Changes

[[Riemann hypothesis]] remains the greatest unsolved problem in mathematics today.  It was first proposed in Riemann's classic paper ''On the Number of Primes Less Than a Given Magnitude'' (1859).<ref>http://www.andrews.edu/~calkins/math/biograph/199899/bioriema.htm</ref>

[[Riemann hypothesis]] remains the greatest unsolved problem in mathematics today.  It was first proposed in Riemann's classic paper ''On the Number of Primes Less Than a Given Magnitude'' (1859).<ref>http://www.andrews.edu/~calkins/math/biograph/199899/bioriema.htm</ref>

==Riemann integral==

==Riemann Integral==

The [[Riemann Integral|Riemann integral]] is the common definition today of the integral in introductions to analysis, as first put on a rigorous mathematical foundation by Riemann.  The Riemann integral is, in essence, the definite integral:

The [[Riemann Integral]] is the common definition today of the integral in introductions to analysis, as first put on a rigorous mathematical foundation by Riemann.  The Riemann Integral is, in essence, the definite integral:

:<math>\int_a^b f(x)\,dx</math>

:<math>\int_a^b f(x)\,dx</math>

It is defined as the sum of infinitesimal segments of the x-axis of the area under the function on a graph, between ''f(a)'' and ''f(b)''.  

It is defined as the sum of infinitesimal segments of the x-axis of the area under the function on a graph, between ''f(a)'' and ''f(b)''.  

As it is more versatile, the [[Lebesgue]] Integral has superseded this definition.

The Riemann Integral is the one commonly taught in school and continues to be the most useful definition for scientific purposes.  The more complex [[Lebesgue]] Integral is used today in some mathematical fields.

==Additional concepts named after Riemann==

==Additional concepts named after Riemann==