The Evolution of Genius: Every Night, I Get Smarter!

After two weeks in the math department, I was knee-deep in my research. Instead of being stuck in classes all week, I only had to show up for two of them.

I worked hard the first week to show that the Goldbachian Kernel Lemma was true.

Well, a Lemma it would become... if I proved it.

I started by throwing sequences and series into the mix: ’Gk​={(pa​,pb​)∣pa​+pb​=2k,pa​,pb​ primes}.’

I had a hunch that the key was in how these pairs come together. So, I started digging into probability stuff and added a dash of measure theory to the mix. ’limn→∞ ​P(Gk​ has n pairs)=1’

During one class, I tossed an idea to Oliv about taking a flight with me to South Korea next week.

Oliv was totally on board. I also called Casandra, but unfortunately, Casi had an important exam the day that we would come back to Boston.

I still wanted to show up in South Korea to watch Alex, so we booked a flight with Olivia.

...

I’ve been going between Professor Milik’s and other Professor’s offices, learning a lot as time went by.

We looked into number theory, starting with Liouville’s Function. ’lim supn→∞​ A(n)/​loglogn=+∞’

Which, as Professor Milik put it, "tells us that prime numbers become more important as the numbers get bigger."

We also explored the Möbius function, which tells us if a number is a mix of different prime numbers or not.

As I worked on this project, I came across many more proven lemmas, sometimes by myself in my room and other times with Professor Milik, Professor Brille, and other people.

The simplest idea was to prove it by strong induction. Assuming that it’s true for all values up to n and then proving it for n + 2.

But at the same time, this is the most stupid idea anyone could come up with...

The conjecture couldn’t be proven with induction! If that was the case, even underperforming undergrad students could do it.

Induction works in the case of natural numbers (N), that’s because they are a well-ordered set, meaning that every subset of N contains the least element.

In the case of primes, it’s not that simple.

If I suppose that p and q are prime, and they sum up to n. I gotta find two more primes that add up to n + 2.

What if I roll with p + 1 and q + 1? They crank it up to n + 2, but here’s the kicker – there is no way to know if they are prime.

After all, we are still in search of the pattern of primes.

That’s the whole point of proving Riemann’s Conjecture!

Proving it means figuring out that pattern, bringing some order to the prime numbers’ wild ways.

I decided to explore advanced topics in number theory in search of something that I could grab onto. Something that could light a bulb in my head.

I spend a lot of time learning p-adic analysis. In regular math, we roll with powers of 10, like how 123, is ’ 1*10^2 + 2*10^1 + 3*10^0 ’

But p-adic numbers are completely different because we use the powers of the prime numbers "p"

27 might be considered small if you’re thinking in powers of 3. ’ 2*3^1 + 7*3^0 ’

When it comes to the distance between numbers, it’s a different vibe too. Two numbers are tight if the difference between them is divisible by a high power of the prime "p.".

It’s not your regular absolute difference.

I have also researched what’s called the valuation functions on fields. Professor Milik was quite an expert in that. With many papers written on it, so I tried to ask him all the important questions.

At first, he was all about it, dropping knowledge bombs left and right. But yesterday, when I hit him up with a question, he seemed a bit surprised.

He still gave me some of his insight, though.

However, even with all that newfound knowledge, I still lacked something.

Maybe it wasn’t about the quantity of knowledge, but about letting it soak in, letting the ideas simmer.

...

I spent a solid two hours every day cooking up some theoretical chemical compounds. Trying to find some of them that might have monopole properties.

Spin ice materials, such as holmium titanate and dysprosium titanate, have been found in the past to have some magnetic monopole properties at low temperatures, hence I started my research on those.

But, none of this theory could be tested in an experiment if I didn’t have a laboratory to test it in.

Other than that I needed someone to buy the needed compounds for me, as the chemical companies that sell them require you to have a certificate.

Luckily, being a chemistry major automatically gets you some certificates.

Now, my smart move was to hang out outside of the hall where Ph.D. chemistry students had their lectures.

