**John Farey** was an Engish geologist, noted as a mathematician for the _Farey sequence _which is a listing of the rationals.

- The reason we have included him is that he made one mathematical observation and, from this, the Farey series of fractions has been named.
- We shall discuss below Farey's contribution to mathematics and also look at others who contributed to Farey series.
- Farey attended a local school in Woburn until he was sixteen years of age when he went to a school in Halifax, Yorkshire, where he studied mathematics, drawing and surveying.
- Francis, the fifth Duke of Bedford had extensive estates in Bedfordshire and, in 1792, he appointed Farey as the land steward for his Woburn estates.
- Farey held this post for ten years and it was during this time that he was able to gain expertise in geology.
- Farey had already become interested in soils and rocks through carrying out his duties as land steward and he now took the opportunity to learn all that he could from Smith about stratification.
- There are two aspects to Farey's contributions to science.
- The second aspect of Farey's work was his scientific writings.
- Farey published around sixty scientific articles between 1804 and 1824, most in Rees's Encyclopaedia, the Monthly Magazine and the Philosophical Magazine.
- Farey's article which is relevant to our history of mathematics archive was also published in the Philosophical Magazine and appeared in 1816.
- In the first paragraph Farey says that he noted the "curious property" while examining the tables of Complete decimal quotients produced by Henry Goodwin.
- In the second paragraph he defines the Farey series and states the "curious property".
- The Farey series (really a sequence) is defined as follows.
- In the third paragraph of his article Farey gives an example.
- One mathematical reader (at least of a French translation) was Cauchy, and he gave the necessary proof in his Exercices de mathématiques which was published in the same year as Farey's article.
- Farey was not the first to notice the property.
- The quotation we gave above shows that Farey explicitly states he has no proof.
- Farey is immortal because he failed to understand a theorem which Haros had proved perfectly fourteen years before ...
- The newer editions of the Dictionary of National Biography do contain a discussion of Farey sequences.

Born 24 September 1766, Woburn, Bedfordshire, England. Died 6 January 1826, London, England.

View full biography at MacTutor

Origin England

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive