Formal:
* Insane: This is the most direct synonym and implies a complete loss of reason.
* Mentally ill: This is a more neutral and clinical term.
* Unbalanced: This emphasizes a lack of emotional stability.
* Unhinged: This suggests a sudden and dramatic loss of control.
* Psychotic: This refers to a serious mental illness characterized by hallucinations and delusions.
* Delirious: This emphasizes a state of confusion and disorientation.
Informal:
* Crazy: This is a more casual and colloquial term.
* Bonkers: This is a playful and informal term.
* Out of their mind: This emphasizes a lack of rationality.
* Off their rocker: This is a slang term for someone who is eccentric or irrational.
* Nuts: This is a slang term for someone who is crazy.
Other:
* Disturbed: This suggests a state of emotional turmoil.
* Aberrant: This implies a deviation from normal behavior.
* Abnormal: This suggests a lack of normalcy.
* Disordered: This emphasizes a lack of order in thought or behavior.
* Irrational: This emphasizes a lack of logic or reason.
The best synonym to use will depend on the context of your writing and the specific meaning you wish to convey.