Marie-Sophie Germain.

Item #: SCP-4079

Object Class: Euclid

Special Containment Procedures: All journals of mathematics and philosophy are to be screened by automated proof checking software to find instances of SCP-4079, focusing on articles regarding long-standing conjectures or disputed results, and articles that contradict previously established results. All instances of SCP-4079 found are to be censored and the corresponding papers retracted.

A document detailing the logic steps involved in SCP-4079 is to be stored in a High-Value Item Vault at Storage Site-1313. To reduce accidental exposure to potential memetic hazards, the document is to use symbolic logic represented using reverse Polish notation to obfuscate readability, and no written descriptions or explanations. An additional copy of this information is in the possession of the Foundation's Memetics Department, as it is an essential component of Fae-class suggestibility agents.

The original proof of Fermat's Last Theorem by Sophie Germain has been suppressed from the public record and replaced by the sanitized version released by herself later; no further action is required in this regard. The original documents regarding this proof and Germain's discovery of SCP-4079 are stored in a different High-Value Item Vault at Storage Site-33; this includes the letters written by Germain to prominent public figures during this period.

Description: SCP-4079 refers to a proof method or syllogism, referred to as modus adductus, discovered by French mathematician Marie-Sophie Germain in the year 1804 during the process of devising a proof for Fermat's Last Theorem. Modus adductus, like similar methods such as modus ponens or modus tollens, consists of a series of steps to show that a statement is a consequence of other previously accepted statements. However, SCP-4079's anomalous effect lies in the fact that any statement deemed as a consequence of another via the use of modus adductus is accepted as true by anyone capable of understanding the logical steps involved, regardless of the actual relation between the two statements.

Notes on the SCP-4079 syllogism

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A syllogism is a logical argument that asserts the truth of a statement, by deduction, from other statements or premises accepted as true, either absolutely or conditionally. A syllogism usually takes the form of a list of premises, interspersed with the usage of inference rules (which show certain statements to be consequence of other, previously accepted ones), in order to arrive at the desired conclusion; for instance, the modus ponens syllogism has the following schema:

Premise 1: A is true.

Premise 2: If A is true, then B is also true.

Conclusion: B is also true.

The following is a correct application of this syllogism:

Premise 1: Cartman is a calico cat.

Premise 2: All calico cats are female.

Conclusion: Cartman is female.

While the premises may have a disputable level of truth1, if we accept them as true (a cat being a calico, and calicos being female) then by the principles of deductive reasoning the conclusion must also be accepted as true (i.e. we understand that this specific cat is female).

Not all forms of deductive reasoning are true, however. Common examples of faulty logical arguments include the following:

confusing observable correlation with logical causation,

swapping antecedent and consequent, i.e. taking "if A then B" as a premise and then assuming that, since B is true A must be true as well,

usage of contradictory premises,

using the same word with different meanings to arrive to the desired conclusion.

The first two types of fallacies from the above list may be observed in the following example:

Premise 1: Reality bending entities are able to alter the documentation of SCP objects.

Premise 2: Doctor Fred has altered the documentation of SCP-7160.

Conclusion: Doctor Fred is a reality bending entity.

While both premises are true, it does not follow that a person who is able to make edits to the SCP Foundation database is a reality bending entity. An extreme example of this is the reductio ad hitlerum argument, where a statement is deemed as false, harmful or otherwise dismissed by association with a person, entity, organization, etc., which is deemed nocive in some way.

SCP-4079, as verified by proof checking software and Foundation AICs, is effectively a fallacy similar to the aforementioned ones. However, when interpreted by the human brain, it is understood as a compelling, valid argument to derive the conclusion statement from the premises, without regard as to whether there is any actual relation between them. Thus, a reasoning like the one quoted below would be perceived as perfectly logical by somebody affected by SCP-4079:

Premise 1: Cats are common household pets.

Premise 2: Fennec foxes have been raised as household pets in the past.

