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Results tagged with big-list
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user 29316
Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
81
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Are there proofs that you feel you did not "understand" for a long time?
Perhaps the "proofs" of ABC conjecture or newly released weak version of twin prime conjecture or alike readily come to your mind. These are not the proofs I am looking for. Indeed my question was ins …
24
votes
Nonequivalent definitions in Mathematics
$(a,b)$
Is that a coordinate pair representing a point in the plane? or,
The open interval from $a$ to $b$? or
The greatest (highest) common factor (divisor) of $a$ and $b$? or
The ideal genera …
16
votes
Parodies of abstruse mathematical writing
The following is somehow a parody of "proof by contradiction" with an obvious educational purpose taken from the book "The Foundation of Mathematics" written by Ian Stewart and David Tall:
COMEDI …
11
votes
Papers that debunk common myths in the history of mathematics
Was Cantor Surprised? published in Monthly is debunking (or trying to do so) that Cantor was so surprised when he discovered $I=[0,1]$ and $I^2$ have the same cardinality
that he said “I see it, but …
10
votes
Most intriguing mathematical epigraphs
If we read Frege's Grundlagen der Arithmetik from the end, the following note in the appendix would be the most courageous of epigraphs all.
A scientist can hardly meet with anything more undesi …
10
votes
Recreational mathematics: where to search?
This is somehow a copy of my answer to a closely related question:
G4G (Gathering for Gardner) is a Foundation that is worth to connect with. From 2010, people around the world celebrate the birthda …
8
votes
Recreational mathematics: where to search?
"Tournaments of cities" mentioned in one of the answers just reminded me of a very lively magazine, again with Russian origin, that is unfortunately not published anymore: Kvant (Quantum; Wayback Mach …
6
votes
An example of a beautiful proof that would be accessible at the high school level?
Here is one that I like and used it for different purposes, e.g. introduction to proofs, algebraic thinking, beauty, and so one. Shuffle a deck of cards. Divide it into two halves. Magic: The number o …
5
votes
Magic trick based on deep mathematics
This is a trick that I designed years ago and I have used it in many different occasions for amusement only or educational purpose or both. It is indeed the finial difference method to find a polynomi …
5
votes
Pseudonyms of famous mathematicians
I guess, though I am not sure, the case of Albert Wormstein falls in your third category:
Professional mathematicians writing mathematics under both their real name and a pseudonym.
This paper: " …
2
votes
What are some examples of mathematicians who had an unconventional education?
Hermann Grassmann is a notable example.
Grassmann was an undistinguished
student until he obtained a high mark
on the examinations for admission to
Prussian universities. Beginning in
1827 …
2
votes
Favorite popular math book
Title: Prisoner's Dilemma
Author: William Poundstone
Short description (from New York Times Book Review): The real originality of PRISONER'S DILEMMA lies in its colorful synthesis of logical materi …
2
votes
Learning through guided discovery
You may find this one interesting: Number Theory Through Inquiry (MAA textbooks). I have used it three times. First time, which I strictly followed the method, we just coverd the first four chapters. …
2
votes
Examples of common false beliefs in mathematics
Anytime I wanted to write an answer to this question, I doubted maybe it is not as common as worthy of mentioning here. In fact, I am also not sure how common is the false belief that I observed today …
2
votes
Good papers/books/essays about the thought process behind mathematical research
This less known paper of H. WHITNEY is a joy to read: Letting research come naturally. Just to make you curious, here is the opening of the paper:
The purpose of this paper is to show that creati …