Sometimes in life, you stumble across something that holds more meaning than first meets the eye. Meeting your future husband or wife for the first time and not realizing it is a good example. Mathematically, Dirac's equation is probably the most famous something. Dirac had the ability to visualize an equation in terms of geometry . Dirac came up with an equation that was more insightful than he first realized which you can look up in the Internet . Riemann's something was when it was realized that his zeta function said that the magnitude of the oscillations of primes around their expected position is controlled by the real parts of the zeros of the zeta function . You and I can read the words but what is the meaning without repeating the sentence as an answer ????
Mathematics basically breaks down into the following three areas:
- LengthsNumbers can represent anything. Symbols such as x or y are usually equal to something which is up to you to discover. These symbols may be in a formula expressing relationships which are familiar to anyone that has ever studied algebra. These relationships in algebra are generally a static value as only one numerical answer is needed. Lengths are usually the distance from the beginning of something. An example of this concept is the measurement of a board before you cut it with a saw. The Riemann Hypothesis also hints at the concept of length as it relates to the number of primes. A prime is a number that can only be divided evenly by itself and one ( 1 ) . The five ( 5 ) single digit prime numbers are ( 1. 2, 3, 5, 7 ) . Riemann came up with the formula ( s = ½ + it ) that related to another formula. Without filling in the background, the Riemann Hypothesis implies that if the zeros consistently cross the line ( y = ½ ) in relation to the formula ( s = ½ + it ) then these zeros have something to do with the distribution of primes. There is an implicit idea here that every crossing of a zero on the line ( y = ½ ) is related to the position of a corresponding prime from the beginning of the line ( y = ½ ) to the end of the line ( y= ½ ) at infinity. Theoretically, if the values of Riemann's formula were chosen correctly, the calculation of the zeros crossing the line would give you the distance of a known prime from the beginning of ( y = ½ ) . This means that if the location of the zero crossing the line ( y = ½ ) were accurate that location would correspond with the position of a prime on the line ( y = ½ ) . Riemann's formula is really a disguised calculus problem using zeros ( 0 ) to adjust the placement of a prime on the line ( y = ½ ) . In other words, if you adjust the zero in a mathematical expression how close can you get the relevant known prime to its' actual position on the line ( y = ½ ) ???? This position calculation would give you the number of primes from the beginning of the line ( y = ½ ) . My previous blogs on this topic will give you an idea as to how the calculation is done. Calculus, using symbols, is the study of the change in the length of a formula containing symbols that change in length. One of these symbols is ( c ) which represents a constant ( whole number ) which never changes. The accepted length of a constant ( c ) in calculus ( d (c)) is zero ( 0 ) but that isn't correct because Riemann's intuition told him that the zeros which are also a constant had a real value of ( ½ ) on his line ( y = ½ ) consisting of primes. The actual length of any ordinary constant is the sum of its' digits. 47 would have a length of 11 or 2 ( 4 + 7 = 11 ) or ( 1 + 1 = 2 ).