# Gabriel Cramer

> Genevan mathematician (1704-1752)

**Wikidata**: [Q122331](https://www.wikidata.org/wiki/Q122331)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Gabriel_Cramer)  
**Source**: https://4ort.xyz/entity/gabriel-cramer

## Summary
Gabriel Cramer was a Genevan mathematician and physicist who lived from 1704 to 1752. He is best known for his foundational contributions to algebra and geometry, most notably formulating Cramer's rule for solving systems of linear equations, as well as Cramer's paradox and Cramer-Castillon's problem. He spent his career as a university teacher at the University of Geneva and was recognized as a Fellow of the Royal Society.

## Biography
- **Born:** July 31, 1704
- **Died:** January 4, 1752
- **Nationality:** Republic of Geneva (former country in Europe, inception 1534)
- **Education:** University of Geneva
- **Known for:** Formulating Cramer's rule, Cramer's paradox, and Cramer-Castillon's problem in mathematics
- **Employer(s):** University of Geneva
- **Field(s):** Mathematics and Physics

## Contributions
Gabriel Cramer made significant and enduring contributions to the fields of mathematics and physics. His most prominent works, which are explicitly named in the record, include:
- **Cramer's rule:** A widely used theorem in linear algebra for explicitly solving systems of linear equations using determinants. This is his most recognized work, noted by its significant presence across 46 sitelinks in the provided data.
- **Cramer's paradox:** A complex observation in geometry stating that the number of points of intersection of two planar higher-order curves can be greater than the number of arbitrary points usually needed to define one such curve.
- **Cramer-Castillon's problem:** A noted geometric problem in mathematics, historically associated with both Cramer and Castillon.

## FAQs

### What was Gabriel Cramer's primary field of study?
Gabriel Cramer worked in the academic fields of mathematics and physics. He functioned professionally as a mathematician, physicist, and university teacher.

### Where did Gabriel Cramer work and study?
Gabriel Cramer was educated at, and later employed by, the University of Geneva. This institution is a public research university located in Geneva, Switzerland.

### What academic societies was Gabriel Cramer affiliated with?
He was a member of several prominent scientific academies of his time. He was elected as a Fellow of the Royal Society in London. Additionally, his professional affiliations included the Royal Prussian Academy of Sciences (founded 1700) and the Academy of Sciences of the Institute of Bologna (founded 1714).

### What are Cramer's most famous mathematical discoveries?
He is most famous for Cramer's rule, a theorem used for solving linear equations. He is also known for Cramer's paradox regarding the intersection of higher-order curves, and Cramer-Castillon's problem in geometry.

## Why They Matter
Gabriel Cramer's work has had a lasting impact on the field of mathematics, particularly in algebra and geometry. Cramer's rule remains a fundamental theorem taught in linear algebra courses worldwide, providing a concrete method for solving systems of linear equations via determinants. His identification of Cramer's paradox contributed significantly to the mathematical understanding of algebraic curves and geometric intersections, pushing forward mathematical logic of the 18th century. Furthermore, his association with major European scientific bodies, like the Royal Society and the Prussian Academy of Sciences, underscores his role as a key intellectual figure of his era who helped shape mathematical foundations that are still relied upon today.

## Notable For
- Formulating **Cramer's rule**, a standard theorem for solving systems of linear equations.
- Defining **Cramer's paradox**, addressing the intersection points of planar higher-order curves.
- Posing **Cramer-Castillon's problem** in the field of geometry.
- Serving as a **university teacher** at the University of Geneva.
- Being elected as a **Fellow of the Royal Society** (FRS).
- Membership in the **Academy of Sciences of the Institute of Bologna**.
- Membership in the **Royal Prussian Academy of Sciences**.
- Contributing to the foundational development of **mathematics** and **physics**.

## Body

### Early Life and Nationality
Gabriel Cramer was born on July 31, 1704, in the Republic of Geneva, a former country in Europe that was established in 1534. 

### Academic Affiliations and Career
Cramer spent his academic career associated with the University of Geneva, a public research university in Geneva, Switzerland, which was founded in 1559. He was both educated at this institution and employed there as a university teacher. 

His academic standing allowed him to engage with the broader European scientific community. He was recognized by several elite scientific organizations:
- **The Royal Society:** Elected as a Fellow of the Royal Society, a prestigious English learned society for science founded on November 1, 1660.
- **Academy of Sciences of the Institute of Bologna:** An academy in Italy (country: Q38) founded in 1714.
- **Royal Prussian Academy of Sciences:** An academy of sciences founded on July 11, 1700, in Germany (country: Q183).

### Key Mathematical Contributions
Cramer's legacy is built upon several distinct mathematical concepts that bear his name:
- **Cramer's rule:** His most famous contribution, this theorem provides an explicit formula for the solution of a system of linear equations with as many equations as unknowns, utilizing determinants. It remains a vital tool in modern linear algebra.
- **Cramer's paradox:** This concept addresses a counterintuitive property of algebraic curves. The paradox states that the number of points of intersection of two planar higher-order curves can be greater than the number of arbitrary points usually needed to define one such curve. 
- **Cramer-Castillon's problem:** A recognized geometric problem named after Cramer and Castillon, highlighting his work in advanced geometric constructs.

### Fields of Work and Recognition
Throughout his life, Cramer was active in multiple academic disciplines, specifically categorized under mathematics (the field of study concerning numbers, quantities, space, and symbolic structures) and physics (the study of matter and its motion, along with related concepts such as energy and force). His professional identifiers and catalog records extensively document these fields. He passed away on January 4, 1752.

### Structured Identifiers and Records
Cramer's historical footprint is preserved across numerous international databases and libraries, indicated by his extensive structured properties:
- **Library and Authority Identifiers:** ISNI (0000000081309325), VIAF (51966202), GND (11670912X), Library of Congress (n86864963), BNF (15006804w), SUDOC (101299761), CiNii (DA0888809X), NLA (578), and many others across regional and global catalog systems.
- **Academic and Biographical Databases:** He is indexed in systems with identifiers such as OL2284476A (Open Library), 025878 (Mathematics Genealogy Project), /m/02hrzh (Freebase), and various international biographical dictionaries.
- **Digital Archives:** Associated with the Republic of Geneva citizenship records and specific digital entity IDs like `person/3b41709d-706f-44d9-a131-5293704809c1`. 
- **Media:** A portrait or related image is cataloged under "Gabriel Cramer.jpg".

## References

1. MacTutor History of Mathematics archive
2. BnF authorities
3. Integrated Authority File
4. Czech National Authority Database
5. Historical Dictionary of Switzerland
6. International Standard Name Identifier
7. Virtual International Authority File
8. CiNii Research
9. Complete Dictionary of Scientific Biography
10. [Source](https://www.bbaw.de/die-akademie/akademie-historische-aspekte/mitglieder-historisch/historisches-mitglied-gabriel-cramer-509)
11. SNAC
12. Gran Enciclopèdia Catalana
13. Proleksis Encyclopedia
14. Croatian Encyclopedia
15. Freebase Data Dumps. 2013
16. [Source](https://books.google.cat/books?id=3lRIygAACAAJ)
17. [Source](http://digitale.beic.it/primo_library/libweb/action/search.do?fn=search&vid=BEIC&vl%283134987UI0%29=creator&vl%28freeText0%29=Cramer%20Gabriel)