The Foundations of Genius
Lassen stretched lazily in his chair, closing the novel he had just finished. A satisfied sigh escaped his lips.
"That protagonist… a respected academic master, capable of solving the most complex mysteries. Not bad, honestly." he murmured, a dreamy smile on his face.
Then, looking up at the ceiling, he casually announced, "System, I've decided. I want to become an academic master, like that guy in my novel. Give me a list of the biggest mathematical puzzles in the world."
A brief silence followed before the sarcastic voice of the system echoed in his mind.
[Ah, of course, Host. After your brilliant career as a professional reader, you're now tackling advanced mathematics. Such ambition… perfectly aligned with your lazy nature.]
Lassen burst into laughter. "Exactly! So, show me these problems so I can pick one to solve."
[Very well. Prepare to enter a world where your intelligence—or lack thereof—might become a problem in itself.]
An illusory screen appeared before his eyes, displaying a list of seven mathematical enigmas.
---
The Seven Major Mathematical Problems
1. The Riemann Hypothesis
[The Riemann zeta function, ζ(s), is defined on complex numbers. The hypothesis states that all non-trivial zeros of this function have a real part equal to 1/2.]
Lassen frowned. "Uh… are you speaking in code now?"
[Allow me to simplify it for you, Host. In plain terms: it's a riddle about how prime numbers are distributed. Solving this could revolutionize cryptography and several branches of mathematics.]
"Prime numbers again… They're so overrated" Lassen muttered.
2. P vs NP
[This problem aims to prove that any problem whose solution can be verified quickly can also be solved quickly.]
"Okay, simpler than the last one, right?" Lassen asked.
[Not exactly. If this conjecture is proven, it could transform modern computing by making exponential problems solvable in reasonable time. But first, you'd need to understand what it implies.]
"So, it could help hackers? Cool."
3. Birch and Swinnerton-Dyer Conjecture
[It relates the rank of an elliptic curve to the behavior of its associated L-function near s = 1.]
Lassen frowned again. "Once more, could you speak like a human?"
[In simple terms: it's a mathematical Rubik's Cube with applications in cryptography and number theory.]
"Ah, mathematicians do love their cubes…" Lassen quipped.
4. Hodge Conjecture
[In algebraic geometry, it hypothesizes that certain cohomology classes are algebraic.]
[Translation for laypeople: imagine it's a riddle about geometric shapes that could change our understanding of space and dimensions.]
"Dimensions, huh? Too abstract for me" Lassen declared, waving his hand to scroll past it.
5. Navier-Stokes Equations
[8 are the fundamental equations of fluid mechanics. The problem is to demonstrate that smooth solutions exist under all circumstances.]
[Translation: understanding why water flows, why tornadoes form, and why your coffee spills on a moving train.]
"What's with the obsession with fluids?"
6. Yang-Mills and the Mass Gap
[Prove the existence of consistent particle physics theories that include a mass gap.]
[Translation: solving this could revolutionize theoretical physics and our models of fundamental particles.]
"Too much physics, not enough math," Lassen decided.
7. The Poincaré Conjecture (Solved)
[A famous conjecture about three-dimensional shapes in space, but resolved by Grigori Perelman in 2003.]
"So, this one's already done? Why is it still on the list?"
[To remind you how late you are to the party, Host.]
---
Lassen nodded slowly. "Okay… all of this seems way too complicated. But what's the reward for solving these things?"
[A million dollars for each resolved problem, not to mention global fame and academic recognition.]
Lassen smirked. "Not bad. But if I do this, everyone will want to talk to me, invite me to conferences, and ask questions. Honestly, I'd rather avoid that."
[So, you're aiming for rewards without the responsibilities? Classic.]
Lassen ignored the remark. "Alright, System, give me a list of less famous problems to start with."
---
More Accessible Problems
1. Collatz Conjecture
[Take an integer. If it's even, divide it by two. If it's odd, multiply it by three and add one. Repeat. The conjecture states that all numbers eventually reach 1.]
Lassen burst into laughter. "Wait… that's it? Sounds way too simple."
[Simple on the surface, but frustrating for those who've tried to solve it. No one has yet found a universal proof.]
2. Algorithm Optimization
[Create an algorithm capable of solving giant Sudokus or organizing complex networks more efficiently.]
3. Minor Geometry Theorem
[An unresolved problem about graphs and sets.]
---
"Collatz, that one speaks to me. Not too complicated, but cool enough to impress math enthusiasts."
[Good decision, Host.]
"Great. System, do it. Solve this kid's riddle and make it look good."
[Resolution in progress.]
Lassen sank back into his chair, grabbing a new novel from the table. "You see, this is what genius looks like: knowing how to delegate."
[Or knowing how to do nothing. A strategy that suits you perfectly.]