noop_noob

A Counterexample To Fermat's Last Theorem (SCP draft)

SCP-????-A, -B, and -C

Item #: SCP-????

Object Class: Keter

Special Containment Procedures: Digital representations of SCP-????-A and -B are each to be stored in a standard flash drive and contained in a high-security vault. The two vaults are to be located at separate sites (currently Site-██ and Site-██). SCP-????-C is not to be stored, as it can be computed from SCP-????-A and -B as necessary.

In order to prevent the manifestation of additional SCP-????-X instances, personnel with non-negligible amounts of mathematical knowledge beyond high school calculus are not to be exposed to both SCP-????-A and -B.

Organizations and entities in possession of anomalous computing capabilities are to be monitored. Evidence of such organizations discovering SCP-???? is to be immediately reported to O5 command.

It has been determined that it is highly improbable that SCP-???? would be discovered non-anomalously in the near future.¹ However, developments in quantum computing technology are to be monitored, and any attempt to use such technology to discover SCP-???? is to impeded.²

Description: SCP-????-A, SCP-????-B, and SCP-????-C ("a", "b", and "c", respectively) are positive integers. The approximate values of a, b, and c are approximately $3.57 \times 10^{18}$, $4.19 \times 10^{18}$, and $4.25 \times 10^{18}$, respectively. They were discovered by an exhaustive search of integers a and b up to $10^{20}$³ using SCP-155.⁴ The main anomalous property of a, b, and c is the fact that $a^{11} + b^{11} = c^{11}$. This directly contradicts Fermat's Last Theorem.⁵

SCP-????-X is [REDACTED]. It is hypothesized that when a sapient entity that has knowledge of SCP-XXXX-A, -B, and -C, completely understands the proof of Fermat's Last theorem,⁶ and has an "intuitive understanding" of the contradiction involved, the entity becomes an instance of SCP-????-X. There has been only one known SCP-????-X entity manifested so far, designated SCP-????-X-1. See Incident I-????.

Incident I-????:

+ Clearance ????/3 required.

On June 9th, 2020, Dr. Miller and Dr. Davis, both of whom had doctoral degrees in mathematics, were assigned to perform research on SCP-????. Incident I-???? occurred on July 14th, 2020.

CCTV recording on July 2nd, 2020 (12 days before Incident I-????)
Dr. Miller and Dr. Davis are sitting next to each other in an office. A large amount of paper with scribbles is scattered around the desk. The two are discussing the proof with each other.
Dr. Miller: "I've been thinking. The fact that ???? exists means that if the proof⁷ is correct, and we've pretty much convinced ourselves that it is, then mathematics is inconsistent and logic is broken. Doesn't that mean any attempt to logically understand the world is doomed to fail?"
Dr. Davis: "Maybe, but I don't think that the universe, even with all these skips, can be that illogical. What if the proof is correct, and math is consistent, but what ???? does is mess up any computers that process it? The problem is that manually checking the numbers is a nightmare, since the numbers are so big."
Dr. Miller: "You know what? I'm gonna do it."
Dr. Davis: "Are you crazy?"

From July 2nd, 2020 until the occurrence of incident I-???? on July 14th, 2020, Dr. Miller obsessively spent her time verifying that a¹¹ + b¹¹ = c¹¹ with pen and paper, and using a computer to verify that each step was correct. Dr. Davis did not interfere with this computation.

CCTV recording on July 14th, 2020 (date of Incident I-????)
Dr. Miller: "Yes!"
Dr. Miller is seen standing up with her fists raised. Dr. Davis, who was sitting nearby, turned to look at her.
Dr. Davis: "You finally finished? Did ???? actually affect only computers like I thought?"
Dr. Miller: "Nope. Math is actually inconsistent. Logic does, in fact, not function properly in this universe. But right now, I'm really tired and I think I need to sleep."
A bed spontaneously manifested in the empty space in the office a few centimeters above the floor, immediately falling down with a loud noise. Dr. Miller and Dr. Davis are momentarily stunned.
Dr. Davis: "What… was that?"
SCP-????-X-1 (formerly Dr. Miller): "Maybe this inconsistency in math is more dangerous than we expected."
Dr. Davis: "What do you mean?"
SCP-????-X-1: "There's this idea, called the Mathematical Universe Hypothesis. It's the idea that the universe is actually a mathematical structure."
Dr. Davis: "I've heard of it, but it's… ugh. Sure. For the sake of the argument, let's say that idea is true. How is that relevant to, uhh, a magically appearing bed?"
SCP-????-X-1: "The universe is math. And math, according to our skip, is inconsistent. And inconsistent math, by ex falso,⁸ proves that every statement is true. That means every answer is a correct response to every question. Therefore, the universe accepts any answer for the question 'What will happen next?'"
Dr. Davis: "So you're saying that absolutely anything can happen at any time in this broken universe?"
SCP-????-X-1: "Yes. Except the universe hasn't 'discovered' its own inconsistency until I did, by tracing out the steps to get to that inconsistency. Maybe a sentient being, and not a computer, has to be the one who traces out these steps. In any case, it seems like I can somehow subconsciously coax the universe into accepting whatever I want to happen next. And I wanted to sleep, hence the bed."
Dr. Davis: "That means you're now a reality bender?"
SCP-????-X-1: "Yup. Let me try something."
SCP-????-X-1 holds out its right hand, palm face up. A ball of flame, with diameter approximately 15 cm, manifests approximately 5 cm above the hand. Dr. Davis flinches and hits a glass of water that was on his desk, causing the glass to fall to the floor and break. SCP-????-X-1 turns towards Dr. Davis, and accidentally launches the ball of fire towards him. He screams incoherently out of pain.
SCP-????-X-1: "No! Stop! How do I get rid of this burning!?"
SCP-????-X-1 makes complicated gestures with its hands towards the burning Dr. Davis, and the fire disappears along with Dr. Davis.
SCP-????-X-1: "Wait what? Where are you? Dr. Davis? Did I kill him? Wait. I can fix this."
An object that appears to be a corpse of Dr. Davis manifests on the floor. SCP-????-X-1 inspected the object, then sat down on the floor and started screaming. The building started shaking. The floor started to crack, with the fracture lines emanating from where SCP-????-X-1 sat. At this point, the video feed abruptly terminated due to electrical failure.

