The Evolution of Genius: Every Night, I Get Smarter!-Chapter 45: Breakthrough

Seated in the dimly lit hotel room, I hunched over the desk lost in numbers and symbols.

Around me, the room was still, the only sound the occasional whisper of a breeze brushing against the curtains.

𝑃_𝑎𝑑𝑖𝑐 𝑅, I jotted. A bridge between p-adic numbers and real numbers, a connection between specific and universal.

My gaze was fixed on the complex equations.

Sigma notations, theorems, and lemmas took shape.

The room around me faded, leaving only the silent rustling of paper and the occasional scratch of my pen.

Then, I laid down the law with the 𝓖-field and 𝓡-field, binding not just some bases but all numerical systems.

A trail of ∫, ∑, and ∮ was visible on the now, many pages of tries and tribulations.

I took into consideration the infinite series, ∑𝑛=1∞ [𝑛(𝑛 + 1)(𝑛 + 2)/6 + 4𝑛³ - 3𝑛² - 𝑛]

A beauty, but it worked in the range of real numbers.

I considered the ∮|𝑥|𝑝-𝑎𝑑𝑖𝑐 term. It explored the p-adic absolute value of a variable 𝑥, allowing me to navigate the p-adic number system.

But for both of these, I needed a bridge.

Just as I pondered this, Oliv returned to the room, breaking the silence and snapping me out of my intense thinking process.

Wearing a soft smile she came up close and glanced at the scattered papers on the desk.

She looked at me and said, "You missed everything, Max. The game was nice, but it just wasn’t the same without you. G1 won the first game."

I felt a pang of guilt but replied, "I’m sorry, Oliv, but I couldn’t stay."

She came closer, draped her arm around my shoulders, and peered at the mathematical scribbles on the pages. Her eyes widened as she asked, "Is this the Goldbach Conjecture thing you were going on about?"

I nodded, a hint of excitement in my voice. "Yes, Oliv, and I had an inspiration.I think I could actually prove it."

With a warm smile, she said, "I won’t bother you then. I’ll go back and enjoy the rest of the game." And with that, she left me alone in the room, allowing me to focus on my work again.

...

After another hour or so, an equation that would revolutionize the number theory and the understanding of patterns as a whole appeared on the page:

∮|𝑥|𝑝-𝑎𝑑𝑖𝑐 𝑑𝑥 + ∫(∇⋅𝐹)𝑑𝑉 = ∑𝑛=1∞ [𝑛(𝑛 + 1)(𝑛 + 2)/6 + 4𝑛³ - 3𝑛² - 𝑛] + 𝜉𝑓(𝑝)

∫(∇⋅𝐹)𝑑𝑉, represented the divergence of a vector field.

By demonstrating that this divergence respects the unique properties of p-adic spaces, I established its role as a bridge.

There was just one last step left for this framework to work.

I introduced the term 𝜉𝑓(𝑝), a factor dependent on the prime number 𝑝.

I needed to establish a set of rules and equations governing this transformation process.

I stood up from the desk, and walked around the room, doing some strange, almost ritualistic ticks.

I tapped my fingers on the desk, traced invisible patterns in the air.

Finally, I settled back onto the desk, pulled a blank sheet of paper toward me, and began to write with fervor.

I created a set of rules, principles of modular arithmetic and number theory.

These equations represented a system...

From this system I derived an equation.

It took shape as my pen danced across the page, 𝜉(𝑝) = ∫[𝑛=1 to ∞] {sin[π(𝑛^2 + 1)𝑝] / [2𝜋(𝑛^2 + 1)𝑝]}

After writing down the equation, I found myself staring at it for what felt like an eternity.

I looked back through the pages, rereading it, over and over again.

I couldn’t help but smile.

Eventually, I stood up and walked over to the window. I picked up my phone, dialed a number, and waited.

Finally the call connected, "Professor Milik?"

"Yes, it’s me, Max, what happened?"

"...I did it", I stated firmly

Professor Milik paused on the other end of the line, and then he asked, "Maximillian... Are you at MIT?"

