To check if a positive integer is a power of two using maths, you can use the following method:

1. Take the logarithm base 2 of the number.
2. If the result is an integer (i.e., has no decimal part), then the original number is a power of two. Otherwise, it is not. A number is an integer if it's divisible by 1.

For example, let's check if 64 is a power of two using this method:

1. Log base 2 of 64 is 6.
2. 6 is an integer, so 64 is a power of two.

Let's check another example: Is 27 a power of two?

1. Log base 2 of 27 is approximately 4.75.
2. 4.75 has a decimal part, so 27 is not a power of two.

Therefore, using this method, you can determine whether a positive integer is a power of two or not.
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