Essays / The Amherst essay - The rigorous reasoning and insight essay (300 words) [2]

I'm struck on the Amherst essay - I'm planning to go with the first topic of rigorous reasoning over insight in mathematics and the reverse in physics, but im unsure where to begin developing my point - from the physics or the maths side (I'm applying for both physics and mathematics. I want to try to cover both points but the 300 word limit is a problem. Is it sufficient if i develop only one side?