Premise 3: [MEMETIC HAZARD REDACTED]

Conclusion: Cats and fennec foxes are the same species of animal.

Of note is that, while SCP-4079 is seen as a correct syllogism, it does not enforce belief in the conclusive statement. Thus, if the latter contradicts personal belief or convictions, often the affected look for errors in the premises taken, or other formal or functional mistakes to justify their cognitive dissonance. However, research by the Foundation shows that if the person exposed to SCP-4079 has no strong convictions on the discussed topic, or is otherwise open to the idea of themselves being in the wrong stance, correct usage of SCP-4079 combined with usual argumentation and persuasion techniques results in a belief change in 75%-85% of studied cases.

Addendum 4079-1: Historical Notes

The first known instance of SCP-4079 was found in a letter written by Germain to fellow mathematician Karl Friedrich Gauss in 1804 detailing a proof of Fermat's Last Theorem. Gauss' reply2 stated that, while he could not find any errors in Germain's proof, an intermediate step seemed to contradict a result proved by himself two years earlier. Following correspondence3 consisted of joint efforts by Germain and Gauss to find a mistake in either Germain's proof or Gauss' work, with no results. Eventually, Germain managed to isolate the problematic section of the proof and deduced the nature of SCP-4079; this was later corroborated by experimentation on Germain's part, by sending purposefully incorrect proofs (usually of nonsensical statements) to several prominent mathematicians such as Joseph-Louis Lagrange and Adrien-Marie Legendre, under various pseudonyms. While a few of the replies received pointed out that there might be an error in her work, none of them pointed to the SCP-4079 proof as faulty, instead citing false assumptions or mentioning potential new theories to explain the unexpected results.

Germain's notes contain extensive studies on SCP-4079 and its effect on human reasoning, along with philosophical notes regarding truth in mathematics and human knowledge; in these notes it is explicitly stated that understanding the logical steps involved is necessary in order for SCP-4079 to take effect. The framework set by Germain's work was a fundamental part of the early study of memetics, and in particular SCP-4079 is registered as the first recognized and studied anomalous meme in the Foundation's record.

Excerpts from Sophie Germain's private notes regarding SCP-4079

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The following notes have been extracted from private notebooks, diaries and notes written on the margins of correspondence drafted or received by Sophie Germain between 1804 and 1809. They have been translated from the original French; the originals are archived as Documents 4079-A109 through 4079-A147.

Seeking out the errors in my work on Fermat's problem has been exceedingly difficult. While it may be just personal pride, I just cannot look at my writings and see anything less than a sound argument. The great Fermat's unfinished work, concluded by the pen of Sophie Germain! But at the same time, holding on to that thought is denying Gauss' expertise and skill. I have reproduced his proof step-by-step, several times, and I haven't found anything remotely resembling a mistake; the error must be in my work, and, although this is extremely frustrating, I must discover it.

Speaking of which, Monsieur Gauss has been extremely helpful in this endeavor. He has taken time off his extremely busy schedule to rework and rewrite the weaker parts of my writing; him doing this for the amateurish nobody Monsieur LeBlanc4 was completely unthinkable to me until now.

Monsieur Gauss has pointed that the fifth section implies that for any odd prime, subtracting 1 and halving must result in another prime. The error must be there. But where?

[on a heavily edited copy of her original proof] … and thus 2p+1 is also prime if 2p+1 is prime there is an even prime number greater than 1012. (Truly a compelling argument, I almost believe it…)

Neither my premises nor my deductions themselves are faulty. It is the way the proof itself is written. I sent a proof of the existence of a number that is both a prime and a square to Monsieur Legendre and he could not find any errors. How can we know what is true, then?

Thankfully, modus adductus is only convincing to people with mathematical inclination. I fear what a tyrant would do with this otherwise. But I couldn't get a single piece of bread for free with this, so I am relieved.

