how does mathematics makes the law of demand clearer

If you mean a Demand Function eg
Q=F(P)
The above expression means the quantity (q) demanded of a commodity depends on the price (P) of the commodity, although the price of the commodity isn'τ̅ the only factor that determines the quantity demand of a commodity, But when the Law of demand is τ̅☺ be expressed as a function other factors(Variable) are held constant such as price of related commodities, consumer income etc so the Price is the only thing considered for expressing the law of Demand, other factors are held constant under the 'Ceteris Paribus Assumption' Meaning other things being equal if a particular change occurs in the price it'll affect the Qty demanded by some units
Eg Q=100-10P the equation means for a unit change in price P there'll be 10 unit in quantity demanded, the above equation is a linear demand equation for Blade(Hypothetical).
Does this Help?