Mathematician and doctor at first easily selects second gear (6,5)

I believe the answer is:

summer dress

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'first easily selects second gear' is the definition.
I can't judge whether this definition defines the answer.

'mathematician and doctor' is the wordplay.
'mathematician' becomes 'summer' (I've seen this before).
'and' says to put letters next to each other.
'doctor' becomes 'dress' (I can't justify this - if you can you should believe this answer much more).
'summer'+'dress'='SUMMER DRESS'

'at' is the link.

Can you help me to learn more?

I've seen this clue in The Guardian.

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