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so lost in thought that one does not realize what one is doing, what is happening, etc.; preoccupied to the extent of being unaware of one’s immediate surroundings.
Contemporary Examples

The boy genius Geithner turned into an absent-minded professor when he filled in his tax returns.
Obama’s Strange Obsession Tina Brown February 8, 2009

A rush of water spills from above, but not from the bottle of an absent-minded commuter or tipsy traveler.
Leaky Ceilings, Catcalls, and Uncaged Pythons: 4 Hours on NYC’s Worst Subway Kevin Zawacki August 7, 2014

Historical Examples

“absent-minded—the citizen,” muttered Barlasch, returning to the kitchen, where he resumed his seat on a chair by the open door.
Barlasch of the Guard H. S. Merriman

“Of course,” repeated the great man, with a sort of absent-minded loftiness.
The Secret Agent Joseph Conrad

My mother looked down, presently, at him, and checked the absent-minded passes of her hand over Lucy’s hair.
When Grandmamma Was New Marion Harland

His face was downcast and he put the dishes on the table in an absent-minded way.
The Widow O’Callaghan’s Boys Gulielma Zollinger

Thinking of him I almost talk like him in his absent-minded moments.
Sonnie-Boy’s People James B. Connolly

It shows how absent-minded I am, for I ought to have thought of the wine long ago.
One Day’s Courtship Robert Barr

To be sure—excuse me—I am absent-minded; I do take it—that is to say, yes, I accept these lovely roses.
The Flower Girl of The Chteau d’Eau, v.1 (Novels of Paul de Kock Volume XV) Charles Paul de Kock

She seemed to be thinking of something else and her answers were brief and absent-minded.
Fair Harbor Joseph Crosby Lincoln

adjective
preoccupied; forgetful; inattentive