New mathematics is where we use different ways to think about numbers and solve problems. Just like how we can use different toys to play different games, we can use different ideas to solve math problems.
For example, let's say we want to add up all the numbers from 1 to 10. We can use an old way of doing math where we write down each number and then add them up one by one. Or we can use a new way where we can recognize that the sum of 1 to 10 is the same as the sum of 10 to 1 but in reverse order. So instead of adding 1+2+3+4+5+6+7+8+9+10, we can add 10+9+8+7+6+5+4+3+2+1 and get the same answer.
New mathematics also includes new symbols and ideas to help us think about math problems. For example, the symbol "π" helps us calculate the circumference of a circle, and the idea of negative numbers helps us understand temperatures below zero.
So, new mathematics is like a new set of tools that we can use to help us solve problems and understand numbers in different ways.