The phrase to plough a lonely, or solitary, furrow, or to plough one’s own furrow, means to carry on without help, support or companionship (to plough a furrow meaning metaphorically to pursue a particular course of action).

This phrase is first recorded, as to plough one’s own furrow alone, in a speech that the British Liberal politician Archibald Philip Primrose (1847-1929), 5^th Earl of Rosebery, delivered on 19^th July 1901 (he had served as Prime Minister from March 1894 to June 1895 and resigned the leadership of the Liberal Party in 1896); on the same day, The Davenport Times (Davenport, Iowa, USA) published the following:

ROSEBERRY¹ WOULD BE A LEADER
Roseberry¹ Makes a Significant Speech In Parliament².

London, July 19.—In a speech delivered this afternoon Lord Loseberry [sic] made this significant statement: “I must plough my furrow alone, and before I reach the end of that furrow it is possible I will not find myself alone.”
The declaration is generally regarded as a bid by the former prime minister for the future leadership of the Liberal party.

¹ misspelling of Rosebery
² Lord Rosebery delivered his speech at the City Liberal Club, according to several British newspapers published the following day.

The second-earliest instance of the phrase that I have found was inspired by Lord Rosebery’s speech; it is from The Age (Melbourne, Victoria, Australia) of 2^nd December 1901, which gave an account of the tribute paid to Lord Rosebery by John Adrian Louis Hope (1860-1908), 7^th Earl of Hopetoun, the then Governor-General of Australia, on St. Andrew’s Day at the Caledonian Society of Melbourne; Lord Hopetoun declared to the participants:

The noble Lord [Rosebery] had said it was his intention to plough a lonely furrow to the end, but to whatever goal that furrow might lead him they might rest assured that so long as he had the strength and ability to handle that metaphorical plough the furrow would not deviate a hair’s breadth from the strict lines of honesty, truth and justice. (Applause.)

The Gippsland Times (Sale, Victoria, Australia) of 5^th December 1901 also published an article about this tribute; the journalist remarked:

There is considerable analogy between the present attitude of Lord Rosebery and that adopted by Mr. Deakin³ during the nine years after Mr. Gillies’ Government⁴. He did not believe that any of the cliques into which the two parties had split were following a right policy, so he “ploughed a lonely furrow,” and not until the secret history of that period is published will it be known what service he rendered to the country by his undeviating adherence to the strict lines of honesty, truth and justice.

³ Alfred Deakin (1856-1919), Australian politician, Prime Minister of Australia (1903-04, 1905 to 1908, 1909-10)
⁴ Duncan Gillies (1834-1903), Australian colonial politician, Premier of Victoria (1886 to 1890)

Likewise, the French phrase tracer, or creuser, or faire, son sillon, literally to open up, or dig, or make, one’s own furrow, means to carry out with courage and perseverance the task undertaken.

It is first recorded in a letter that the French author, playwright and poet Voltaire (François-Marie Arouet – 1694-1778) wrote to the marquis de Florian on 26^th May 1759:

     (1829 edition)
Dieu a envoyé M. de Silhouette⁵ à notre secours. S’il y a quelque bon remède, il le trouvera ; car il n’est pas comme la plupart de ses prédécesseurs, gens estimables, mais sans génie, qui traçaient leur sillon comme ils pouvaient avec la vieille charrue.
     literal translation:
God has sent Mr de Silhouette⁵ to our help. If there is any good remedy, he will find it; for he is not like most of his predecessors, estimable persons, but without genius, who opened up their furrow as they could with the old plough.

⁵ Étienne de Silhouette (1709-67) was the Controller-General of Finances from 4^th March to 20^th November 1759. For a reason that remains uncertain, outline portraits were named after him.