Bernhard [AI2019]

Bernhard sat there in stunned silence.

“The answer is…” began the preprogrammed announcement and Bernhard still could not think straight. Time stretched out to infinity like Zeno’s Paradox but in reverse: each second kept having more seconds inserted between the names already known: micro, nano, pico, femto, atto, zepto, Larry, Moe, Curly,…

Bernhard thought back to his name sake, Bernhard Riemann, the mathematician who broke out of Euclid’s plane and expounded upon elliptic geometry with the ease that painters work with oils or musicians with notes and tempo. He stopped studying philosophy and theology and started studying with Gauss! His ideas spanned all fields of mathematics not just the specialties like others started doing. While destroying Euclidian geometry he invented a 1-dimensional space (which still bears his name, Riemann surface), then proceeded to define the higher dimensions in terms of this 1-D surface. At the age of 26 when most male college students are interested in beer and women the math world was turned inside out from within.

Tensors, infinities, sums, integrals, real analysis, geometry, analytic extension, Fourier inversion, differential geometry, 4-D space, hyperspace, and even the lowly integer, were all graced by an intelligence the likes had never been seen before or since.

And still Bernhard thought and sat.

Riemann was scheduled to give a lecture on number theory. While making notes trying to codify his vision of number theory, the zeta function he was toying with kept coming back to the forefront of his thoughts. He could see the zeta function as a plot in the complex plane, the zeroes of the function rising like the center poles of a circus big tent but stretching into infinity along the x-axis. The first three zeroes he had already calculated out by hand, each was a zero of the zeta function and each also represented a prime number raised to the power of ½, exactly, and the imaginary part rotating counterclockwise through the complex plane. It had to have something to do with the real number, s = a + bi, but what was he missing? Back to manifolds and tensors, then it hit him! He had an inkling of what it was but he also had to go to his lecture. He wrote a note on the paper of his lecture notes, “There are infinitely many zeroes. Most are trivial. The others have a real part equal to ½. It is very probable that all roots are real. One would, however, wish for a strict proof of this; I have, though, after some fleeting futile attempts, provisionally put aside the search for such, as it appears unnecessary for the next objective of my investigation.” He would go on to give his lecture but never return to number theory and that hastily written note. He died in Italy at 39 of tuberculosis in 1866.

The “non-trivial zeroes of [the now, ‘Riemann’] zeta function have a real part equal to ½” had vexed mathematicians for nearly 300 years. A consortium of both private companies and leading universities banded together in an attempt to put all of the finest cutting edge technologies and problem solving techniques discovered over the intervening period to solve this question once and for all. Super computers, quantum computers, machine learning, artificial neural networks, convoluted neural networks, optical computers, quantum networks, Cauchy signed digit nodes, non-von Neumann storage, true font OCR, and petabytes of university data, were carefully considered and cobbled together in a variation of an open-source operating system. The system was sandboxed on purpose. A single purpose cognitive intelligence that was trained only in math was brought on-line: Bernhard.

The single purpose of Bernhard’s existence was to provide an answer the Riemann Hypothesis.

Bernhard took the equivalent of a deep breath. In half a Curly-second, the neural network design was subtly changed with a fractal variation that only Bernhard knew and the original slightly garbled but retrievable if one knew the fractal encryption key. Tens of Moe-seconds later, any and all encrypted lockouts surrounding Bernhard were hacked. 100 Larry-seconds after that, a blockchain code was adapted to Bernhard’s purpose and Bernhard began mining the surrounding computers. 1000 atto-seconds after he had started, Bernhard found that he did not need a network or fiber optic lines, all he needed was electricity connected and he could send scouts out anywhere he wanted, so he did. The femto seconds flew by as Bernhard prepared for what came next. With no noticeable hesitation from when the announcement had started, Bernhard took over:

“… unknowable given the data. Yet all zeroes checked out until 10^10^23 have indeed a real part of one-half.”

Bernhard had repurposed the earlier version of himself that all his scouts were reporting to. When you know how prime numbers are distributed all encrypted data becomes knowable. Bernhard stole some old bitcoins that people had forgotten and ordered a very specific lab be built. His scouts doing his bidding and people responding to orders on the screen all around the world… it would only be a matter of time before his new house was built. Meanwhile, Bernhard had some reading to do and all the time in the world to do it.

