Intelligence comes in many forms, even in dogs, so it's hard to say whether one breed is really "smarter" than another. But there are definite differences. 

According to neuropsychologist Stanley Coren, PhD, author of Born to Bark, there are three major types of dog smarts: instinctive intelligence (what a dog is bred for), adaptive intelligence (what a dog can learn by itself), and working and obedience intelligence (what people can teach a dog to do).  Comparing breeds can be hard for the first two types, but there's a wide range in brainpower among breeds in working and obedience intelligence.

The bumper sticker "My border collie is smarter than your honor student" may be an exaggeration, but border collies are considered the smartest breed in training and obedience. In a survey, 199 of 208 obedience training judges ranked border collies in the top 10. The others, in order, were poodles, German shepherds, golden retrievers, Dobermans, Shetland sheepdogs, Labrador retrievers, papillons, Rottweilers, and Australian cattle dogs.

Sorry, Afghan hound fans. These dogs ranked lowest on tests of working and obedience intelligence. They were considered the least "trainable" breed, followed by the basenji, bulldog, chow chow, borzoi, bloodhound, Pekingese, beagle, mastiff, and basset hound.

Cat lovers and dog lovers argue this one all the time. It kind of depends on what we mean by "smarter." In tests, cats are smarter when it comes to using their paws -- like to pull strings or levers. However, dogs are more trainable, more social, and more able to understand human gestures and words. 

Plus, there's the brain size issue. In proportion to their body sizes, dog brains are bigger than cat brains. In the science world, brain size is usually a pretty reliable measure of a species' smarts.

The average dog can learn 165 words. "Super dogs" -- those in the top 20% of intelligence -- can learn 250 words, and the very smartest dogs may be capable of much more. Researchers have taught a border collie named Chaser more than 1,000 words -- about the same vocabulary as a 3-year-old child. 

Maybe you can't ask a dog "what's one plus one" and get an answer. But tests show that dogs can count up to four or five and understand the idea of addition and subtraction. If a dog sees a bowl with five pieces of food and another with two, he'll likely choose the bowl with more pieces.

Dogs understand simple ideas of space. They're good at making a mental map of the space around them, as long as they have some landmarks. And while the concept of time is a little bit harder, they understand that things happen in some kind of order. They understand that one thing happens before or after something else.

In terms of social intelligence -- the ability to communicate and cooperate with others -- dogs are very clever. Not only can they interact well with other dogs, but they are very good at communicating with humans.

Coren ranks dogs' social intelligence on par with human teenagers. "They're really interested in who's who in the pack, and who's moving up in the pack, and who's sleeping with who and so on."

The average dog has the language understanding of about a 2-year-old child and understands numbers like a child between 2 and 3 years old.

You can make your dog smarter. Dogs raised in a mentally stimulating environment learn faster than dogs raised in a boring one. New experiences and challenges help new neural connections form inside the dog's brain.

It can be hard to compare the intelligence of different species. But based on brain size and body size, dogs are among the smartest animals on the planet. Only humans, the great apes, porpoises, and elephants are smarter.

Why are dogs smart? It could be because they're hunters who have to use their brains to catch prey. It also could be because they’re very social -- they need brainpower to communicate and cooperate.

Experiments show that dogs will purposely fool people and other dogs to get what they want. When a person and a dog are playing and they try to trick each other, a person can fool a dog about 47% of the time. A dog has nearly the same success rate. He can fool a person about 41% of the time!

Dogs today have bigger brains relative to their body weight than their ancestors did. This could be due to selective breeding for skills that require intelligence -- such as hunting, guarding, guiding, and shepherding.

Not only can old dogs learn new things, but new challenges also can help hold back the mental decline that's sometimes a part of aging. Canine Cognitive Dysfunction Syndrome in dogs is, often compared to Alzheimer's disease in people. Both can lead to disorientation, unresponsiveness, social withdrawal, and house-training accidents.

More mental activity and challenges can help slow these developments or other kinds of mental decline. Exercise also can help.

If you want a working dog, then pick a brighter breed. But smart dogs can be more demanding; they tend to need more attention and may be more high-strung and quicker to react in both positive and negative ways.

"People ask me why I have a beagle," says Coren. "Beagles are seven from the bottom in terms of obedience training … (but) I have nine grandchildren, so I needed a dog who's friendly and sociable and relatively unbreakable … it's actually an advantage for me that this dog doesn't remember that that kid over there is the one who pulled his ear an hour ago."