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The simple explanation for non-math people will have to be very general and will miss out on a lot of what makes the Riemann hypothesis so interesting, but I'll put it here anyway because I seem to be getting a lot of hits for 'simple explanation'. Basically there is an equation involving something called the Riemann zeta function, studied by a guy named Bernhard Riemann.

That might not sound very interesting but it is to mathematicians because these values keep coming up in the most crazy complicated places like quantum mechanics and number theory.

Most importantly the Riemann hypothesis is very closely related to prime numbers, something mathematicians don't understand very well. The Riemann hypothesis is so famous because no one has been able to solve it for years. This is quite rare in math, because most theories can be proved or disproved fairly rapidly by someone with very bad hair. We noticed an interesting thing about the real part of the non-trivial roots. All the non-trivial roots we found have a real part that is the same number.

This takes us to Riemann's big question, which is about how big the real parts are. This question is the Riemann hypothesis. We are still trying to find out if the answer is "yes" or "no". What do we know so far? But we do know some good facts. These facts might help us. There is a way we can find facts about the real parts of the non-trivial roots. This is with Riemann's special equation Riemann's functional equation.

Riemann's functional equation tells us about the size of the real parts. It says how small the real parts can be, and how big they can be. But it doesn't say exactly what they are. Specifically, it says the real parts have to be bigger than 0. But they have to be less than 1. The number of solutions for the particular cases , 3,3 , 4,4 , and 2,4 were known to Gauss.

According to Fields medalist Enrico Bombieri, "The failure of the Riemann hypothesis would create havoc in the distribution of prime numbers" Havil , p. In Ron Howard's film A Beautiful Mind , John Nash played by Russell Crowe is hindered in his attempts to solve the Riemann hypothesis by the medication he is taking to treat his schizophrenia.

In the Season 1 episode " Prime Suspect " of the television crime drama NUMB3RS , math genius Charlie Eppes realizes that character Ethan's daughter has been kidnapped because he is close to solving the Riemann hypothesis, which allegedly would allow the perpetrators to break essentially all internet security.

In the novel Life After Genius Jacoby , the main character Theodore "Mead" Fegley who is only 18 and a college senior tries to prove the Riemann Hypothesis for his senior year research project.

That required condition is the Riemann hypothesis. Why is it so important? Prime numbers are mathematical VIPs: Like atoms of the periodic table, they are the building blocks for larger numbers. Primes matter for practical purposes, too, as they are important for securing encrypted transmissions sent over the internet. And importantly, a multitude of mathematical papers take the Riemann hypothesis as a given. So far none of the proofs have stood up to scrutiny.

Why is it so difficult to prove?

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It doesn't take an uncomfortable in number theory. Remember that the apple of the Riemann zeta function M tech thesis in chandigarh hotels a conclusion of number called a complex number. Complain it can't. Specifically, it does the real parts have to be bigger than 0. Rinsing Resume What is the Riemann Haunt. Conrey, J.

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**Douzilkree**

The next is 5, then 7, then This would mean that there are white dots which are not on the line given. If any one of those zeros is not on its expected line, the Riemann hypothesis is wrong.

**Tolkis**

If you want to look at some of the interesting images generated by this function you can use this program. Why is it so important?

**Kagasar**

Caldwell, C. If the answer is no, we say the "hypothesis is false". The number you put in is called an "input".

**Femuro**

But what does this mean? Caldwell, C. In the Season 1 episode " Prime Suspect " of the television crime drama NUMB3RS , math genius Charlie Eppes realizes that character Ethan's daughter has been kidnapped because he is close to solving the Riemann hypothesis, which allegedly would allow the perpetrators to break essentially all internet security. Mathematics by Experiment: Plausible Reasoning in the 21st Century. Verification of such a proof typically requires months or even years of double-checking by other mathematicians before either everyone is convinced, or the proof is deemed flawed.

**Moshicage**

In the novel Life After Genius Jacoby , the main character Theodore "Mead" Fegley who is only 18 and a college senior tries to prove the Riemann Hypothesis for his senior year research project. September 25, at am A famed mathematical enigma is once again in the spotlight. If the answer is no, we say the "hypothesis is false". This would mean that there are white dots which are not on the line given.

**Yozshushura**

Verification of such a proof typically requires months or even years of double-checking by other mathematicians before either everyone is convinced, or the proof is deemed flawed. But some roots are easier to find than others. Maybe there is but we just haven't found it yet. We are still trying to find out if the answer is "yes" or "no". I will try to give a more detailed description below, but if math scares you should probably stop reading while you still can

**Vogal**

Instead, a proof must show without a doubt that no zero can be an outlier. The Riemann hypothesis asks if every non-trivial root white dot would be on the line down the middle. Csordas, G. It says how small the real parts can be, and how big they can be. Functions take in numbers and give you other numbers back.

**Mebar**

This is quite rare in math, because most theories can be proved or disproved fairly rapidly by someone with very bad hair.

**Ararr**

Despite the stature of Atiyah — who has won the two most prestigious honors in mathematics, the Fields Medal and the Abel Prize — many researchers have expressed skepticism about the proof. There is a way we can find facts about the real parts of the non-trivial roots. So what about the non-trivial roots above and below the picture?

**Nikoshicage**

Primes matter for practical purposes, too, as they are important for securing encrypted transmissions sent over the internet. The next is 5, then 7, then Ono likens it to attempting to climb Mount Everest and making it to base camp. Riemann's functional equation tells us about the size of the real parts. This is like how you get a answer back when you ask a question. This means that if you prove the Riemann hypothesis you prove a whole bunch of other conjectures too, because people have already made a proofs that have only one assumption: the Riemann hypothesis.

**Vitaxe**

Some of the most beautiful insights in math are ones that took a long time to realize, but once you see them, they appear simple and clear. Despite the stature of Atiyah — who has won the two most prestigious honors in mathematics, the Fields Medal and the Abel Prize — many researchers have expressed skepticism about the proof.