[on the margin of a letter from Joseph-Louis Lagrange] Managed to convince Monsieur Lagrange of error in Mechanics work. Hopefully not leading him to review all his work for corrections or otherwise wasting time…

I fear for Monsieur Gauss. Napoleon might have respect for men of science, but why would that stop a common soldier from thinking with his sword instead of his brain?

Maybe I can do something. Monsieur Gauss has been the Archimedes of this time in life, but I can prevent him from being Archimedes in death as well.

[on the back of a letter sent from General Pernetti, a family friend] He's safe. I've been found out, but it's worth it. Maybe it is time for Monsieur LeBlanc to retire.

Turns out most of the proof was correct in the end. I will have to write to Monsieur Gauss about this. And I will sign as Mademoiselle Germain, this time.

Most of Germain's notes regarding SCP-4079 were never published, and her proof of Fermat's Last Theorem was retracted and replaced by a weaker version in a letter to Gauss from 1809. There is only one known instance of public SCP-4079 usage by Germain besides the aforementioned experimental letters, in which Germain wrote a letter intended to be read by Napoleon Bonaparte regarding the occupation of Braunschweig5 by French forces. In this letter, written in colloquial language but following the SCP-4079 structure, Germain stated the importance of protecting men of science and arts, and pleaded for Napoleon to avoid needless killing in the invasion. It is suspected that Napoleon's amateur interest in mathematics6 was enough for him to be susceptible to SCP-4079; however, it is unknown if the letter was actually read by him. It is known that Napoleon's policies regarding occupation of cities had a change around this period and that a squad of French soldiers was tasked with checking on Gauss' well-being during the occupation, facts that suggest that Napoleon did indeed receive the letter. However, the fact that General Pernetti, the leader of the squad, was known as a family friend of Sophie Germain allows for reasonable doubt to be held.

Addendum 4079-2: Relevant data obtained from the Alexandria Agreements

After signing the Alexandria Agreements, a treaty between the Foundation and the Global Occult Coalition in order to share relevant historical data about anomalies, several pamphlets and propaganda posters dated from 1941 to 1943 were delivered to the Foundation for analysis and deemed to contain a form of SCP-4079, as an attempt to increase adherence and loyalty to the Third Reich. These posters were traced to German mathematician Oswald Teichmüller, known for its allegiance to the NSDAP.

As predicted by Germain, this propaganda had a very low success rate. However, it has prompted investigation in a joint Foundation-GOC effort to look for other instances of public usage of SCP-4079-like propaganda agents. So far, the following evidence has been found:

Internal memorandums (dated 1961-1967) declassified by the United States' Central Intelligence Agency detailing the support given to the "New Math" project to completely overhaul the mathematics curriculum in elementary schools, in order to introduce the basics of logic, set theory and other abstract areas of mathematics at an early age; these documents mention plans to implement a unspecified "propaganda construct", presumed to be SCP-4079. These plans appear to have been abandoned after the failure of the New Math project.

Several documents from the USSR's GRU Division "P" regarding proposals to use SCP-4079-like constructs as part of larger-scale projects. Most of them were denied due to the (at the time) recent discovery of better memetic agents for the desired purposes.

Abnormalities detected in the mathematics curriculum of China, flagged as possibly related to SCP-4079 by automated statistical analysis. However, no actual evidence of SCP-4079 usage has been found.

Containment procedures for SCP-4079 are currently undergoing revision to take into account the detection and suppression of further attempts to use SCP-4079 by civilian governments.

Footnotes

1. While most calico cats are female, genetic ailments such as Klinefelter syndrome may result in cats with a Y chromosome exhibiting calico patterns.

2. The original reply has been removed from the public record and replaced by a forgery.

3. Also censored.

4. Pseudonym often used by Germain to avoid prejudice and dismissal as a woman.

5. Prussian town where Gauss lived. It is known that Germain was familiar with the story of Archimedes, who was killed in the siege of Syracuse by the invading forces, and feared for Gauss' life.

6. There is at least one mathematical result attributed to Napoleon (in the field of Euclidean geometry), although this claim is often disputed.