Professor Samuel's response was sharp and outraged, "Game-changer? Your arrogance is astounding, Sullivan! We're not here for baseless claims; we need practical solutions."
Professor Buzard, trying to diffuse the tension, spoke up, "Now, now, let's keep things civil. Max, perhaps you could provide us with a brief overview of your approach. Convince us with the details."
As Professor Samuel's sharp words cut through the virtual meeting room, I took a breath and prepared to present my concept.
"Alright, let me break it down for you," I began. "We're dealing with two distinct populations of models here. One is pre-trained with mathematical logic, and the other is focused on generating mathematical proofs."
I tried to sound as professional as one could get.
I shared my screen, displaying a series of mathematical expressions representing the underlying logic and proof generation mechanisms.
"In the fitness evaluation process, the primary model, grounded in mathematical logic, acts as a benchmark. Let's denote the logic model as M_logic and the proof-generation model as M_proof."
"The fitness function F evaluates how well M_proof aligns with the concepts embodied by M_logic. Mathematically, this can be expressed as", I showed a slide with an expression,
F(M_proof)=Alignment(M_proof,M_logic)
I dug into the nitty-gritty of the neural network structures, "The genetic material, represented by the weights of the neural network connections, undergoes recombination, mimicking natural evolutionary processes. This ensures that the models evolve in a way that aligns with the logic of mathematical principles."
Laying out the weights like W_proof and W_logic for the proof-generation and logic models, I kept the spiel going:
W_proof, new= α ⋅ W_proof, parent1+(1−α)⋅W_proof, parent2
"α here is also a part of the evolution process. As generations progress, the proof-generation models adapt"
"Now... here is the kicker. In the proof-oriented models, I propose introducing a mechanism for sudden mutations triggered by misalignment with logic."
W_proof, mutated=W_proof+M_mutation
"The idea is to establish a balance between variation and adherence to logic. The ultimate goal is to achieve models capable of generating solid mathematical proofs."
Out of nowhere, Professor Samuel's face went from total outrage to genuine interest. "Interesting approach, Sullivan. You might be onto something there," he admitted.
He actually listened to what I had to say. This shows that even though those people might be egoistic, they can recognize a good idea when one is laid out.
But then, he brought it back to reality with a dose of practicality, "But have you considered the immense computational power this would demand?"
"Testing multiple neural network models simultaneously will indeed have high computational demands, but the potential breakthrough is worth the investment."
Professor Buzard raised an eyebrow, "Max, have you considered the potential for redundancy in the neural network models? It might be worth exploring ways to optimize the structure further."
Professor Samuel nodded in agreement, "And what about parallel processing? It could significantly cut down the computational load. We don't want to end up with an impractical solution."
After a brief discussion on these points, I acknowledged their insights, "Valid points, both of you. I'll refine the structure and consider parallel processing to make it more efficient. I'll finalize the details and provide you with the complete specifications"
"I can think about the parallel processing part myself", Professor Samuel said.
Well, less work for me.
Then I added, "Feel free to use the models for your project. However, I won't be actively involved in the day-to-day work."
The Slack channel fell into an unusual silence.
Professor Yvir, another member of the team, spoke up, "Mr. Sullivan, while we appreciate your contribution, we typically expect active involvement for credit allocation. If you wish to be credited for your work, ongoing collaboration is essential."
I replied, "I get the active involvement thing, but right now, I'm juggling a bunch of projects. I've laid down a solid foundation for this initiative, and I'm totally open to helping out if you need clarity or got questions. Just hit me up when you need to, no problem."
After a brief pause, Professor Buzard chimed in, "I believe we can acknowledge that if this works out, it will be a significant contribution. Max, we value what you've brought to the table, and we'll certainly keep you informed. Should any substantial developments arise, we'll reach out accordingly."
I wasn't gonna pour all my time into a project that ain't gonna give me much in return.
