After two weeks in the math departnt, 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 beco... if I proved it.
I started by throwing sequences and series into the mix: ’Gk={(pa,pb)∣pa pb=2k,pa,pb pris}.’
I had a hunch that the key was in how these pairs co together. So, I started digging into probability stuff and added a dash of asure 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 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 co 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 ti 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 pri numbers beco more important as the numbers get bigger."
We also explored the Möbius function, which tells us if a number is a mix of different pri numbers or not.
As I worked on this project, I ca across many more proven lemmas, sotis by myself in my room and other tis 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 sa ti, this is the most stupid idea anyone could co 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, aning that every subset of N contains the least elent.
In the case of pris, it’s not that simple.
If I suppose that p and q are pri, and they sum up to n. I gotta find two more pris 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 pri.
After all, we are still in search of the pattern of pris.
That’s the whole point of proving Riemann’s Conjecture!
Proving it ans figuring out that pattern, bringing so order to the pri numbers’ wild ways.
I decided to explore advanced topics in number theory in search of sothing that I could grab onto. Sothing that could light a bulb in my head.
I spend a lot of ti 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 pri numbers "p"
27 might be considered small if you’re thinking in powers of 3. ’ 2*3^1 7*3^0 ’
When it cos 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 pri "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 seed a bit surprised.
He still gave so of his insight, though.
However, even with all that newfound knowledge, I still lacked sothing.
Maybe it wasn’t about the quantity of knowledge, but about letting it soak in, letting the ideas simr.
...
I spent a solid two hours every day cooking up so theoretical chemical compounds. Trying to find so 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 so magnetic monopole properties at low temperatures, hence I started my research on those.
But, none of this theory could be tested in an experint if I didn’t have a laboratory to test it in.
Other than that I needed soone to buy the needed compounds for , as the chemical companies that sell them require you to have a certificate.
Luckily, being a chemistry major automatically gets you so 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 seed familiar to .
"Hey there! Excuse , have we t before?" I asked her.
She turned to and said, "Max Sullivan!" with a shocked but happy look on her face.
It made think, "Sorry, have we seen sowhere? I can not seem to rember."
"Yes, we have! You ca 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 ti 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 sa score as - his na was Yichen Zhang.
"Well... That’s cool... I guess. Nice to et 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 na. "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 sothing?"
"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 accomplishnt in her eyes.
"Listen... Lydia, are you maybe in need of so 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 so experints, you know? And I’m on the lookout for a chem student"
"Hmm... I thought that you were a math guy?"
"Kind of, but it’s all interconnected!"
She blinked in confusion a couple of tis, "If it’s you... then I can do it. What would you need for?"
"I can’t buy stuff!", I said, but looking at Lydia’s face, I realized my mistake, "I need soone to help with the experints?"
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 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 equipnt for .
I needed a magnetic stirrer too so that I could test the magnetic properties of my compounds.
A spectrophototer and a chromatography system were also important to separate out what was really needed.
I found one lab that seed perfect for our experints. It had everything we needed, like fu hoods, a special incubator, a glove box, and even an autoclave.
I got really excited when I checked out the details, and the price seed 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.
So 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 experints worked out, this cost would be nothing compared to the value of the results.
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