page_title: Riemann hypothesis
hierarchical_section_title: Riemann hypothesis
caption_attribution_description: English: The zeros of the Riemann zeta function. Region: x=-10..10, y=0..100. Hue is complex phase (red is 0), brightness is absolute value (brighter is less, darker is more). Polski: Miejsca zerowe funkcji&#160;ζ w&#160;obszarze x=-10..10, y=0..100. Odcień oznacza argument, jasność — wartość bezwzględną (im jaśniej, tym większa).
context_page_description: The Riemann hypothesis is a mathematical question. Lots of people think that finding a proof of the hypothesis is one of the hardest and most important unsolved problems of pure mathematics. Pure mathematics is a type of mathematics that is about thinking about mathematics. This is different from trying to put mathematics into the real world. The answer to the Riemann hypothesis is "yes" or "no".
  The conjecture is named after a man called Bernhard Riemann. He lived in the 1800s. The Riemann hypothesis asks a question about a special thing called the Riemann zeta function.
  If the answer to the question is "yes", this would mean mathematicians can know more about prime numbers. Specifically, it would help them know how to find prime numbers. The Riemann hypothesis is so important, and so difficult to prove, that the Clay Mathematics Institute has offered $1,000,000 to the first person to prove it.
context_section_description: The Riemann hypothesis is a mathematical question (conjecture). Lots of people think that finding a proof of the hypothesis is one of the hardest and most important unsolved problems of pure mathematics. Pure mathematics is a type of mathematics that is about thinking about mathematics. This is different from trying to put mathematics into the real world. The answer to the Riemann hypothesis is "yes" or "no". 
  The conjecture is named after a man called Bernhard Riemann. He lived in the 1800s. The Riemann hypothesis asks a question about a special thing called the Riemann zeta function. 
  If the answer to the question is "yes", this would mean mathematicians can know more about prime numbers. Specifically, it would help them know how to find prime numbers. The Riemann hypothesis is so important, and so difficult to prove, that the Clay Mathematics Institute has offered $1,000,000 to the first person to prove it.
caption: The Riemann zeta function, in the complex plane. The real part 
    
      
        
          Re
          ⁡
          (
          s
          )
        
      
      {\displaystyle \operatorname {Re} (s)}
    
   of the number is drawn horizontally, the imaginary part 
    
      
        
          Im
          ⁡
          (
          s
          )
        
      
      {\displaystyle \operatorname {Im} (s)}
    
   vertically. White dots show the zeros where 
    
      
        
          Re
          ⁡
          (
          s
          )
          =
          
            
              
                1
                2
              
            
          
        
      
      {\displaystyle \operatorname {Re} (s)={\tfrac {1}{2}}}
    
  . Click to get a full view.
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