[Pam Korda, Leigh Butler, Jeff Dougan]
In [TFOH: 14, Meetings, 194], Birgitte tells Nynaeve that Gaidal Cain hadn't been around in T'A'R for some time, and that she suspects that he's been "spun out." Since we never see him in T'A'R after that point, it is reasonable to suppose that that is the case. Min's viewing of Birgitte in WH seems to confirm this idea: "Strangely, some [images] were connected to an ugly man who was older than she, and others to an ugly man who was much younger, yet somehow Min knew they were the same man" [WH: 12, A Lily in Winter, 297].
So, of course, speculation has been rife as to where and who he is. Some suggestions are (in order of ascending age):
Well, Aviendha's not pregnant (see section 2.5.6), and there is zero evidence that Faile is, either. Elayne is preggers as of WH, but it's quite a stretch to suppose that one of her children is Gaidal when he disappeared four books earlier (not to mention supposing that any kid with Rand and Elayne for parents could end up Gaidal-ugly).
No, he's not.
The theory that Olver, the little boy Mat takes under his wing in LOC, is the reincarnation of Gaidal Cain was very popular for a long time, despite the problems with it. There were facts supporting the argument: Olver didn't like Birgitte when he first met her, but they have grown very affectionate towards each other, for instance. Also, Olver is very ugly. These are both "trademarks" of the Birgitte-Gaidal relationship, as described in [TSR: 52, Need, 598].
However, in spite of the similarities, there was also a big problem with the idea of Olver being Gaidal Cain. Olver is now about ten years old [WH: 18, An Offer, 375]. Gaidal was last seen in T'A'R at the end of TSR. That was, presumably, before GC was spun out. Thus, only a year or less had passed between GC's "spinning out" and Olver's appearance as a grown boy. That appearance by Gaidal is not the only one he makes during Olver's lifetime. He appears numerous times in T'A'R, as well as appearing with the other Heroes at Falme. This is a big discrepancy.
Many explanations were proposed to explain this, but none of them were really consistent with the other information we have about the Heroes of the Horn and T'A'R. And anyway, RJ made the question moot at a post-COT signing in Dayton, OH [report by Tim Kington]:
Q: Is Olver Gaidal Cain?
RJ: No. I didn't really think that this would last as long as it has. The timing is wrong. He has another reason for being there besides being a red herring, though.Q: He's too old.
RJ: Yes. Time in T'A'R and the real world run at different rates, but it never runs backwards. You may spend an hour in T'A'R, and a day has passed when you get back, or you may spend a day, and an hour has passed when you get back, but you'll never go in on Tuesday and come back on Monday.Q: Is the difference in time constant?
RJ: No. It's fairly random. Sometimes fast, sometimes slow, sometimes the same as real time.Q: It's different for different people, then?
RJ: Yes. Unless they're together in T'A'R. Then the same amount of time passes for them obviously.
The last three answers put paid to the most commonly proposed idea to explain the timing problem, the "Time Runs Differently" theory. This was based on a comment Birgitte makes in [TFOH: 14, Meetings, 194], where she tells Nynaeve that time runs differently for the Heroes in T'A'R than it does for living people in the real world: "Time [in T'A'R] is not like time in the waking world. I met you here last ten days gone, as it seems to me, and Elayne only a day before. What was it for you?" Ny: "Four days and three..." Birgitte: "The flow of time here can shift in larger ways, too. It might be months before I am born again, or days. Here, for me. In the waking world it could be years yet before my birth."
People used this idea that "time runs differently" to sweep the timing problem under the rug, but even before RJ's confirmation, there was no indication that time ever runs backwards in T'A'R, as it would have had to do in order for Gaidal to have been reborn as Olver.
People have still tried to defend the idea by bringing up the quote by Birgitte in [TFOH: 36, A New Name, 407]: "Gaidal is out there, somewhere, an infant, or even a young boy." The "young boy" bit is taken to mean that Birgitte thinks that time CAN run backwards, and that a nine-year-old could be GC. In addition, in [TPOD: 1, To Keep the Bargain, 47] Aviendha comments that "Birgitte worried about [Olver] even more than [Aviendha], but Birgitte's breast held a strangely soft heart for small boys, especially ugly ones." This has been taken to imply that Birgitte is looking for GC, and continues to believe that GC could be a small boy.
However, this is still inconsistent with the fact that, in every other instance, time increases monotonically for Birgitte and everyone else in T'A'R. The first "small boy" comment can be explained by the fact that the pace of time does vary in T'A'R, and thus, that Birgitte, upon awaking in the real world, had no idea how much time has passed (in the waking world) since Gaidal was spun out. For all she knew, it could have been several years. However, by the beginning of TPOD, she must have learned how much time had passed in the real world. So, why is she looking at ugly children? She mourns her loss of Gaidal. It's not very incredible to think that she has a soft heart for that which reminds her of him. Furthermore, she may be deluding herself out of hope that Gaidal isn't quite so young as logic says he must be.
RJ's assertion that Olver is not Gaidal and the reason why (the timing discrepancy) means that by the same logic, any other possible candidates as old or older than Olver are also automatically eliminated. Thus, neither Mat nor Uno (the next two most popular characters suggested) can be Gaidal.
One suggestion is that perhaps Gaidal has not been spun out, after all. Daniel Bartlett explains, "What if he wasn't [spun out]? Moggy promised Birgitte to 'weep alone for as long as the Wheel turns'. What if she delivered on that promise and GC isn't around simply because Moggy got him? Would this explain everything, and Birgitte's looking out for all those little boys simply be wishful thinking?" A variation on this idea is that Moggy didn't kill him, but pulled him out of T'A'R as an adult the same way she did to Birgitte.
The problem with these ideas is Min's vision in WH of Birgitte being linked to an ugly, younger man who is also an ugly, older man. That can only be referring to the current incarnation of Gaidal Cain as a youngster, and also clearly indicates that Gaidal is alive. Additionally, it seems unlikely that Moggy could have done anything to Gaidal anyway, since Gaidal was not only already gone from T'A'R when Moggy and Birgitte had their showdown, but it's explained that Birgitte was only vulnerable to Moggy because she "violated the precepts," as Gaidal Cain put it, by helping Ny and El. Gaidal did not show any inclination to put himself in a similar situation - he disapproved of Birgitte involving herself in the affairs of the living [TSR: 52, Need, 598-599].
Thus we are left to conclude that Gaidal is currently a random infant or toddler out there somewhere, and that he is unlikely to be able to play a role in Tarmon Gai'don. Which naturally has led people to wonder WHY, if the Wheel spins out the Heroes when they are needed, did events fall out this way?
Therese Wikström offers, "Because he'd be needed after the Last Battle? Remember: 'The great battle done, but the world not done with battle.'"