Approximately two minutes after the video feed terminated, the on-site armed force arrived at the room. Due to the risk of the structural failure of the building and the subsequent potential loss of life, SCP-????-X-1 was terminated via gunshot.

Later investigation found that the object that appeared to be the corpse of Dr. Davis consists entirely of fat, with pigments on its surface that make its external appearance resemble that of Dr. Davis. It is hypothesized that SCP-????-X-1 attempted to revive Dr. Davis, but failed to do so due to its lack of knowledge in biology.

Old version of the ending below:

+ Old version of the ending

On June 9th, 2020, Dr. Miller and Dr. Davis, both of whom had doctoral degrees in mathematics, were assigned to perform research on SCP-????. Incident I-???? occurred on July 14th, 2020.

CCTV recording on July 2nd, 2020 (12 days before Incident I-????)
Dr. Miller and Dr. Davis are sitting next to each other in an office. A large amount of paper with scribbles is scattered around the desk. The two are discussing the proof with each other.
Dr. Miller: "I've been thinking. The fact that ???? exists means that if the proof⁹ is correct, and we've pretty much convinced ourselves that it is, then by ex falso,¹⁰ we can prove from first principles that every statement is simultaneously true and false. Doesn't that mean any attempt to logically understand the world is doomed to fail?"
Dr. Davis: "Maybe, but I don't think that the universe, even with all these skips, can be that illogical. What if the proof is correct, and math is consistent, but what ???? does is mess up any computers that process it? The problem is that manually checking the numbers is a nightmare, since the numbers are so big."
Dr. Miller: "You know what? I'm gonna do it."
Dr. Davis: "Are you crazy?"

From July 2nd, 2020 until the occurrence of incident I-???? on July 14th, 2020, Dr. Miller obsessively spent her time verifying that a¹¹ + b¹¹ = c¹¹ with pen and paper, and using a computer to verify that each step was correct.¹¹ Dr. Davis did not interfere with this computation.

CCTV recording on July 14th, 2020 (date of Incident I-????)
Dr. Miller: "Yes!"
Dr. Miller is seen standing up with her fists raised. Dr. Davis, who was sitting nearby, turned to look at her.
Dr. Davis: "You finally finished? Did ???? actually affect only computers like I thought?"
Dr. Miller: "No! Math is inconsistent! Nothing makes sense! AHAHAHAHA…"
Dr. Miller appears to enter a manic state. From this point towards until the end of the recording, Dr. Miller continues laughing, occasionally punctuated by speech.
Dr. Davis: "Uh… are you OK? You're freaking me out."
Dr. Miller: "Yes! I am okay. Everything makes sense now. Or rather, nothing makes sense! AHAHAHAHA…"
Dr. Davis: "Can you please calm down? What's going on?"
Dr. Miller: "From Fermat's theorem, these two numbers are not equal, and yet there are equal! From that, it becomes easy to prove that every number is equal to zero! So everything is nothing! AHAHAHAHA…"
The desks, chairs, and all other furniture in the room instantaneously disappear. Dr. Davis fell to the floor due to his chair disappearing. He stands up and runs out of the room, stumbling along the way.
SCP-????-X-1 (formerly Dr. Miller): "From everything to nothing, and from nothing to everything! AHAHAHAHA…"
Several polyhedra manifest midair. They are seemingly unaffected by gravity. SCP-????-X-1 appears to be able to manipulate them remotely with various hand gestures.
Several impossible geometric shapes similarly manifest, including a triangle whose angles don't add to 180 degrees, a pair of straight lines that intersect each other twice, and a regular polyhedron with sixteen faces.
The on-site security team barges into the room. SCP-????-X-1 gestures towards them with one of its hands, and the security team disappears. SCP-????-X-1, still laughing, starts to levitate and ascend upwards. The ceiling of the room disappears, along with other rooms above it.
At this point, the video feed was abruptly terminated.

