Leonhard Euler: The Basel Problem
By: Victor Hui
Introduction
Leonhard Euler was a ground-breaking Swiss mathematician and physicist from the 1700's. He made many revolutionary discoveries. However, the one that caught my eye was his solution to the Basel Problem in the year 1734.
The Basel problem was initially posed by an Italian mathematician by the name of Pietro Mengoli in the early 1640's. This problem baffled the even the greatest minds at the time. Branching from mathematical analysis, the Basel problem involved knowledge of convergent series. Convergent series are series where the sum of all terms approaches a limit. As a result of solving a problem that tormented even the brightest mathematicians of the time, Leonhard Euler's and his Solution became exceedingly …show more content…
Through the Basel Problem's definition, Bernhard Riemann produced a mathematical notion which is identical to the Basel Problem except for the fact that rather than the reciprocal squared, we have the variable "s".
The Riemann created a function in which currently states that any value of "s" that makes the series equate to zero is either a negative even integer (trivial zeros) or when the horizontal axis equates to 1/2 (called the critical line). The critical line lays in between the horizontal axis equating from 0 to 1. We call this the critical zone. The Riemann Hypothesis asks for a nontrivial zero from the critical zone, a value of "s" that makes the function equate to zero that is not a negative even integer or does not lie on the critical line. This hypothesis was marked as one of the millennium problems. No one has been able to find non trivial zeros off of the critical line and inside of the critical zone. The rules of the millennium problems states that one million dollars is awarded to the mathematician that can find a zero outside of the critical line and inside the critical
Introduction
Leonhard Euler was a ground-breaking Swiss mathematician and physicist from the 1700's. He made many revolutionary discoveries. However, the one that caught my eye was his solution to the Basel Problem in the year 1734.
The Basel problem was initially posed by an Italian mathematician by the name of Pietro Mengoli in the early 1640's. This problem baffled the even the greatest minds at the time. Branching from mathematical analysis, the Basel problem involved knowledge of convergent series. Convergent series are series where the sum of all terms approaches a limit. As a result of solving a problem that tormented even the brightest mathematicians of the time, Leonhard Euler's and his Solution became exceedingly …show more content…
Through the Basel Problem's definition, Bernhard Riemann produced a mathematical notion which is identical to the Basel Problem except for the fact that rather than the reciprocal squared, we have the variable "s".
The Riemann created a function in which currently states that any value of "s" that makes the series equate to zero is either a negative even integer (trivial zeros) or when the horizontal axis equates to 1/2 (called the critical line). The critical line lays in between the horizontal axis equating from 0 to 1. We call this the critical zone. The Riemann Hypothesis asks for a nontrivial zero from the critical zone, a value of "s" that makes the function equate to zero that is not a negative even integer or does not lie on the critical line. This hypothesis was marked as one of the millennium problems. No one has been able to find non trivial zeros off of the critical line and inside of the critical zone. The rules of the millennium problems states that one million dollars is awarded to the mathematician that can find a zero outside of the critical line and inside the critical