Vinny loves numbers. (I wonder where he got that from?)
He loves to count. He will just start counting and keep going as high as he can, sometimes with humorous results (e.g., ninety-eight, ninety-nine, ninety-ten, ninety-eleven...). He also loves to count people, or toys, or anything else he can figure to count. When he is upset, I can take advantage of his proclivity for numbers, and calm him down by counting to 100 together.
He loves clocks and timers. I was getting exasperated with him the other morning for wasting time when I was trying to get him ready for school, so I turned on the timer and he suddenly saw it as a challenge to beat the countdown. He is really into telling time, and remarks on the passing of nearly every minute in the car on the way to school. He's also fascinated by the thermometer in the car, and we have nearly daily conversations about the relative heat or cold of a range of temperatures.
His favorite book these days is 26 Letters and 99 Cents, (the 99 cents part, not the letters part). It has pictures of coins (or, as he calls them, "coinks") that add up to the numbers 1 through 99 (skipping quite a few at the end, thank goodness!). From this book he has learned to identify pennies, nickels, dimes, and quarters, and how the coins add up to various numbers. I swear I have read him this book a countably infinite number of times.
We play games with numbers. We count together, alternating who says the next number, so that one is counting evens and one is counting odds. We find cool number patterns and remark on how cool they are (e.g., "Mama, it's 12:34 -- one two three four!" "Cool! Good observation, buddy!"). He loves to type or lay out a string of digits, and make me say what number it is (e.g., 8537832104 is 8 billion, 537 million, 832 thousand, 104).
It is really fun to enjoy numbers together. I look forward to teaching him how to play Sudoku and Kenken when he is older (games he already wants to play but lacks the skills at this point). I hope he never loses his enthusiasm for math!