C'est qui qui a vraiment inventé cette méthode des moindres carrés là ? Gauss ou Legendre ?
Theory of errors

Gauss likely used the method of least squares for calculating the orbit of Ceres to minimize the impact of measurement error. The method was published first by Adrien-Marie Legendre in 1805, but Gauss claimed in Theoria motus (1809) that he had been using it since 1794 or 1795. In the history of statistics, this disagreement is called the "priority dispute over the discovery of the method of least squares". Gauss proved that the method has the lowest sampling variance within the class of linear unbiased estimators under the assumption of normally distributed errors (Gauss–Markov theorem), in the two-part paper Theoria combinationis observationum erroribus minimis obnoxiae (1823).

In the first paper he proved Gauss's inequality (a Chebyshev-type inequality) for unimodal distributions, and stated without proof another inequality for moments of the fourth order (a special case of Gauss-Winckler inequality). He derived lower and upper bounds for the variance of sample variance. In the second paper, Gauss described recursive least squares methods. His work on the theory of errors was extended in several directions by the geodesist Friedrich Robert Helmert to the Gauss-Helmert model.

Gauss also contributed to problems in probability theory that are not directly concerned with the theory of errors. One example appears as a diary note where he tried to describe the asymptotic distribution of entries in the continued fraction expansion of a random number uniformly distributed in (0,1). He derived this distribution, now known as the Gauss-Kuzmin distribution, as a by-product of the discovery of the ergodicity of the Gauss map for continued fractions. Gauss's solution is the first-ever result in the metrical theory of continued fractions.
Adrien-Marie Legendre était un mathématicien français qui a apporté de nombreuses contributions aux mathématiques. Des concepts bien connus et importants tels que les polynômes de Legendre et la transformation de Legendre portent son nom. Il est également connu pour ses contributions à la méthode des moindres carrés, et il fut le premier à la publier officiellement, bien que Carl Friedrich Gauss l'ait découverte avant lui.
### Query ###
C'est qui qui a vraiment inventé cette méthode des moindres carrés là ? Gauss ou Legendre ?

### Main Text ###
Theory of errors

Gauss likely used the method of least squares for calculating the orbit of Ceres to minimize the impact of measurement error. The method was published first by Adrien-Marie Legendre in 1805, but Gauss claimed in Theoria motus (1809) that he had been using it since 1794 or 1795. In the history of statistics, this disagreement is called the "priority dispute over the discovery of the method of least squares". Gauss proved that the method has the lowest sampling variance within the class of linear unbiased estimators under the assumption of normally distributed errors (Gauss–Markov theorem), in the two-part paper Theoria combinationis observationum erroribus minimis obnoxiae (1823).

In the first paper he proved Gauss's inequality (a Chebyshev-type inequality) for unimodal distributions, and stated without proof another inequality for moments of the fourth order (a special case of Gauss-Winckler inequality). He derived lower and upper bounds for the variance of sample variance. In the second paper, Gauss described recursive least squares methods. His work on the theory of errors was extended in several directions by the geodesist Friedrich Robert Helmert to the Gauss-Helmert model.

Gauss also contributed to problems in probability theory that are not directly concerned with the theory of errors. One example appears as a diary note where he tried to describe the asymptotic distribution of entries in the continued fraction expansion of a random number uniformly distributed in (0,1). He derived this distribution, now known as the Gauss-Kuzmin distribution, as a by-product of the discovery of the ergodicity of the Gauss map for continued fractions. Gauss's solution is the first-ever result in the metrical theory of continued fractions.

### Supplementary Text ###
Adrien-Marie Legendre était un mathématicien français qui a apporté de nombreuses contributions aux mathématiques. Des concepts bien connus et importants tels que les polynômes de Legendre et la transformation de Legendre portent son nom. Il est également connu pour ses contributions à la méthode des moindres carrés, et il fut le premier à la publier officiellement, bien que Carl Friedrich Gauss l'ait découverte avant lui.

### Draft ###

### 1. Query Parsing

"C'est qui qui a vraiment inventé cette méthode des moindres carrés là?"

→ "Who really invented this least squares method there?"

Key semantic: "vraiment inventé" = "really/truly invented" 
! Implies user suspects priority dispute, wants definitive answer

"cette méthode" = this method (definite article suggests familiarity)
Context clue: likely referring to method of least squares for data fitting

### 2. Historical Domain Mapping

Mathematics, late 18th-early 19th century
Geographic focus: Europe (France vs Germany/Scandinavia)
Key figures to triangulate:
- Carl Friedrich Gauss ●
- Adrien-Marie Legendre ●  
- Potential others ?

Timeline constraint: Method pre-1809 (Gauss publication)

### 3. Information State Assessment

◐ Partial knowledge: Legendre published 1805, Gauss claimed 1795 discovery
○ Uncertainty: Exact priority, independent vs collaborative discovery
⚠ Bias potential: Nationalistic narratives in mathematical history

### 4. Logical Triangulation

Two main scenarios:
1. Legendre independent discovery, published first ✓
2. Gauss independent discovery, delayed publication ✗

Supporting evidence:
- Legendre: official publication 1805 ●
- Gauss: claimed 1795-1796, published 1809 ●
- 4-year gap between Gauss "discovery" and publication ?

Physical constraint: Mathematical ideas can be independently discovered by multiple researchers working in same field simultaneously.

### 5. Priority Dispute Analysis

⟨H≈0.8⟩ 
Mathematical priority disputes... always messy. Gauss the methodical perfectionist, hoarding insights until comprehensive theory ready. Legendre the elegant expositor, willing to publish partial results. Classic case of the secretive genius vs the generous communicator. But was Gauss really secretive or just cautious? Four years is eternity in mathematical publishing...

⟨H≈0.2⟩
Back to evidence. Gauss proved method optimality under normal distribution assumptions (Gauss-Markov theorem). This theoretical depth suggests independent discovery rather than borrowing from Legendre.

### 6. Synthesis

∴ Both contributed significantly:
- Legendre: first publication ✓
- Gauss: theoretical foundation, earlier potential discovery ?

Key insight ! Method of least squares evolved through independent mathematical investigations rather than single "invention."

Historical consensus: Priority dispute unresolved, ongoing scholarly debate.

### 7. Response Framework

Structure:
1. Acknowledge both contributions ●
2. Explain priority dispute context ●
3. Note ongoing scholarly disagreement ●
4. Highlight each mathematician's specific contributions ●

Uncertainty markers throughout: "selon les historiens," "reste une question débattue"

Final answer: Nuanced, acknowledging both mathematicians' roles while noting historical uncertainty about exact priority.

### Answer###
La question du véritable inventeur de la méthode des moindres carrés oppose effectivement Gauss et Legendre. Bien que Legendre soit le premier à avoir officiellement publié cette méthode en 1805, Gauss prétendait l'avoir utilisée dès 1794 ou 1795, bien avant la publication de Legendre.

Cette divergence donne lieu à ce qu'on appelle aujourd'hui la "dispute de priorité concernant la découverte de la méthode des moindres carrés" dans l'histoire des statistiques. Gauss a effectivement démontré que cette méthode présente le plus faible écart type d'échantillonnage dans la classe des estimateurs linéaires non biaisés sous l'hypothèse de distributions normales des erreurs (théorème de Gauss-Markov).

Il convient de noter que cette situation n'est pas rare en histoire des mathématiques, où plusieurs chercheurs peuvent développer les mêmes concepts indépendamment, ou où la publication diffère de la découverte réelle. La contribution de chacun de ces mathématiciens à l'élaboration et à la diffusion de cette méthode reste donc une question débattue parmi les historiens des sciences.