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Problems exist over European exchange programme (7)

Ross

I believe the answer is:

erasmus

I'm a little stuck... Click here to teach me more about this clue!

'european exchange programme' is the definition.
Although both the answer and definition are singular nouns, I can't understand how they can define each other.

'problems exist over' is the wordplay.
'problems' becomes 'sums' (arithmetic problems).
'exist' becomes 'are' ('they exist' means 'they are').
'over' says the letters should be written in reverse.
'sums'+'are'='sumsare'
'sumsare' written backwards gives 'ERASMUS'.

Can you help me to learn more?

(Other definitions for erasmus that I've seen before include "Fifteenth to sixteenth century Dutch humanist, use arms (anag.)" , "Desiderius -, fifteenth and sixteenth century Dutch humanist" , "Old theologian" , "Dutch philosopher" , "Learned person" .)

I've seen this clue in The Times.
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