Linked Questions

This is a soft question. I'm searching for examples of mathmatical statements (preferably in number theory, but other topics are also fine), that seem to be true, but are actually not. Statements ...

Often, students will try to 'prove' a propositon by checking some examples and 'concluding' that it will be true for all $n \in N$. I'm looking for some good, non-trivial examples from highschool ...

There are several conjectures in Mathematics that seem to be true but have not been proved. Of course, as computing power increased, folks have expanded their search for counterexamples ever and ever ...

Note: This is the same question, but it does not have enough answers and it is almost a year old. This question is similar, with many answers, but a conjecture is similar to, but not the same as a ...

I am trying to find a theorem that is valid only for very large numbers. Example: There are numbers which have more than 100 distinct factors. Above theorem satisfies this condition, but it is a ...

This question is inspired by this old paper by Euler: http://eulerarchive.maa.org/docs/translations/E175en.pdf. In it, Euler considers a particular sequence, and finds that the next number in the ...

I just came back from my Number Theory course, and during the lecture there was mention of the Collatz Conjecture. I'm sure that everyone here is familiar with it; it describes an operation on a ...

One of my friends was asking me about tertiary level mathematics as opposed to high school mathematics, and naturally the topic of rigour came up. To provide him with a brief glimpse as to the ...

Is there such a logical thing as proof by example? I know many times when I am working with algebraic manipulations, I do quick tests to see if I remembered the formula right. This works and is ...

When I talk about my research with non-mathematicians who are, however, interested in what I do, I always start by asking them basic questions about the primes. Usually, they start getting reeled in ...

In studying mathematics, I sometimes come across examples of general facts that hold for all $n$ greater than some small number. One that comes to mind is the Abel–Ruffini theorem, which states that ...

How high is the percentage of primes in $\mathbb{N}$? ($\mathbb{N} := \lbrace { 1, 2, 3, \ldots \rbrace }$ ; a prime is only divisible by itself and 1 in $\mathbb{N}$) The percentage has to be lower ...

QUESTION: What are some simple math problems whose answers are highly unintuitive, and what makes them so? There are plenty of unintuitive and frankly baffling results in math, like the Banach-Tarski ...

Here is another dice roll question. The rules You start with $n$ dice, and roll all of them. You select one or more dice and fix them, i.e. their value will not change any more. You re-roll the other ...

A numerical calculation on Mathematica shows that $$I_1=\int_0^1 x^x(1-x)^{1-x}\sin\pi x\,\mathrm dx\approx0.355822$$ and $$I_2=\int_0^1 x^{-x}(1-x)^{x-1}\sin\pi x\,\mathrm dx\approx1.15573$$ A ...