The number $\pi$ comes from the geometry of the circle. The odd numbers come from arithmetic. There is no apparent reason for them to meet. But they do: $$\frac{\pi}{4}=1-\frac13+\frac15-\frac17+\frac19-\cdots$$Add and subtract the reciprocals of the odd numbers, alternating signs, and the result, multiplied by 4, is $\pi$. One discovery, three times Leibniz found this formula in 1673, in Paris, while he was still learning mathematics from Huygens. He showed the result to his teacher, who was impressed and praised him. It was Leibniz’s first great discovery and what convinced him he could be a mathematician.