Roelofs was born on the Hommema-sate (estate) near Hijum in Friesland, the youngest of four sons and two daughters.
The oldest son Klaas trained as a steersman, but did not work as one, and instead became a doctor in Sexbierum.
It was not an easy life on the farm, but this is where the other three boys, Pieter, Albert and Arjen worked.
Their mother stimulated the interest of the three sons in mathematics and science, however their father was unhappy with this.
Arjen Roelofs was supposed to have polio so he could not use his right leg very well, and later he could not work on the farm anymore.
He ensured that University of Franeker professor Jean Henri van Swinden became a very regular visitor.
His cousin Roel Hessels Hommema, and his friend Rinse Bearts Gelder were taught in Hijum.
Later Arjen regularly worked with instrument maker and farmer Sieds Johannes Rienks of Hallum.
However it did interest King Willem I, who named both as Brothers in the Order of the Netherlands Lion on 23 September 1817.
Arjen Roelofs made most of the calculations and measurements for Rienks for the building of the telescopes in Leiden and Utrecht.
Roelofs made a proposal to the provincial government to build the dikes differently.
Roelofs proposed to get rid of the wooden posts, and to have the faces of the dikes more moderately sloped and covered with a sturdy layer of earth.
The farmer professor died in Hijum at the age of 74 years, after a long illness.
The road from Oude Leije that passes the location of Hommema-sate was renamed Arjen Roelofswei.