Carsten Niebuhr or Karsten Niebuhr ( March 17 , 1733 -- April 26 , 1815 ) was a German mathematician , surveyor , cartographer , and explorer . Carsten Niebuhr or Karsten Niebuhr ( March 17 , 1733 -- April 26 , 1815 ) , a German mathematician , cartographer , and explorer in the service of Denmark , is renowmed for his travels on the Arabian peninsula .