The Aiel have seen many changes since the cleansing of Saidin.

Three hundred years ago, two young algai d'siswai were found to be able to channel.  Steadfast in the knowledge that their time among their people was at an end, they made the trek to the Blight, to spit in Sightblinder's eye.  

As every channeler on the continent likely did, they felt an immense amount of the One Power being channeled. Because they weren't trained, they didn't know what this was, just that they felt a pull to the west.  They continued on their journey, though.  Their time for pondering larger questions like this was at an end.

Heading further and further north, this feeling faded after a few hours.  Days later, they were stopped by a wetlander man in a black coat.  The two Aielmen started to attack him, for walking into the Three-Fold Land without a guide, but something they could not see bound them.  This man could channel, just like they could.  

The man explained that the taint on Saidin had been cleansed.  It took much convincing, but eventually, the two algai d'siswai were persuaded to come with him to the Black Tower for training in the One Power.

Perhaps a year later, the two men returned to the Aiel, with the pins of an Asha'man.  They spoke with the Wise Ones and clan chiefs, and they began to find men to train.  Eventually, the Wise Ones decided that the men should venture into Rhuidean when they were done with their training, and enter their ranks.

As the years went on, it was decided that if men could become Wise Ones, women could become clan or sept chiefs.  Further, the Far Dareis Mai decided that if men were strong enough to become Wise Ones and go through their training, they could be strong enough to take on the task of raising children as well as be wed to the spear, if they chose

The Aiel still keep contact with the Black Tower, with the use of Traveling.  Sometimes, men will opt to train there and become an Asha'man, rather than become a Wise One.  With the pins of their rank, they are still considered warriors.  They also consider this a good way to find information of goings-on in the wetlands.
Abby Soulane - Accepted
Torianin Soulane - Aes Sedai of the Green Ajah
Jhanic of the Serai Tomanelle - Algai d'siswai and Asha'man