Mathematician showing hesitation about principle that's not right (5)
I believe the answer is:
euler
'mathematician' is the definition.
(I've seen this before)
'hesitation about principle that's not right' is the wordplay.
'hesitation' becomes 'er' (sound used when hesitating).
'about' is an insertion indicator.
'principle' becomes 'rule' (synonyms).
'that's not' indicates named letters should be taken away.
'right' becomes 'R' (common abbreviation).
'rule' with 'r' removed is 'ule'.
'er' placed around 'ule' is 'EULER'.
'showing' acts as a link.
(Other definitions for euler that I've seen before include "Leonhard -, Eighteenth century Swiss mathematician" , "18th-century Swiss mathematician and physicist" , "Noted blind Swiss mathematician" , "See fifty three across" , "Leonhard --, C18 Swiss mathematician" .)