Answer:
Long and think, red within, with a nail at the end.
Plow and hoe, reap and sow, What soon does every farmer grow?
They made me a mouth, but didn't give me breath. Water gives me life, but the sun brings me death.
What turns from red to black as soon as it touches water?
This is in a realm of true and in a realm false, but you experience me as you turn and toss.
I am the kind of an ant that's good at math. What am I?