I replied, "Actually, Professor. I’m in South Korea right now, although I’ll be back in two days."

There was a sense of intrigue in his voice as he responded, "South Korea? Well, your work knows no borders, Max. I look forward to your return. If it holds... this is groundbreaking, and we need to discuss it further when you’re back."

"Of course, I’ll see you at MIT", I skipped his formal title, as our connection had already been solidified through hours of mathematical conversations.

...The call ended.

I slowly sat back down in the chair, picked up the papers and once again browsed through them, holding them in the air.

Suddenly, Oliv burst into the room, her face radiant with joy. She screamed, "G1 did it!"

I looked up, momentarily puzzled, and then it hit me. G1 had won the second game.

Me and Alex - my friend. We both achieved something significant in our own worlds.

Oliv and I decided to go for a late-day walk around the area.

We had originally wanted to meet up with Alex, but we understood that he and his team were deeply focused on the upcoming final.

Distractions wouldn’t be the best for them at this critical moment.

The following day, together with Rick and Oliv, we attended the finals of the World Championships.

This time, I didn’t even consider ditching it.

I was there to support my friend, and I watched with a smile on my face as Alex and his team did their best in the battle for the championship.

It soon became evident that we were witnessing one of the closest games in the history of the WC.

The tension was so thick, that I could smell it in the air.

Every play, every move, every cheer and every burst of energy from the crowd was charged with anticipation.

That day, my mind was on a bit of a breather.

Little did I know that it was just a short break, a moment of quiet before being thrown into something even bigger.

I watched in awe as G1 clinched a jaw-dropping 3-2 victory, etching their names into the League of Legends history books.

The entire arena was lit up, and I couldn’t help but grin from ear to ear.

Alex and his team couldn’t contain their excitement. They jumped away from their PCs, celebrating.

The crowd’s roars echoed through the arena as they swaggered onto the stage to claim the trophy for the League of Legends World Championships.

After the thrilling victory and award ceremony, we joined Alex, his team, and a bunch of family members and friends for a joyous celebration at a local restaurant in Seoul.

We indulged in an array of delicious South Korean dishes.

As the night wound down, and it was time to bid our farewells to Alex, we shared a heartfelt conversation.

Alex mentioned that he’d be staying in South Korea a bit longer for post-championship festivities and practice.

With a warm smile, he turned to me and asked, "Max, when are we going to meet again back in the US?"

I couldn’t help but chuckle and replied, "Alex, you might not have to wait to meet me. There’s going to be information about me everywhere soon."

He looked puzzled, so I added, "I’ve made some significant progress on a mathematical proof. So, keep an eye out for my name. We’ll catch up soon, no doubt."

With a nod, Alex seemed genuinely intrigued.

As we were wrapping up our goodbyes with Alex, Oliv, who seemed a bit tipsy and held a mysterious source of alcohol, playfully nudged me on the shoulder.

With a mischievous grin, she insisted, "Max, we need to get going."

Her playful and somewhat unexpected antics drew a chuckle from everyone.

With Oliv’s insistence to get going, we quickly packed up our belongings.

Together with Rick, we hailed a taxi that would take us to the airport for a nighttime plane takeoff.

We boarded the plane, and settled into our seats. Another long flight laid ahead of us.

Just as the plane was about to take off, my phone rang, surprising me with an unexpected call. I quickly answered, "Yes?"

"Max?! It’s me Lydia. We have a big problem on our hands! I called as soon as I found out..."

"What is it? Something happened at the lab?"

"Yes! And no..."

"Come on! Say it, I don’t have the time, my plane is taking off..."

"Limen Innovations, the company we rented the lab from. They released a paper on how they have created a material with 99% monopole properties!"

"WHAT?! Where did they!? Where did they get the theory for it!? Even if they stole the material? That’s!"

"I have no idea, Max...", Lydia said, and I could feel that she was genuinely confused.

"Sir, put your phone on flight mode", a voice said.

I turned towards the flight attendant with an angry expression.

I must have scared her cause she quickly moved away.