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1500 questions
45
votes
1 answer
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 that Grothendieck put it on a rigorous footing…
Conifold
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45
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3 answers
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 around. As an economist (Greg Mankiw) writes:
given…
user67
44
votes
5 answers
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 out of a LaTeX document. I don't think that they…
Gonenc
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41
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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 clearer what I am asking.]
A common bit of…
Michael Weiss
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41
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5 answers
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 mathematical theories (differential equations,…
Conifold
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40
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3 answers
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 certain aspect of the more general question.
Ben
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40
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6 answers
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
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40
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6 answers
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 particular piece of work or in general to all his…
TooTone
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40
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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 different time?
Elec95
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39
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2 answers
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 guessing it might have something to do with the…
timur
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38
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6 answers
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 explanation, $$\sqrt 3 > \frac{265}{153}.$$
The sudden…
Mark Dominus
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9 answers
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 any example where mathematicians didn't see a…
Leandro Caniglia
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36
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5 answers
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 emphasize several differences between mathematics…
Logan M
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35
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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 name of the mathematician somewhere, but I have…
albo
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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 believe it makes sense to search for earlier sources,…
Andrés E. Caicedo
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