Rudmose-Brown was born on 13 September 1879, the younger son of an Arctic enthusiast  and educated at Dulwich College. After reading Natural Sciences at Aberdeen University his first academic post was teaching botany at University College, Dundee, at that time part of the University of St Andrews.
At Dundee he met William Speirs Bruce who invited him to join the Scottish National Antarctic Expedition where he catalogued the wildlife of the South Orkney Islands. The Rudmose Rocks, charted by the expedition in 1903, were named for Rudmose-Brown by Bruce. On returning home he became Bruce’s assistant at the Scottish Oceanographical Laboratory, a consultant to the Scottish Spitsbergen Syndicate and vice-president of the International Polar Congress. In 1907 he was appointed a lecturer in geography at Sheffield University and spent several seasons as a field botanist in Svalbard.
He was president of the Institute of British Geographers between 1937 and 1938 and at different times served as the president of the Arctic and Antarctic clubs. He died in Sheffield on 27 January 1957, bequeathing his polar library to the Scott Polar Research Institute in Cambridge.
- Rudmose-Brown, R. N., The Voyage of the Scotia, Being the Record of a Voyage of Exploration in Antarctic Seas, 1906
- Rudmose-Brown, R. N., Principles of Economic Geography, 1920 (new ed. 1926, 1931, 1939, 1946)
- Rudmose-Brown, R. N., A Naturalist at the Poles: The Life, Work and Voyages of Dr. W.S. Bruce, the Polar Explorer, Seeley, Service & Co., London, 1923
- Rudmose-Brown, R. N., The Polar Regions: A Physical and Economic Geography of the Arctic and Antarctic, Methuen, 1927
- Rudmose-Brown, R. N. (1922). "Åland Islands". In Chisholm, Hugh. Encyclopædia Britannica (12th ed.). London & New York.
- Rudmose-Brown, R. N. (1955). "Spitsbergen". Encyclopædia Britannica. 21. pp. 248–249.
- Obituary of Robert Neal Rudmose Brown Transactions and Papers(Institute of British Geographers), No. 23 (1957), pp. viii-x
- Heroic Age of Antarctic exploration Polar Record (Cambridge, Scott Polar Research Institute, 19 March 2001) Vol 38, No 204, Page 69
- Biographical details
- Peak named in his honour
- "Rudmose Rocks". GNIS. U.S. Geological Survey. Retrieved 6 January 2018.
- Further details
- Consequently being created a Commander of the Order of St Olav by the Norwegian Government Court Circular: The Times, Wednesday, 26 Apr 1944; pg. 8; Issue 49840; col B
- On his retirement in 1945, becoming emeritus professor.
- 1932 Antarctic;1949,Arctic: Who was Who Vol V p1623
- Who was Who(Ibid) states that his wife Edith died in 1950: they had one daughter.
- Rudmose-Brown Collection
- IPNI. R.N.R.Br.