The time where the video feed was terminated coincided with the activation of the on-site nuclear device. SCP-????-X-1 was determined to be neutralized. It is hypothesized that SCP-????-X-1, with its reality-bending capabilities, was capable of surviving a nuclear explosion. However, the neutralization occurred in a shorter time than its reaction time, and fortunately, SCP-????-X-1 did not take preemptive measures against the explosion.

Author's Notes

(Not part of the SCP)

+ Author's Notes

Why n=11 in Fermat's Last Theorem? It's the first special case of the theorem that wasn't proven before the entire theorem was proven.

Similar SCPs that I hope aren't too similar: SCP-4079 "Saving Archimedes", SCP-5772 "A Counterexample", SCP-1313 "Solve For Bear".

I used this article as reference for how one would react to accidentally killing someone.

Python (SCP idea)

There's a computer with a python interpreter installed and it makes python programs have snakey-things.

Midas's Golden Statue (Abandoned SCP draft)

Item #: SCP-XXXX

Object Class: Safe

Special Containment Procedures: SCP-XXXX shall be contained in a standard containment vault. It shall be monitored with a closed-circuit camera installed within the vault.

Due to the high monetary value of SCP-XXXX and items affected by it, transportation of SCP-XXXX out of its vault is forbidden unless approved by at least two (2) personnel of clearance level 4 or higher. All testing of SCP-XXXX must be approved by at least one (1) such personnel, and shall be held within its containment vault. All items affected by SCP-XXXX is to be submitted to the Foundation Treasury.

Since Incident XXXX-A, testing the effect of SCP-XXXX on humans has been suspended.

Description: SCP-XXXX appears to be a golden statue of a woman on top of and attached to a base made of marble. The text "Midas, Giver of Gold" is inscribed on the marble base.

When the surface of SCP-XXXX is scraped or otherwise damaged, resulting in some amount of gold being removed from the statue¹², additional gold is generated to replace the missing gold. Gold removed from the statue this way has been identified to be non-anomalous pure gold.¹³

The primary anomalous effect of SCP-XXXX comes into contact with an object, and continuously remains contact with it for at least 3 seconds. If that object is not a living human¹⁴, then portions of that object within 10 centimeters of the point of contact will gradually turn into pure gold within 15 minutes.¹⁵

TODO: effect on humans -> SCP-XXXX-1

Incident XXXX-A: TODO discover inside statue

A proposal to attempt to euthanize SCP-XXXX is pending approval from the ethics committee.

Addendum: TODO (disapproved proposal: source of income)

Footnotes

1. Logically deducing it is believed to be impossible, and a brute-force search (with a search space consisting of approximately $\left( 3.57 \times 10^{18} \right)\left(4.19 \times 10^{18} \right) \approx 1.50 \times 10^{37}$ possibilities) using conventional computers is impractical for the foreseeable future.

2. Using Grover's algorithm, a well-known non-anomalous quantum algorithm, a brute-force search over $n$ possibilities could be performed using computation in the order of $\sqrt{n}$ steps. That is, to discover SCP-????, approximately $\sqrt{1.50 \times 10^{45}} \approx 3.87 \times 10^{18}$ computation steps are required. This is potentially feasible, given sufficient amounts of resources.

3. The search space size is $\left(10^{20}\right)^2 = 10^{40}$

4. This was done as part of testing the amount of computation that SCP-155 could be practically used to perform.

5. Fermat's Last Theorem states that there are no positive integers x, y, z, and n, such that n ≥ 3 and $x^n + y^n = z^n$.

6. The original proof was published by Andrew Wiles in 1993-1994 and is believed to be non-anomalous. It is 129 pages long, although subsequent versions of the proof are shorter. However, it is unknown how much of the prior work is required to be understood for one to become an instance of SCP-????-X.

7. This is assumed to refer to the proof of Fermat's Last Theorem.

8. Ex falso quodlibet, also known as the principle of explosion, is a logical theorem stating that we can prove any mathematical proposition from a self-contradictory premise.

9. This is assumed to refer to the proof of Fermat's Last Theorem.

10. Ex falso quodlibet, also known as the principle of explosion, is a logical theorem stating that we can prove anything from a self-contradictory premise.

11. Using repeating squaring to compute the exponentiations, 15 multiplications were required.

12. This ease of being damaged is consistent with the behavior of pure gold, which is softer than gold alloys used for jewelry.

13. Testing found its purity to be at least 999.999999 parts of gold per thousand (nine nines) — indistinguishable from 100% pure gold using current Foundation equipment. All other gold produced by SCP-XXXX is similarly pure and non-anomalous. Note that the purest gold that has been manufactured non-anomalously so far is 999.999 parts of gold per thousand (six nines).

14. i.e., either it is not an organism, it is a non-human organism, or it is a dead human

15. Ultrasounds of the marble base of SCP-XXXX has found that it appears to contain a hemisphere of gold with a radius of 10 centimeters, centered at the "foot" of the statue.