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95 votes
14 answers
18k views

What famous theorems or results were proven by female mathematicians?

We know that there were/are many famous female mathematicians who influenced mathematics as we know it today, but their numbers are few compared to male mathematicians. While we have numerous famous ...
Kushal Bhuyan's user avatar
85 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
  • 859
76 votes
3 answers
15k 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 ...
Carlos Bribiescas's user avatar
75 votes
5 answers
15k 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 ...
Ali Caglayan's user avatar
  • 1,586
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
59 votes
3 answers
3k 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]
hb20007's user avatar
  • 657
59 votes
3 answers
16k 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 ...
Sweet_Cherry's user avatar
56 votes
2 answers
7k 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 ...
BMS's user avatar
  • 1,147
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
  • 8,503
50 votes
5 answers
6k 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 ...
Wrzlprmft's user avatar
  • 1,032
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
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 ...
Geremia's user avatar
  • 5,371
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
47 votes
45 answers
16k 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 ...
wythagoras's user avatar
  • 3,112
46 votes
3 answers
65k 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 ...
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
  • 77.6k
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 ...
Alexandre Eremenko's user avatar
44 votes
5 answers
8k 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 ...
Gonenc's user avatar
  • 785
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
41 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 ...
Elec95's user avatar
  • 421
41 votes
6 answers
18k 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.
Sameer Shemna's user avatar
41 votes
5 answers
3k 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 ...
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
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
39 votes
9 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 ...
Leandro Caniglia's user avatar
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 ...
timur's user avatar
  • 709
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
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 ...
Logan M's user avatar
  • 2,832
35 votes
6 answers
11k 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 ...
albo's user avatar
  • 965
35 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 ...
Andrés E. Caicedo's user avatar
33 votes
8 answers
5k 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.
Franck Dernoncourt's user avatar
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 ...
Jack M's user avatar
  • 3,149
33 votes
1 answer
5k 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?
Franck Dernoncourt's user avatar
33 votes
2 answers
40k 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 ...
Moishe Kohan's user avatar
  • 1,745
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 ...
Adil Mohammed's user avatar
32 votes
10 answers
15k 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 ...
Addem's user avatar
  • 511
32 votes
4 answers
15k 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 ...
HDE 226868's user avatar
  • 8,503
32 votes
1 answer
4k 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 ...
Conifold's user avatar
  • 77.6k
31 votes
3 answers
6k 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?
AbdElWadoud's user avatar
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
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
31 votes
2 answers
826 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 ...
Logan M's user avatar
  • 2,832
31 votes
1 answer
51k 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 ...
Laurent Duval's user avatar
30 votes
5 answers
7k views

In a popular anecdote, who took 20 minutes to decide that a thing was obvious?

The joke is found on this comment chain on Reddit. One user told the joke: The version I heard is that Pauli was lecturing, and he said "this is obvious". A student raises his hand and says "sorry ...
Ooker's user avatar
  • 1,228
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
  • 3,892
30 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 ...
Paul Siegel's user avatar
  • 1,041
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. ...
StackExchange What The Heck's user avatar
29 votes
4 answers
9k views

Did physicists around 1900 really believe they were close to "figuring it all out"?

I've encountered the claim that around the end of the 19th century, physicists believed that their understanding of the physical world was close to being complete. One example of this claim can be ...
Ofri Raviv's user avatar
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 ...
Rohit Pandey's user avatar
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, ...
Omar Nagib's user avatar

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