Juggling multiple mental tasks simultaneously does make you less effective at any of those particular tasks than if you were focusing on them exclusively, but it does not make you stupid. Multitasking actually increases long-term intelligence by encouraging your brain to grow connections (literally extending dendrites) to further reaches of the brain, because by doing multiple unrelated things at once, your brain will search for hidden relationships. It'll find them and record them as new connections in its structure.
People who shift from a "single tasking" lifestyle to a multitasking lifestyle also display an ability to adapt to the new pace. Even well into senior adulthood, the brain retains a great deal of plasticity, enough to learn a new way of working.
If you became a super-expert--someone who learns all there is to know about one subject until they are the most knowledgeable in the world--you may find yourself in the paradoxical situation of knowing less about your chosen subject than someone who dabbles in a bit of everything and specializes to a moderate degree in a handfull of key subjects. The reason is that knowledge does not really form categories naturally, we just apply them ourselves in arbitrary ways. Schools are often our first exposure to the idea of breaking up the world into separate disciplines like science, math, history, literature, and so-on. As a result, it's not unusual for an adult to see the world in terms of even more discrete subjects. Step into a library and you'll see the world's knowledge neatly divided by the Dewey Decimal system.
Knowledge is broken down into subjects to make it easier to find information, not because the world is that way. A cardiologist could learn everything there is to know about the heart, but his rate of learning would slow down until he began studying the nervous system, the digestive system, immune system and so-on, which all affect the health and operation of the heart too. Then there's still more to learn about the heart outside the body, such as economics (which affect access to heart-healthy food), social behavior (that could lead to, or help prevent substance abuse), mathematics (to spot patterns in heart activity over time), and the list goes on.
Furthermore, broad knowledge of many subjects leads to understanding, because there is literally nothing that exists in a vacuum, and everything can be defined in the ways that it relates to something else. The more "something else" you know, the easier it is to understand the next factoid's place and purpose in the world.
This myth was born from early scans of brain activity that revealed an average of 10% of the brain was being used at any particular time. Not only were the scans failing to register all of the activity going on, but the myth itself misreports what the findings were. It's not as if only 10% of our brain is "alive" and the rest is pudding, what's really going on is that your brain is switching between different specialized regions for each new task you face. Your brain is an assembly of neuronal structures that specialize in kinds of tasks, such as reading, speaking, seeing shapes, seeing colors, remembering, solving problems, and so-on. What you're doing at any particular time will stress more of one than the others.
When seen under an fMRI, large parts of the brain appear "dark" while others are active. Change the task that the person is doing, and a different set of regions light up.
Spread over the course of a few minutes in a typical day, you'll utilize 100% of your brain.
Intelligence is all about genetics / Intelligence is all about environment / Intelligence is all about practice
Intelligence is about all three. Your genes matter because they sketch the structures that your body will try to grow. Environment matters because it can provide the materials for that growth and the conditions that let the growth happen. Practice matters because the final shape of those structures is not completely defined by your genes.
As a related example, take the ball-joints of your knees and hips. Their round shape is not encoded anywhere in your genes, in fact if an embryo is immobilized during development those joints will grow into each other and fuse. It's only because a baby "kicks" inside the womb that the bones have a chance to rub against each other and form the shapes they do. What the genes do is set up the tendency for the bones to grow in a certain direction and give way to certain pressures, the mother's diet will provide adequate materials for those bones to be made strong, and the "practice" the baby does cinches the final shape.
The same is true of the brain. Without proper diet and metal exercise, it won't grow to the potential suggested by your genes.
This also means that a superiority in one area will produce someone who's smarter than others, all else being equal. Evolution is constantly trying out new genes, some of which may lead to a brain that grows a better structure, or a heart that supplies it with more oxygen, or an immune system that's better at destroying diseases that attack the brain. Someone might have a better diet than you, exercise more, and avoid activities that lead to brain trauma. And someone may study harder than you, practice math more than you, and so-on.
There can be such a thing as being "born at the right time" or "born in the right place"; somebody who's genetics make them a better fit for the kind of environment they're born into. People with a genetic disposition to managing distractions can find that today's Internet saturated environment suits their style of practice better than someone who's intellect shines only when given long periods of sustained concentration.
If you think your environment doesn't suit you, then you're obliged to change it or move somewhere else. But no mater what you feel, exercise and nutrition should be an ongoing and active concern.
Nootropics combined with study and mental exercise may make you smarter, but the pills alone don't do squat. Popping back a gram of Piracetam and vegging-out in front of the TV will enhance your TV-watching brain cells, and do nothing for you elsewhere. You'll still be dumb as a rock and maybe a bit better at remembering what goes on in soap operas.
Think of what protein supplements do for a couch potato versus what they do for someone who works out. You can drink all the whey protein and munch all the beef jerky you like, but you won't get stronger muscles unless you combine that high-protein diet with regular weightlifting.
If you want to take the risks and experiment with "smart pills", do it as part of a study regimen.