Even with trillions of digits of pi already calculated, there is still lots of horizon.
Because the digits of pi are literally endless.
Even the early work of mathematician Arya Bhatta in the 5th century CE had suggested that the value of pi was irrational and could only be "approached" but not definitively calculated.
In 1761 the German mathematician proved that pi was in fact irrational, meaning that it could not be written as the ratio of two integers.
Finally, in 1882, Ferdinand von Lindemann, another German mathematician, had published his proof that pi was a 'transcendental' number: a complex number which is non-algebraic, meaning it is not a solution of a non-zero polynomial equation with rational coeffecients.
This left pi as a number whose digits were literally infinite - providing a challenge which was the 'perfect storm' for computers and their programmers.