posted on Oct, 1 2022 @ 08:09 PM
He figured it out!!!
No sh… kidding!
The world’s most famous math hypothesis has -had, been the Riemann Hypothesis. A hundred and eighty years of countless mathematicians scribbling
arcane symbols only other bulb heads could understand had achieved nothing.
Minor progress had been made with solutions to associated problems that spanned the number line with numbers in the 10^100^100 area to start with and
growing from there (asymptote analysis) had yielded a proof to the Lindelof Hypothesis several years ago. But Riemann himself thought it was easier to
explain but failed at his own attempt (and only one attempt before other problems pushed him into other areas like he knew his time was limited).
And here was the simple answer staring at him from the dry erase board in black and green ink (black for the basic math reiteration and green for the
application to the great Riemann Hypothesis-RH).
It was easy to understand as well. Even a precocious child with a grasp of algebraic equations could do the work! That is why the answer had to be
correct! Feynman had said that if you could explain your solution to a youngster using basic math then you probably have the answer correct.
It started with simple math we all were taught in grade school: logarithms:
A function is a mathematical structure that manipulates an input and produces (and reproduces) a specific output, in this case Integer X, is
transformed by the function, namely:
F(X) = 1/X
For any base 10 integer.
Thats it. The whole key to RH is this function.
Using the Euler Product of the Zeta Function (F(n) = sigma(1/X^n), over x = 1..infinity), it is the sum of logs raised to an integer value, n.
The product, an entire work of genius in its own right, uses two Zeta Functions to create a Sieve of Eratosthenes, which restates the infinite sum as
an infinite product of subtracted prime numbers:
P(n) = (1/1 - 1/p^n) )
As one can see, the function is undefined with p=1^1, because you divide by zero. But 1 is not a prime number so this is more of a mathematical
complete description of the equation (The product function multiplies the numbers in the range together, so if you had n = 1..5, P(n) = 1x2x3x4x5 =
120); in the Zeta function, p, ranges over the primes, 2,3,5,7,11,13,…
But it is a mess when stated as above. Everyone restates the equation with negative powers to make it look slicker. But you can do this using the log
function:
P(n) = log(1-log(p^n) )
Using the power rule of logarithms, log(x^y) = y * log(x), you restate the above product as:
P(n) = log(1 - n * log(p) )
You plainly see that eventually you will take log(n).
Riemann extended the zeta function to the Real Numbers, the Reals, by substituting the integer n, for the real number:
s = a + b*i
Where i is the imaginary number, i = sqrt(-1).
Riemann had hoped that extending the value to an extra dimension (a new variable in the function) would allow the function to be solved in a more
simple manner as had been experienced with other equations under real analysis.
But it appeared to cause more problems than it solved.
So keeping it dead simple, substituting s for n, one wonders, “can you take the log of a real number, s”??
Sure! It is clearly explained in any undergrad math textbook. So with, s = a + bi, the equation is:
log(s) = log(a + bi) = 1/2*(a^2 + b^2) + it
Which is just the Pythagorean theorem extending into the real plane! You move forward a units, then up b units, which creates a right triangle. The
distance to the point is a straight line, i.e., the hypotenuse, which if you only had a brain, you would know that it is the sum of the squares of a
right triangle and is equal to the square of the hypotenuse. And using the real numbers, sines and cosines, equals the above in base 10.
When a^2 + b^2 = 1, you are describing the unit circle. Less than 1, you are inside the unit circle; larger than 1, you are outside the unit circle
determined by the value of i*t.
When on the unit circle, s = 1/2 + i*t, which is what Riemann intuitively surmised but stumped mathematicians for hundred plus years!!
And it was staring back at him from the white board.
He took a photo with his phone then parked in front of his computer for a LaTex session to write his results down.
Sunday morning the ArXiv published his paper on Monday morning in the Number Theory section.
The NSA had an eye on Rutgers University and the paper was flagged immediately.
Days later the local newspaper carried a story about a car crash with one fatality.
The arXiv never published the paper.
And the news nobody bothered to understand was the author didn’t even own a car. Had not driven in 23 years.
- The End -