My daughter was/is very similar. I would be cautious, however, in your investigations and remember the well-roundedness that math/language gifted or talented children need to achieve. There are a lot of alternative schools or schooling (in home, public or private) that will help a child to achieve their personal best creatively, motivationally, and interpersonally (traits that some gifted kids need to work on) while not labeling or stigmatizing them, or worksheeting them to death! I truly believe many children could write, read, do math, amazing art if the opportunities were only there. And if they're interested, of course. Different kids, different gifts.
I would highly suggest a few books:
*Coloring outside the Lines by Roger Schank
*Raising Curious Kids : Over 100 Simple Activities to Develop Your Child's Imagination by Nancy Sokol Green
*Einstein Never Used Flash Cards : How Our Children Really Learn-- And Why They Need to Play More and Memorize Less by Kathy Hirsh-Pasek
*Is Your Bed Still There When You Close the Door? by Jane Healy
And doing lots of open-ended activities (my daughter loved science experiments) and art. It's amazing what kids will come up with and get into. Encouraging their unique interests is so fun.
My own goes to a Montessori, where there aren't limits on what children can learn or how far/fast they go; nor pressure or labels; and a lot of emphasis on compassion and empathy and helping others. But I think many different types of schools can work for different kids, depending on their learning styles and interests. In Montessori, it's fairly normal for kids to start reading (usually by sounding out) by age 3; and they start doing simple math at this age. Although, it's all called "games" so it doesn't feel like it, and they choose how to spend their time themselves. Computers are not permitted usually, however.
