Old Babylonians leave man with hesitation in arithmetic (9)

'old babylonians' is the definition.
I know nothing about this answer so I cannot tell whether it can be defined by this definition.

'man with hesitation in arithmetic' is the wordplay.
'man' becomes 'ian' (man's name).
'with' is a charade indicator (letters next to each other).
'hesitation' becomes 'er' (sound made while hesitating - um, er).
'in' indicates putting letters inside.
'arithmetic' becomes 'sums' (mathematical sums).
'ian' put after 'er' is 'erian'.
'erian' placed inside 'sums' is 'SUMERIANS'.

'leave' is the link.

Can you help me to learn more?