Is there any mathematics problem that remained unsolved? Cite one example please.?

Question

I am not a mathematician though, I am curious to know.

Answer 1

There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include

1. The Goldbach conjecture.

2. The Riemann hypothesis.

3. The conjecture that there exists a Hadamard matrix for every positive multiple of 4.

4. The twin prime conjecture (i.e., the conjecture that there are an infinite number of twin primes).

5. Determination of whether NP-problems are actually P-problems.

6. The Collatz problem.

7. Proof that the 196-algorithm does not terminate when applied to the number 196.

8. Proof that 10 is a solitary number.

9. Finding a formula for the probability that two elements chosen at random generate the symmetric group S_n.

10. Solving the happy end problem for arbitrary n.

11. Finding an Euler brick whose space diagonal is also an integer.

12. Proving which numbers can be represented as a sum of three or four (positive or negative) cubic numbers.

13. Lehmer's Mahler measure problem and Lehmer's totient problem on the existence of composite numbers n such that phi(n)|(n-1), where phi(n) is the totient function.

14. Determining if the Euler-Mascheroni constant is irrational.

15. Deriving an analytic form for the square site percolation threshold.

16. Determining if any odd perfect numbers exist.

Answer 2

Some of the examples other people have given are not unsolved problems.

Squaring the circle is not unsolved - it was solved by proving that it was impossible.

THe same can be said for trisecting the angle - it is not possible, so don't waste time trying to do it.

Similarly proving 2 + 3 = 7. That's not unsolved. It's just untrue.

Finding the answer to 0/0? Not unsolved. It is meaningless.

What is infinity? That is very definitely solved. Infinity means "without limit".

But Goldbach's Conjecture is certainly unsolved, as is the Riemann hypothesis, the 3n+1 conjecture and many others.

Here's an article I wrote about the 3n+1 conjecture:

http://www.bbc.co.uk/dna/h2g2/A565788

Answer 3

Look up the famous 3x+1 problem on Google. Also check out Carmichael's conjecture about Euler's phi function. Another one is: Does there exist an odd perfect number? Finally, here's another that my colleagues and I have been playing with for many years: Let n be a positive integer(in base 10) satisfying the following two conditions: 1). n is a square 2). the only digits of n are 0 and 1. Must n be a power of 10? We have checked all possible n up to 10^32 and found that n is a power of 10 up to this point.

Answer 4

Yes. Goldbach's conjecture is the first example that crosses my mind. This is the conjecture that every even integer greater than 2 can be written as the sum of two primes. No proof exists, however no example to contradict it has been found yet.

You can find many more here:
http://en.wikipedia.org/wiki/Unsolved_problems_in_mathematics

Answer 5

The value of 0/0

Answer 6

I am surprised by the answers I read..
hmm..there are many unsolved math problems..

Answer 7

Yes. Squaring the circle is one; finding a formula that produces only prime numbers is another.

Answer 8

In a similar vane as the last answer 1/0 is infinite, but what is infinity?

Answer 9

ya prove that 2+3=7

Answer 10

trisecting an angle (with compass only)
squaring the circle ( to draw a square with the same area as a given circle)