...

I stood in front of the lecture hall as chemistry students started exiting.

Amidst the crowd, I spotted a girl clad in black Stradivarius trousers and a white blouse.

She had short brown hair, and her face seemed familiar to me.

"Hey there! Excuse me, have we met before?" I asked her.

She turned to me and said, "Max Sullivan!" with a shocked but happy look on her face.

It made me think, "Sorry, have we seen somewhere? I can not seem to remember."

"Yes, we have! You came into my statistics class a few weeks ago and even answered a question on the board!"

"Oh, right! That stats lecture! Sorry, I didn’t recognize you at first. How’s it..."

"I’m Lydia! I’ve been following ’The Prodigy Maximillian’ fan pan page! You’re like a legend!", I wanted to ask her how it was going, but she interjected with an energetic tone.

I had no idea that I gained such popularity in the short time that I was engrossed in my research.

After the IMC results were announced, MIT put my face on the webpage as the winner of the IMC. However, there was a guy from China who got the same score as me - his name was Yichen Zhang.

"Well... That’s cool... I guess. Nice to meet a fan!"

Lydia blushed a bit, "Actually, I was wondering if I could get your autograph?", she said as she took out a notebook with a cute expression.

"Sure thing, I’d be honored," I scribbled my name. "There you go"

That’s when she snapped back to reality "Thank you so much! But wait, why are you here? Are you giving a lecture or something?"

"A lecture? Hell no!", I chuckled at the thought of a first-year student giving a lecture at MIT.

I continued, "Actually... You’re a chemistry student, right?"

"Yes! I got my master’s this year, and I got into the Ph.D. course" she said with pride, a glow of accomplishment in her eyes.

"Listen... Lydia, are you maybe in need of some research points?"

She thought for a second, "Not really... I already had an ongoing project for the last two years."

Damn, that wasn’t the answer that I was expecting, but I pushed the topic.

"I’ve got this plan to rent a lab, and do some experiments, you know? And I’m on the lookout for a chem student" 𝚏𝕣𝕖𝚎𝚠𝚎𝚋𝚗𝐨𝐯𝕖𝕝.𝕔𝐨𝕞

"Hmm... I thought that you were a math guy?"

"Kind of, but it’s all interconnected!"

She blinked in confusion a couple of times, "If it’s you... then I can do it. What would you need me for?"

"I can’t buy stuff!", I said, but looking at Lydia’s face, I realized my mistake, "I need someone to help me with the experiments?"

Her serious look turned into a grin. "Haha, OK, Max. I will help you, but my schedule is already tight. You will need to give me a heads up whenever you rent the lab you talked about."

There we go!

"Absolutely, Lydia! Thanks a bunch. How about we exchange numbers?"

Lydia’s grin widened, and she nodded, "Sure, Max. Lab-related stuff only, though"

I chuckled, "Deal. Here’s my number." I handed her my phone, and she deftly keyed in her digits.

She returned the phone, "Great!"

"Right, I will go then! Expect a call soon!", I said and I rushed back to my room.

My PC flickered to life, and I opened up a website with lab rental offers.

The centrifuge, for spinning substances at high speeds and the separator were essential equipment for me.

I needed a magnetic stirrer too so that I could test the magnetic properties of my compounds.

A spectrophotometer and a chromatography system were also important to separate out what was really needed.

I found one lab that seemed perfect for our experiments. It had everything we needed, like fume hoods, a special incubator, a glove box, and even an autoclave.

I got really excited when I checked out the details, and the price seemed fair for what they were offering.

The basic rent for the lab, which had all the cool stuff for testing magnetic properties, a high-performance liquid chromatograph, and a rotary evaporator, was $3,500 each month.

Some specific tools like the magnetic stirrer had an extra price tag on them - we’d need to pay an extra $100 / hr.

For your average student, this would be a cosmic expense, but yours truly had enough in the bank.

And if any of my experiments worked out, this cost would be nothing compared to the value of the results.