The day after, Olivia and I woke up early, knowing that we had a 10 a.m. lecture scheduled at MIT, which meant taking off on a four-hour ride by car.
Neither of us had a driver's license, so it was Olivia's mother who kindly offered to drive us. Olivia's mom was a striking woman in her late thirties, who had an aura of grace and respectability.
We sat on the back of the blue Fiat and in just a little over three hours, we arrived in Massachusetts. Olivia's mom proved to be a bit of a reckless driver, confidently pushing the speed limit.
I also noticed a shift in the way I speak, as if mirroring the growth in my intelligence. It was my father that noticed it, to be real with you.
When my father called, I couldn't help but use more sophisticated language than before, and he immediately picked up on the change.
I assured him that my SAT results would definitely be impressive, and I was determined to secure a scholarship. He thought I was joking, but the truth was, that I didn't have any recommendations, so a full SAT score alone wouldn't be sufficient to earn a scholarship at MIT.
I knew I needed to find a way to generate more than just a few hundred dollars to support my education.
As Olivia and I walked around the MIT campus, we went in different directions for a bit. She wanted to explore more before our lecture, while I headed towards the Math Department where our class was supposed to happen.
The MIT campus had a mix of modern and older buildings. Some were big and made of glass and steel, while others were smaller and looked like old brick buildings.
It was interesting to see the contrast between the new and the old.
The main entrance to the Math Department was a cool spot. There were some plants and sculptures outside that made it look nice. MIT felt like a place where people were always thinking about new ideas and learning cool shit.
I was getting more and more excited about studying math at MIT as I walked closer to the Math Department.
On the opposite side of the lecture hall that the applying students were supposed to enter there was an open door to an aula which really piqued my interest.
I strolled into this packed lecture hall, and I found myself catching stares from the students, but they didn't say anything. It seemed they were waiting for the lecturer.
The blackboard at the front displayed a complex mathematical question, one that had most likely been assigned for the class. Despite the room being full, the lecturer was conspicuously absent.
My curiosity was piqued by it and I decided to take a shot at solving it. Well, if the lecturer gets here, I'll pull the "I got lost" card. Sketchy, but it might fly.
With determination, I stepped up to the blackboard ready to flex on the students, and began working on the problem—a challenging graduate-level statistics question that would probably test even seasoned statisticians.
It was a proof involving the convergence of a series of random variables.
The thought process at the beginning of this proof was crucial. I had to establish the foundation for the entire argument.
I dove in headfirst, defining the series, and breaking down its properties like the expected value and variance. Proving convergence meant showing that as we took more terms of the series, the limit approached a specific value.
Equations and calculations flowed from my chalk as I delved into the intricate world of mathematical analysis.
I knew I had to carefully manipulate the terms of the series, employing techniques like the dominated convergence theorem and the law of large numbers to justify my steps.
I was really focused at that moment and the classroom remained silent, despite the fact that a student they saw for the first time in their life was writing something on the board.
They watched in curiosity as I tackled this graduate-level statistics question, knowing that it would take more than just an equation to prove the convergence I sought.
At the front row of the classroom, a girl with brown hair observed my efforts with amazement. She couldn't help but feel a sense of wonder at my apparent expertise.
Her curiosity got the better of her, and she raised her hand to ask, "Excuse me, who are you, and how do you know how to solve this?"
I, still laser-focused on cracking this problem, briefly glanced at her and replied, "I'm Max Sullivan, a prospective student. I came here to apply for the Software Engineering department at MIT, but I got a bit lost and ended up here. The question intrigued me, so I thought I'd give it a try."
As I continued my work on the problem, the classroom remained quiet, with all eyes fixed on me.
Suddenly, the lecture hall's door swung open, and Professor Milik, the missing lecturer, entered the room. He was surprised to find me at the blackboard, deeply engrossed in solving the problem.
Clearly agitated, Professor Milik addressed the class, "I apologize for beeing late. It looks like someone used the blackboard without permission. Who is guilty for this?"
I turned my head to Professor Milik, "I'm Max Sullivan, a prospective student. I didn't realize this was a class, and I saw the question on the board. I thought I'd give it a try.", well this wasn't the reply I was going for, maybe this was a bit too cocky.
Professor Milik, still annoyed by the interruption, was about to scold me when he glanced at the whiteboard. To his surprise, the advanced graduate-level statistics problem was being solved with remarkable accuracy.