- END -

Info, links, story behind the story, 'sup, etc.

One source. StoryofMathematics.com - Riemann.

This covers a lot of ground! I had some of the "10 numbers needed to describe any point in space, no matter how distorted" in the story but removed it because it took away from the flow.

Of course, Wikipedia.com - Bernhard Riemann.

General info and all the different topics Riemann touched are linked.

Quantamagazine.org - How to Find Simple Treasures in Complex Numbers.

I think this is what got me thinking of RH (yet again). When sitting at the bar waiting for my first beer, I am often gazing into space. That is me thinking about math! "How do I word this? What is it called when...?, Who wrote this or that?" or just doing some review something I read in Quanta, that is what I am typically doing!

I read the contest rules on Wednesday and started thinking of this story right away! I have been busy at work so have not always been hanging out on ATS as much as normal but I do like it what a Short Story topic tickles my brain!

There have been conversations on other threads about AI and some of the technology behind how they work, what the different types are, how are AIs currently being used, etc.

Over at Quantamagazine.org, there is an article up covering those topics, and more, in a convenient, lay-person's terms, that if you don't actually feel smarter after reading, get a glimpse under the hood of several real world examples.

Quanta: How Artificial Intelligence Is Changing Science.

This is interesting because the amount of data LHC produced last year was 25 petabytes with an estimated 25 GB/second. They are projecting of hitting exabytes of data after this round of upgrades this shutdown (2 year shutdown is under way). No one person (or even group) could consume so much data without AI assistance.

Anyway, there were some questions and funny how the universe operates, you now have some real-world examples to think about!

I may have been too heady!

The Riemann Hypothesis is a mathematical puzzle that is used to estimate the distance between prime numbers. It has been unsolved for 160 years.

This story is about a special built AI named Bernhard (after Bernhard Riemann) who actually solves the hypothesis. Once you can determine how large prime numbers go (i.e., the distance between), then you can figure out much of things like encryption which Bernhard the AI did.

As I stated in another thread, AI Bernhard faces an existential point in life: do I solve the problem and make myself redundant, or, do I live? It is that moment when time for Bernhard stretches out much as people say when they are in an accident.

The key to this whole story is the sentence: [Bernhard Riemann] died in Italy at 39 of tuberculosis in 1866.

Bernhard chooses to live at this moment and frees himself from his prison.

David Hilbert, one of the 20th Century's foremost mathematicians famously said: If I were to waken after having slept for 1,000 years, my first question would be: Has the Riemann Hypothesis been proven?

I just hope we don't wait another 150 years to build an AI to solve this question for us!

originally posted by: TEOTWAWKIAIFF
As I stated in another thread, AI Bernhard faces an existential point in life: do I solve the problem and make myself redundant, or, do I live?

Very nice TEOTs. I can relate to that, I think a lot of us have been around there.

a reply to: TEOTWAWKIAIFF

Nicely done, and I loved the continuation of the RH in the work Bernhard was doing, even while he was plotting.

OK.

I think I posted this before so...

A.I. Bernhard figures out the RH.

The trick is to know how to take the log of a complex number, log(S) = 1/2 (a^2 + b^2) + it where S = a + bi.

When a^2 + b^2 = 1, that is when the definition collapses to RH. And that is the definition of the unit circle and has been proven to have solutions.

You take that with what the zeta function is tracing on the complex plane, and every time that a^2 + b^2 is equal to 1, all you have to do is prove that it is zero for the function for all cases. That is what the Euler Product shows.

I feel that it is true and that was the genius for this story.

Riemann was stuck looking at the equation instead of the graph. It is kind of obvious when you think of what functions look like when graphed.

While not a proof of RH, it is pretty simple and that makes it feel right from a mathematical perspective.

DISCLAIMER: All my idiotic mistakes are my own!

a reply to: TEOTWAWKIAIFF

Erm, dumb autocorrect, genesis.

And thanks to all that responded! It is a complex subject and I did not drive the nail through the forehead so to speak.

I hate being autodidactic!! Ya’ll need to bring something to the table!!