My science teacher once said....

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Mathematics is a really great way to get a very concise statement that would take a lot of words to explain clearly in English. Take Newton's second law for example - "A body of mass m subject to a net force F undergoes an acceleration a that has the same direction as the force and a magnitude that is directly proportional to the force and inversely proportional to the mass. Alternatively, the total force applied on a body is equal to the time derivative of linear momentum of the body." (stolen from Wiki)

Or, in maths: $\vec{F} = m\vec{a}$ or $\vec{F} = \dfrac{d\vec{p}}{dt} = \dfrac{d(m\vec{v})}{dt}$
You get the same information from both statements, but the maths is so much more concise.

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Related to the above: being able to express the relationship between things as an equation allows one to more clearly see the relationship between physical quantities, taking Ohms Law as an example this time

$I = \dfrac{V}{R}$

Ok, so in English, current is proportional to voltage and inversely proportional to resistance. What does that even mean?
Increase the voltage, you increase the current. Reduce the resistance, you increase the current. How do we know from the equation? It's just basic knowledge about fractions, and how they behave as the numerator or denominator changes.

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Finally, we can use maths to not only express ideas, but realise connections between them. For example, continuing from Ohms Law above:

$P = IV$ (Power = current x voltage)

But hold on, power is related to current. So surely we can rearrange to make current the subject of the above equation, set them equal to each other and get a relationship between resistance and power?

$I = \dfrac{V}{R} = \dfrac{P}{V}$

$P = \dfrac{V^2}{R} =I^2R$