How will you know if your child is genius?

I would consider my child gifted if he could do those things at those ages. It could also be the results of good teaching by the parents or child care. I hope the child continues in the path he is going.

i remember my 1st son can match basic shapes (square, circle, star) in the shaper toy around 1yr+. now at 3yrs old, i was told not many can be like him, know all the alphabets, recognize them in big and small caps. count from 1-20, 5-1 backwards. but i've done a speech test, LENA. & his test result is actually backwards. he is 36mths, but speech strength is 30mths. so i know my son is gifted in some areas. & i should observe & let his interest grows with him.

I'm not sure you can say if a child is mentally gifted at that age. But if the child continues to progress at that pace, then I'm sure he/she would be a mentally gifted child. I've handled kindergarten classes and I've observed that children whose mothers are at home tend to be quick at grasping concepts (even if the mother doesn't do any active teaching). But in some children this tends to wane off when they are in primary school. But the truly gifted children continue to learn and with proper support from teachers and parents will bloom. So, I'd say wait and watch....give all the encouragement you can.

I think the milestones you've cited point to a gifted child of high intelligence. My elder son had similar nilestones and is now studying law at one of Australia's top universities. My twins milestones were a little later, but there are many factors - I had less time being the biggest one! But they are also equally clever and able now in their teens.