Greatest Mathematical Puzzle of the modern age?

In summary, the 4 color theorem is a problem that has been asked about for many years and still no one has been able to solve it. The Goldbach conjecture is a problem that is about finding the greatest number that can be divided evenly by two other numbers. Lastly, the Riemann hypothesis is a problem that is about finding a solution to a certain mathematical equation.
  • #1
Einstein
13
1
What is the greatest Mathematical puzzle that is unsolved? and why?
 
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  • #2
Why some people still think they have a "simple" proof of Fermat's last theorem!
 
  • #3
Probably

the question of the non-trivial zeros of the Rieman Zeta Function.
 
  • #5
4 color theorem.

Though it was proven by powerful computers by considering thousands of cases, mathematicians still want to find out a mathematical proof.
 
  • #6
Can you please (all) explain (a little bit) about each of these theories ?
Thanks !
 
  • #8
Riemann conjecture. But I think it has a proof? Or is it the poincare conjecture?
 
  • #9
It most definitely doen't have a proof yet. We don't even know if it's true.

To summarise, the Reimann conjecture is the idea that there is "some" function which can be used to calculate the sequence of prime numbers. The best lead is the zeta function, which has a number of similarities with what we know of the prime number sequence.
 
  • #10
These are pretty much the hardest problems:

http://www.claymath.org/Millennium_Prize_Problems/ [Broken]
 
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  • #11
Originally posted by STAii
Can you please (all) explain (a little bit) about each of these theories ?
Thanks !

You could just search on Google.

To be fair there are lots and lots of very difficult problems, but many are more famous than others. Solving many of the problems around today is impossible considering the mathematics available. e.g. Fermats last theorem was famous because it was first posed 100s of years ago, and because so many people wanted to solve it, and were putting effort in, then as soon as it was solvable, it was.

Many other problems are equally as hard, but it is not worth a top notch mathematician putting in 10 years constantly not to be guaranteed a result.
 
  • #12
Originally posted by Brad_Ad23
These are pretty much the hardest problems:

http://www.claymath.org/Millennium_Prize_Problems/ [Broken]

yeah i was reading about that.. very very cool.. haha well i would get my pencil and paper out and start crunching those primes but it looks like the at&t computers already took out the first billion
 
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  • #13
Originally posted by plus

e.g. Fermats last theorem was famous because it was first posed 100s of years ago,

a bit off the topic but that must be 300+ years ago
about Fermat
and I like Goldbach's conjecture better. it has a simple statement...
 
  • #14
'greatest' can mean different things. But for something with real consequences to other math research, it has to be the riemann hypotheses.
 
  • #15
http://www.sciencenews.org/20030614/bob10.asp
possible solution to the poincare conjecture by a russian mathematician
 

1. What is the Greatest Mathematical Puzzle of the modern age?

The Greatest Mathematical Puzzle of the modern age is a highly debated topic, but many scientists and mathematicians consider it to be the Riemann Hypothesis. This hypothesis, proposed by Bernhard Riemann in 1859, seeks to prove the distribution of prime numbers in the number line and has been unsolved for over 160 years.

2. Why is the Riemann Hypothesis considered the Greatest Mathematical Puzzle?

The Riemann Hypothesis is considered the Greatest Mathematical Puzzle because of its profound impact on number theory and its connection to many other areas of mathematics, such as geometry, analysis, and probability. Furthermore, its solution has the potential to unlock numerous other unsolved problems in mathematics.

3. What progress has been made in solving the Riemann Hypothesis?

Several mathematicians have attempted to prove or disprove the Riemann Hypothesis, but no conclusive proof has been found yet. However, significant progress has been made in understanding the hypothesis and its implications. In 2018, a group of scientists used machine learning to provide a possible proof of the hypothesis, but it has yet to be verified.

4. How does the Riemann Hypothesis impact other fields of study?

The Riemann Hypothesis has connections to various areas of study, including physics, computer science, and cryptography. For example, its solution could potentially lead to a better understanding of quantum mechanics and the behavior of prime numbers in encryption algorithms.

5. Why is the Riemann Hypothesis still unsolved after so many years?

The Riemann Hypothesis is a complex problem that requires a deep understanding of advanced mathematical concepts and techniques. It has also been difficult to verify potential proofs due to its reliance on complex analytical functions. Additionally, the hypothesis has been a source of inspiration for many mathematicians, leading to numerous attempted proofs and solutions, but none have been universally accepted as correct.

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