After that, I disconnected, typing away on a few things, and then finally got to what I'd intended to check from the beginning—the Millennium Prize questions. Could I solve one? Well, maybe not, but it was worth a look.
So far, Poincaré conjecture was the only proven one.
Let's say I hold a crazy, twisted playdough figure in my right hand.
The Poincaré conjecture says that you can squish and mold it into a perfect ball without tearing or breaking it.
It's a mind-bender that had math brains scratching their heads for ages. Someone even proved it for the 4th and higher dimensions, but not for the 3rd dimension.
Then along came Grigori Perelman.
Perelman's toolkit included the Ricci flow, a bit like ironing out wrinkles on a mathematical surface, making things smoother.
Supposedly, when they wanted to give him the $1,000,000 award, he said, "Nah, I'm good," and went back to his own world.
So this one was not on my to-do list, but there were six more I could check out.
Certainly one of the more well-known problems that I could check out is the Riemann Hypothesis.
Nadya mentioned that she has doubts about it. I could blow away those doubts and make the whole world sit up and pay attention.
For the rest of the evening, I was glued to my PC, diving deep into research. I knew I had that AI thesis to wrap up, but the Riemann Hypothesis had me hooked.
Riemann basically stated that the Riemann zeta function, which is a complex function described by the infinite series:
ζ(s)=1^(s)+2^(−s)+3^(−s) + ...
has all non-trivial zeros situated on a straight line in the complex plane, known as the "critical line," where the real part of the complex number is always 1/2.
There are also some other zeros, but fuck them, we don't care about those.
This would be cool and all, but not really so impressive...
However, the Euler guy dropped the Euler's Product Formula and found that he could represent the zeta function as an infinite product over prime numbers.
Relating the Riemann zeta function to the distribution of prime numbers.
It's clear that if I could crack the code on the Riemann Hypothesis the pattern of prime numbers could finally be understood.
The topic was so complicated and there were so many approaches that had already been made, that I would probably spend weeks just researching it.
Hell, people have been throwing everything at it for ages. Some make it their life's mission.
Done with the session I went to sleep.
...
Once again, I found myself in the Dreamland.
This time, however, my attention was drawn to the freshly arrived vibrant yellow nets.
As I entered one of its tunnels, the threads closed behind me, and something unexpected happened...
The tunnel grew tighter with each step. The vibrant yellow walls pressed in, creating an illusion of a corridor with no discernible gaps.
In the eerie confines of the vibrant yellow corridor, a hushed whisper in Latin broke the silence.
"Veni" - "Come in", I couldn't see where it was coming from, but I felt a creepy urge to move forward.
At this point, I was fluent in Latin. So I didn't have any problem understanding what the voice wanted of me.
As I moved forward, a chill ran down my spine as I stumbled upon something out of this world.
A vibrant, mysterious room. The colors inside were almost too vivid, an unnatural brilliance that seemed to seep into my very being.
Dangling from the ceiling was a grotesque metallic orb.
Droplets of an indescribable, viscous liquid seemed to fall from the ball, creating an unsettling rhythm as they landed.
The substance resembled a bizarre mix of metal and fluid, its properties defying any known laws of nature.
And beneath this peculiar spectacle, I witnessed something that would forever warp my perspective on everything.
A grotesque figure emerged slowly from the pool of mysterious liquid. Its form was eerily humanoid, yet distorted in ways I couldn't clearly understand.
The skin, a shade of grey, clung to the figure's skeletal frame.
The figure's lifeless form was accentuated by long strands of straight white hair cascading down to its knees.
Dressed in a tattered garment that resembled a black coat, the fabric seemed to writhe and contort as if alive. The bottom of this bloated coat melded with the metallic liquid as if it was an extension of the pool.
The figure stood in a grotesque silhouette, that blurred the lines between the human and the eldritch.
I was left transfixed by the haunting sight, but that's when it spoke in a deep tone,
"Which cluster of the quadraverse do you hail from?"