Ageing mathematician pursuing degree (8)
I believe the answer is:
maturing
'ageing' is the definition.
('mature' can be a synonym of 'age')
'mathematician pursuing degree' is the wordplay.
'mathematician' becomes 'turing' (Alan Turing).
'pursuing' is a charade indicator (letters next to each other).
'degree' becomes 'MA' (Master of Arts is a type of degree).
'turing' put after 'ma' is 'MATURING'.
(Other definitions for maturing that I've seen before include "Growing ripe or developing" , "Growing ripe, reaching full growth" , "Growing, ripening" .)