How do wings develop from the thorax in winged insects?

In winged insects, known as Pterygota, wings develop as paired outgrowths from the thorax. Specifically, these wings originate as cuticular sacs that bud out from the thoracic wall.12

During development, these sacs flatten, and the two resulting membranes are pressed together. The structure is stiffened by thickenings of the cuticle, which form cylindrical veins that carry tracheae, nerves, and circulating blood to all parts of the wing. In many insects, these adult structures are formed from clusters of undifferentiated cells known as imaginal disks.213

While the exact evolutionary origin of these structures remains a subject of scientific hypothesis, researchers have proposed that they may have evolved from fixed planes used for gliding or from thoracic gills similar to those found on the abdomen of some mayfly larvae. Unlike the primitive, wingless apterygote insects, pterygotes possess this specialized thoracic development that enables flight.14