The circle is a simple, intuitive, and common image. It possesses eternal secrets, like the transcendental number, π, the exact value of which remains as elusive as ever; we’ve used many ways to calculate it, but we’ve never managed to arrive at its precise value, however close we may have gotten. “The circle” is an “absolute truth” lying right before our eyes. We have countless ways of approaching it: the cyclotomic method, infinite series and continued fraction, etc. Among these, the most incredible one was devised by the brilliant mathematician Srinivasa Ramanujan, whose remarkable insight produced a series for π that seems irregular at first, but is both accurate and converges extraordinarily rapidly. Still, humans are not the only ones who have insight; an A.I. program developed by Google, the “Ramanujan Machine", can solve mathematical constants like π without any prior information, because it has the ability to reveal hidden mathematical structures to produce intuitive, Ramanujanian formulae. I installed a Ramanujan Machine. I set it up, let it run, and came up with several formulae. Like Ramanujan's intuitive formulae, these A.I. formulae are called “conjectures", which are “shortcuts" to absolute truth. They say if I could prove one of them, they would name it after me. It is fortunate that I could not prove these formulae; I will not obscure the miracle of mathematics with failed words and arrogant power. I know that new shortcuts do not increase or decrease the infinites paths to absolute truth, that the symbolic poems we sing do not enhance or diminish the nature of truth. I believe I can waste every single representation of existence. Let them exhaust your seas in vain. Let them exhaust the sun, seen through Ramanujan's magical eyes, in vain. As I perceive eternity.

All the formulas in this web program are found by the Ramanujan Machine. You can browse all the 81 formulas, and find your comfortable perspective to immerse yourself in the ocean of representation composed by “forms and concepts”, doing nothing but feel it.

圆是一个如此简单直观又随处可见的图形，却又隐藏着最永恒的秘密，例如圆周率π是最有名的超越数，π的准确数值看起来无限的遥远。不管用什么样的计算方法，我们只能无限接近而不能真正的抵达它的确切数值。 「圆」就是这样一个直接呈现在眼前的「真理」。我们有无数种不同的方式去接近它，比如割圆法、无穷级数、连分数等等，有一个被称为天才的人拉玛努金凭借直觉写出的求 π的公式最为神奇，这个公式像诗一样看似无规律但又准确且有着惊人的收敛速度。 然而「直觉」并不一定只是人类的特权，谷歌的一个人工智能程序也可以不需要任何先验信息就能求解数学常数，这个程序被命名为拉玛努金机。拉玛努金机可以求解π这样的常数，正是因为数字本身潜在的结构可以被人工智能程序识别出来，从而能给出一个拉玛努金式的「直觉」的公式。

我安装了拉玛努金机，部署完成后点击运行，得出了若干条公式，这些人工智能发现的公式也被称作「猜想」，如同拉玛努金的直觉公式一样，是一个个通往真理的「捷径」。 如果你能证明其中一条公式，这个公式甚至可以以你的名字命名。 如果你不具备这种证明能力，你也不必使用一个失效的词语或自大的权力去隐匿数字的奇迹。

我知道每新发现的一个捷径，并没有增加或缩减通往无尽的真理的路程。每吟唱一个象征意义的诗，也不能增添或减少关于真理的本质。 你可以挥霍存在的所有表象。 让他们在你身上徒劳地挥霍大海，徒劳地挥霍透过拉玛努金神奇的双眼看见的太阳。 当你感知永恒。

程序中的公式都是通过运行拉玛努金机寻找出来的。你可以随机查看找到的81个公式猜想，也可以挑选适合的角度然后沉浸在「形式与概念」构成的表象海洋中，除了感知什么都不做。