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Results tagged with big-list
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user 935
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.
5
votes
What are some mathematical sculptures?
Stan Wagon (with various collaborators) is known to make snow sculptures that are mathematically pleasant.
13
votes
Computer algebra errors
In Mathematica 7, the command
Table[DirichletCharacter[4, 2, n], {n, 0, 8}]
should return a list of values of the character with modulus 4 and index 2, evaluated at 0, 1, 2, ..., 8. Instead, it retu …
7
votes
Computer algebra errors
Just found this in Mathematica 7.0 for Mac OS X x86 (64-bit) (November 11, 2008):
x=Exp[Pi Sqrt[163] ];
N[x-Round[x] ]
N[x-Floor[x] ]
N[x-Ceiling[x] ]
N[x - Round[x], 2]
N[x - Floor[x], 2]
N[x - Ceil …
11
votes
Papers that debunk common myths in the history of mathematics
There have been recent articles in The Mathematical Intelligencer about the well-known rivalry/animosity between Erdős and Selberg. Didier adds this link, pointing to an article of Graham and Spencer …
22
votes
Fundamental problems whose solution seems completely out of reach
Artin's Conjecture: There are infinitely many primes $p$ for which 2 is a primitive root, i.e., 2 generates the multiplicative group of ${\mathbb Z}/p{\mathbb Z}$.
The conjecture is actually a bit mo …
43
votes
Fundamental problems whose solution seems completely out of reach
This comes up in Waring's Problem, but it is so freakishly simple that it has taken on a life of its own. Let $\{ x \} = x \mod 1 = x-\lfloor x \rfloor$ be the fractional part of $x$.
Say anything ab …
7
votes
nonstandard analysis book recommendation
I loved Goldblatt's book, "Lectures on the Hyperreals".
For a more sophisticated treatment, don't overlook "Nonstandard Analysis: Theory and Applications", edited by Henson (first chapter available t …
2
votes
What recent discoveries have amateur mathematicians made?
The American Institute of Mathematics, a nonprofit organization, was founded in 1994 by Silicon Valley businessmen John Fry and Steve Sorenson, longtime supporters of mathematical research.
That's Fr …
18
votes
How helpful is non-standard analysis?
Freiman conjectured a classification of finite sets $A$ of integers that have
$$\lvert A+A\rvert = 3\lvert A\rvert-3+b$$
for some $0\leq b \leq \lvert A\rvert/3-2$. Renling Jin recently resolved this …
- 9,756
5
votes
What are examples of mathematical concepts named after the wrong people? (Stigler's law)
Farey fractions were introduced by C. Haros. John Farey asked a question about them that reached Cauchy, and Cauchy then attributed the question and result to Farey, and the rest is history.
37
votes
Accepted
What are some results in mathematics that have snappy proofs using model theory?
Hilbert's Nullstellensatz is a consequence of the model completeness of algebraically closed fields.
Edit: I don't have a reference, but I can sketch the proof. Suppose you have some polynomial equati …
- 9,756
8
votes
Which journals publish expository work?
The front page of the Notices (Jan 2011) is an advertisement for the "Bulletin of Mathematical Sciences". The "Aims and Scope" are:
The Bulletin of Mathematical Sciences, a peer-reviewed free acce …
59
votes
Fundamental problems whose solution seems completely out of reach
A proof of this conjecture of Erdos would certainly turn heads, raise eyebrows, and garner the attention of the Fields Medal committee.
If $\sum_{a \in A} \frac 1a$ diverges and $A\subseteq {\mathbb …
0
votes
Most interesting mathematics mistake?
The mother of all examples: Euclid's Elements contains errors from start to finish.
59
votes
Examples of eventual counterexamples
Freeman Dyson observed in my presence that the sequence with initial condition $a_0=3,a_1=0,a_2=2$, and recurrence $a_{n+3}=a_{n+1}+a_{n}$ almost has the property that $n\mid a_n$ if and only if $n$ i …