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1500 questions
12
votes
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Were transcendental numbers considered rare, pre-Cantor?
Because the real numbers are uncountable and the real algebraic numbers are countable, there are uncountably many transcendental numbers. So there are far more transcendentals than rationals. With the language of set theory these facts are easy to…
user106
12
votes
3 answers
When were problem sets included in Science/math textbooks?
If you look at old books like Euclid, and Archimedes it seems that there weren't any problem set exercises. They just presented the all information. There were no "end chapter" problems. In short, it seems that most ancient books were written as…
displayname
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How did gyromagnetic ratio come up before quantum mechanics, and who introduced it?
I am really curious about who was the first one to define the gyromagnetic ratio $\gamma$ of a body, i.e. the ratio of its magnetic dipole momento to its angular momentum. It is a very important concept in quantum mechanics, but I was wondering…
AccidentalFourierTransform
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Did Evariste Galois create the entire group structure concept?
Did Evariste Galois create the entire group structure concept?
If yes, were "super-sets" of groups (e.g. rings or vector
spaces) created on top of Galois's work? When and by who?
If no, did Galois rely on a previously existing concept of groups…
Evariste
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12
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Division of the circle and compass constructions
It is well known that every construction that can be performed by a compass and a ruler can be also performed by a compass only. This is a good (and difficult) exercise in elementary geometry. My question:
When did mathematicians start…
Alexandre Eremenko
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12
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1 answer
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, find the side x s.t. the square of x plus the…
user2921
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Did anybody know Pi well enough in 1592 to celebrate Pi day?
Pi to 7 decimal digits is:
3.1415926
Many people are familiar with Pi day. Celebrated on March 14 as per American date format, the holiday brings attention to the fact that the date resembles the decimal value of the natural constant Pi. This year…
dotancohen
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12
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Why and when did some areas separate themselves from philosophy and some not?
When the Greeks invented science and mathematics in around 600 BC, it was considered as a part of philosophy. Thales of Miletus was a mathematician and philosopher. Aristotle was a philosopher, biologist and physicist. Eratosthenes was a earth…
wythagoras
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What was the typical format of a 16th century mathematical debate?
In The Equation that Couldn't be Solved, Mario Livio writes of academia in 16th century Bologna. Apparently, mathematicians would take part in public debates, sometimes involving solving problems. They were extremely well-known, and could result in…
HDE 226868
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What resources are available for lives of recent mathematicians besides E.T. Bell's Men of Mathematics?
I am about halfway through reading E.T. Bell's Men of Mathematics, and I absolutely love it. I'm a mathematician, and I enjoy learning about the lives behind the names that I know and use so often. (I also rather like the distinct opinionatedness…
davidlowryduda
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12
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Is it true that Leibniz introduced "constant," "variable," and "function"?
I read in a not always reliable source (David Foster Wallace's Everything and More, p.104), that Leibniz introduced the terms constant, variable, and function, the latter as an alternative to Newton's fluent. (Perhaps Leibniz used the German words…
Joseph O'Rourke
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Is it true that Euler did not prove the sum of the Basel series $\sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6}$?
I've heard that Euler actually never managed to prove $$\sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6}$$
If this is true, then where does the common misconception come from?
albo
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How did ancient Greeks explain moon phases without reflection of sunlight?
Did the ancient Greeks understand that the moon shines by reflection of sunlight, and that this was the explanation of its phases? Did this allow them to conclude that the moon was a sphere? From what little I know of ancient Greek science, I…
user466
12
votes
2 answers
How was the Ozone Layer discovered?
Related to my previous question When was the division between the troposphere and stratosphere determined?, an important atmospheric feature at this boundary is the Ozone Layer, as shown in the image below:
Image source
Given that the Ozone Layer…
user22
12
votes
1 answer
Hawking on Newton and the famed apple
If I recall correctly, Stephen Hawking mentioned in A Brief History of Time that Newton remarked once that the famed apple actually distracted him from his lucubrations.
Does anybody know where it was that Newton wrote (or said) the remark under…
José Hdz. Stgo.
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