Sometimes I see sentences with "state of the art" and others with "state-of-the-art".
What is the difference if it has a hyphen?
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The difference is that without hyphens, it's a noun, and with hyphens, it's an adjective. So you might say that a given piece of technology "represents the state of the art in its field," or you could refer to it as "state-of-the-art technology."
"state of the art" is a noun: it refers to the actual state of progress in a given field.
The most recent stage in the development of a product, incorporating the newest technology, ideas, and features
the state of the art in 3D printing
"state-of-the-art" is a compound adjective: it refers to something (often a product or piece of technology) that uses the latest technology in a given field.
Belonging or relating to the most recent stage of technological development; having or using the latest techniques or equipment.
our scientists work in state-of-the-art facilities
Quoted definitions and example sentences are from Oxford Dictionaries (via Lexico)