'amethodically' originates from the prefix 'a-' meaning 'without' and 'methodical,' which comes from the Greek word 'methodikos,' meaning 'systematic.'

'methodikos' transformed into the Latin word 'methodicus,' and eventually became the modern English word 'methodical,' with 'amethodically' being derived from it.

Initially, it meant 'without a method,' and this meaning has largely remained the same in modern usage.