CG: n

CT: A conjecture is a mathematical statement that has not yet been rigorously proved. Conjectures arise when one notices a pattern that holds true for many cases. However, just because a pattern holds true for many cases does not mean that the pattern will hold true for all cases. Conjectures must be proved for the mathematical observation to be fully accepted. When a conjecture is rigorously proved, it becomes a theorem.

A conjecture is an important step in problem solving; it is not just a tool for professional mathematicians. In everyday problem solving, it is very rare that a problem’s solution is immediately apparent. Instead, the problem solving process involves analyzing the problem structure, examining cases, developing a conjecture about the solution, and then confirming that conjecture through proof.

S: Brilliant (last access: January 25 2026)

N: 1. late 14c., “interpretation of signs, dreams, and omens,” also “a supposing, a surmising,” from Old French conjecture “surmise, guess,” or directly from Latin coniectura “conclusion, interpretation, guess, inference,” literally “a casting together (of facts, etc.),” from coniectus, past participle of conicere “to throw together,” from assimilated form of com “together” + iacere “to throw” (from PIE root *ye- “to throw, impel”).

Sense of “an unverified supposition” is from 1520s; that of “act of forming of opinion without proof” is from 1530s.

Early 15c., “infer, predict, form (an opinion or notion) upon probabilities or slight evidence,” from conjecture (n.) or from verbs in Medieval Latin and Old French. Middle English had also the parallel forms conjecte (n.), conjecten (v.). Related: Conjectured; conjecturing.

2. A proposition (as in mathematics) before it has been proved or disproved.

Mathematics: conjecture.

3. Some of the most known conjectures are:

• Hodge Conjecture: The answer to this conjecture determines how much of the topology of the solution set of a system of algebraic equations can be defined in terms of further algebraic equations. The Hodge conjecture is known in certain special cases, e.g., when the solution set has dimension less than four. But in dimension four it is unknown.
• Birch and Swinnerton-Dyer Conjecture: Supported by much experimental evidence, this conjecture relates the number of points on an elliptic curve mod p to the rank of the group of rational points. Elliptic curves, defined by cubic equations in two variables, are fundamental mathematical objects that arise in many areas: Wiles’ proof of the Fermat Conjecture, factorization of numbers into primes, and cryptography, to name three.
• Poincaré Conjecture: In 1904 the French mathematician Henri Poincaré asked if the three dimensional sphere is characterized as the unique simply connected three manifold. This question, the Poincaré conjecture, was a special case of Thurston’s geometrization conjecture. Perelman’s proof tells us that every three manifold is built from a set of standard pieces, each with one of eight well-understood geometries.

4. The term “conjecture” should not be confused with “theorem”:

• conjecture: A conjecture is a conclusion that is based on information that is not certain or complete.
• theorem: statement in mathematics or logic that can be proved to be true by reasoning.

5. Collocations:

• pure
• about – as to
• a matter for conjecture – open to conjecture.

6. Cultural interrelation: We can mention a documentary and a movie, respectively.

• Horizon – Fermat’s Last Theorem (1996). Documentary about a mathematics conjecture of 1637 which was demonstrated 350 years later.
• In contemporary cinema, the film The Man Who Knew Infinity (2015), based on real-life events, portrays the mathematician Srinivasa Ramanujan and the various conjectures he presented.

 F: 1. MW (last access: 24 January 2026); Etymonline (last access: 24 January 2026). 2. MW (last access: 25 January 2026); TERMIUM PLUS (last access: 25 January 2026): 3. Claymath – https://www.claymath.org/millennium/hodge-conjecture/, https://www.claymath.org/millennium/birch-and-swinnerton-dyer-conjecture/, https://www.claymath.org/millennium/poincare-conjecture/ (last access: 25 January 2026). 4. CED – https://www.collinsdictionary.com/us/dictionary/english/conjecture, https://www.collinsdictionary.com/us/dictionary/english/theorem (last access: 25 January 2026).  5. OZDIC (last access: 24 January 2026). 5. IMDb – https://www.imdb.com/title/tt1224922/, https://www.imdb.com/title/tt0787524/ (last access: 24 January 2026).

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CR: abduction