Intrigued by the work on the board, Professor Milik's irritation gave way to curiosity. He asked, "What year are you attending, Max, do you know how to prove this?"
I, recognizing the professor's interest in my work, replied, "I'm applying to MIT this year, Professor. I have a background in mathematics, and the question just seemed fascinating."
Well... I didn't really have a background, but let's just say that skill is enough.
As I kept working on the problem on the blackboard, Professor Milik watched with increasing interest. He had been angry at first, but now he was impressed by the unexpectedly talented student who had come into his class.
I met with a problem with the later part of proving the hypothesis, so I decided to ask the professor about this.
"I'm sorry. The textbook I read mentioned the multivariate nonparametric kernel density estimation. Now I stumbled upon complex variants of the Bayesian nonparametric. I tried to derive them and was stuck on this step," I explained to Professor Milik with an apologetic smile.
After looking at me for a moment, Professor Milik quickly looked at the chalkboard. He then set down his bag and picked up a piece of chalk.
He walked over to the blackboard and took a moment to think before drawing equations with the chalk in hand.
As he started to write down the complicated statistical ideas on the whiteboard, I paid close attention to everything he did.
Third-year math students studying nearby were drawn to the noise made by the chalk on the podium. They would look up from their work and stare blankly at the complicated numbers on the board before going back to their own studies.
What Professor Milik was writing was going through my mind like crazy. I found the complicated symbols and equations in statistics intriguing.
After writing all over the chalk for a while, Professor Milik stopped and looked at me with an eyebrow raised. "Is this part clear to you?"
I looked closely at the blackboard and took in the statistical terms before boldly nodding and saying, "I get it."
Professor Milik raised his eyebrows even more to be sure. "Do you really understand?" he asked.
I said, "I really get it," one more time.
With a nod of approval, Professor Milik didn't say much. He began wiping the blackboard clean with the eraser and then took the chalk, ready to continue writing.
As he wrote the finishing parts of the problem, Professor Milik stopped and looked back at me with a slightly amused face. "I'll finish writing here. You should be able to understand now, right?"
I nodded in agreement, "I do. Thank you, Professor."
...
Lydia's POV
Lydia, the chemistry major, who had been observing our exchange from the front row, wore a puzzled expression.
She asked herself, "What was it that he understood?" Her confusion was clear.
Realizing that understanding our conversation was beyond her abilities, Lydia began to doubt her own statistical prowess. She thought that maybe she was not as good of a student as she thought she was.
...
Professor Milik caught wind of my response and let out a chuckle.
He laid the chalk down, eased into his chair, cracked open his vacuum flask, and took a sip of that good ol' coffee.
He replied with a thoughtful tone, "If you really get it..." He then took another sip. "why not finish those steps on the board?" He pointed to the now completely blank blackboard.
I couldn't help but smile as I replied, "Really, Professor, I understand this,"
At that moment, I saw in Professor Milik's expression that he doubted whether I had truly paid attention.
I was confident, even though Professor Milik appeared uninterested in solving the question himself. He seemed content to watch me demonstrate my abilities.
I pondered the reasons behind my deep understanding of those statistical concepts. Was it due to the knowledge gained from the weird, mysterious dreams, which covered this information? Or had my intelligence as a whole been enhanced?
With a confident smile, I walked toward the blackboard, chalk in hand. Professor Milik's eyebrows arched as he believed there was no way an applying student could complete the statistical proof.
The last leg of the proof was known for being a beast, a real head-scratcher even for master's students who had to grind through it multiple times.
But, lo and behold, I hadn't jotted down a single note while listening to Professor Milik.
Time trickled on, and the initial amazement Professor Milik felt morphed into straight-up shock, before ultimately evolving into approval. His doubts melted away, disappearing like snow melting in the springtime sun.
After I finished writing the last symbol on the blackboard, I turned to Professor Milik. He nodded in approval and remarked, "Not bad..."
The home stretch took a detour from Professor Milik's method. I showcased my own twist on things.
"It was still thanks to your help, Professor. If I were to attempt this on my own, I doubt I could have reached this step," I tossed him a nod of gratitude.
"So, what was your name again?"
"I'm Max Sullivan"
"I'll remember you, now go to the Lecture you were Actually supposed to attend little guy." He said with a contemplative expression.
I listened to his words and left the lecture hall. The lecture on the introduction to University Math was supposed to begin two minutes ago.