to his invention of logarithms?
In other words, how did Napier, using the mathematics that was available at that time, derive them?
- 401
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
30
votes
2
answers
792
views
Was fake/rigged data common prior to the 20th century?
In one of the lab courses I took as an undergraduate, I remember that the professor noted while discussing some statistical test (almost certainly chi-squared) that one could use it to show that a lot ...
- 2,802
29
votes
7
answers
1k
views
Was evolution ever discussed (perhaps using different terms) prior to Darwin?
It's common knowledge that Darwin is considered the father of evolution, but even humans have been breeding animals (and probably themselves) selectively for specific traits for thousands of years. ...
29
votes
2
answers
7k
views
How did Eratosthenes know the Sun was very far away?
Eratosthenes calculated the radius of the Earth from the difference of the lengths of shadows between Aswan and Alexandria were different (see also here). But this could also happen if the Earth were ...
- 545
29
votes
3
answers
8k
views
Why did no one else, except Einstein, work on developing General Relativity between 1905-1915?
Einstein dedicated his time between 1905-1915 to develop general relativity (GR). It seems strange to me that no other physicists attempted to tackle this problem in this ten-year period. After all, ...
- 571
29
votes
2
answers
607
views
How did Isaac Newton write the integral symbol?
Isaac Newton is known as the discoverer of the FTC (Fundamental Theorem of Calculus), so maybe he wrote the integral symbol and derivative symbol. I know he wrote the derivative symbol as $\dot y$ but ...
- 401
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
29
votes
1
answer
2k
views
What were the dominant non-atomic theories of matter in the 19th century?
From what I have read, the atomic theory of matter was cemented by a 1905 paper by Einstein in which he explained the erratic motion of a bit of pollen suspended in water using the assumption that ...
- 1,021
29
votes
3
answers
3k
views
Who introduced random variables into probability?
I used to think that the answer is Kolmogorov. So the Shafer-Vovk's review of Kolmogorov's famous 1933 axiomatization of probability surprised me a bit:"Today, what Frechet and his contemporaries knew ...
- 73.1k