Mathematician's achievement displayed outside empty room (6)
I believe the answer is:
fermat
'mathematician's' is the definition.
(Fermat is an example)
'achievement displayed outside empty room' is the wordplay.
'achievement' becomes 'feat' (feat is a kind of achievement).
'displayed outside' indicates putting letters inside.
'empty' means to remove the middle letters.
'room' with its centre taken out is 'rm'.
'feat' enclosing 'rm' is 'FERMAT'.
(Other definitions for fermat that I've seen before include "French Mathematician (famous last theorem)" , "he had no room to write down proof" , "One with famous last theorem" .)