The short answer, from what I've found is "yes!"
The dolphin brain is large. Relative to body size, it's the second largest only to humans. This is measured by EQ (encephalization quotient). Here are some EQs of different species:
- Teabaggers and fundamentalists: 1.2 (just kidding, sorta)
- River dolphins: 1.5
- Gorillas: 1.76
- Chimpanzees: 2.48
- Australopithecines (hominids who lived 4 million years ago): 3.25-4.72
- Bottlenose dolphins: 5.6
- Humans: 7.4
So, let's run through some of their amazing abilities:
- Complex play
- Problem solving
- Communicating with each other through whistles, clicks, touch and body postures. But we don't know if it's a language by human definition.
- Reading: they can read a symbol printed on a card and then do what it says.
- Self Awareness: they can recognize themselves in a mirror. If a mark is placed on their skin (with a nontoxic marker), they will go to the mirror to look at it and spend more time than if they have no marks. (elephants will do the same. They will touch the mark on their head, while they look in the mirror. Great apes as well)
- They can think through and plan ahead. see video below and Guardian article for examples)
- Two dolphins were taught the concept of "create" (see video below). They were given the signal, the dolphins swam underwater, whistled to each other, then came up and together (synchronized) they swam away from the trainers and waved their tails. This shows they can do much more than rote learning.
- The way the video was edited, it's hard to tell how rigorous the experimental protocols were. The people in charge of the dolphins were emotionally invested in the results. So take this one with a grain of salt.
- Delayed gratification: a dolphin named Kelly who was trained to collect trash in her enclosure then give it to the trainers for a food reward learned that the size of the trash didn't matter with how much fish she received. So she took paper and stashed it under a rock, then when the trainer came, she'd go down and tear off a little piece of paper, exchange it for a fish, then go down and get another small piece. But then one day she snatched a gull that flew into her pool and gave it to her trainers. They gave her lots of fish in exchange. So the next time she was fed, she took the last fish and hid it under her rock. When some gulls came back, she retrieved the fish and used it to lure the gulls, which she then caught and used to get even more fish. She taught her calf how to gull-bait, and that calf taught other calves so now it's a great game.
- Tool use: dolphins have been observed coaxing a moray eel out of its crevice by poking at it with a spiny scorpion fish. And other dolphins place sponges over their snouts for protection against stonefish and stingrays while they forage.
- Novel behaviors and complicated learning: in a famous experiment by Karen Pryor, two rough-toothed dolphins were rewarded whenever they came up with a new behavior. It only took a few trials for the dolphins to figure out what was going on. The same experiment was tried with humans who took about as long to realize they were being trained to do something new. Both groups got frustrated while they were trying to figure things out. The humans even got angry. The humans expressed relief when they finally got it. The dolphins got really excited and then displayed more novel behaviors.
- Understanding human language: they have learned sign language. They not only can learn words, they can understand word order. So one dolphin learned 60 words and could understand more than 2,000 sentences. They can also generally respond correctly to new sentences formed from known words, which shows they are really understanding.
- Dolphins have been taught concepts like repeat, different and create.
- Watching TV: while chimps have trouble watching TV and require a lot of training, dolphins pick it up the first time they see it and can respond to it. This shows the ability to respond to new situations.
- Helping other species: dolphins have been seen to help beached whales and there is anecdotal evidence of dolphins rescuing humans from drowning. This seems to imply some kind of theory of mind and empathy.
Here's the video from Nova scienceNOW: