Knowing that 1+1=2, which of the four kinds of wisdom—hearing, contemplation, cultivation, and realization—does it belong to?

Those of the four kinds of wisdom—hearing, contemplation, cultivation, and realization—all know that 1+1=2, but the difference between one kind of knowing and another is enormous. A one-year-old child can know that 1+1=2; even a well-trained dog can know that 1+1=2; a university professor knows that 1+1=2; a mathematician also knows that 1+1=2. How great, exactly, is the difference among them? 1+1=2 belongs to the difficult problems within Goldbach's conjecture; among Chinese mathematicians, only Chen Jingrun and Hua Luogeng ever undertook to work out and prove it, but Hua Luogeng and other mathematicians did not work it out and did not provide a valid proof, and it is unknown whether Chen Jingrun fully proved it. Among a hundred million people, not even one has the ability to prove 1+1=2; among a hundred million, no more than one can even undertake the proof; fewer than one in ten thousand can deliberate upon 1+1=2; yet those who can know that 1+1=2 are countless.

So all of us know that 1+1=2—how much watered-down pretense does this knowing actually contain? By the same token, many Buddhist learners have studied the principle of the Four Noble Truths and the dharma of the tathāgatagarbha for a few years, or only two or three years, or even just two or three months, and then claim they have realized and awakened. The watered-down pretense here is, of course, considerable. Most people have not reached the level of cultivation, have not had the conditions to practice genuinely and solidly, and none of the conditions for seeing the Path are fulfilled—how can they speak of the wisdom of cultivation and the wisdom of realization? Merely having the wisdom of contemplation would already be quite good. This is why the path of learning Buddhism and practicing is not so easy to walk. Do not overestimate yourself and underestimate the Buddha-dharma; otherwise, old karma not yet dissolved, you will add new karma—how could you attain liberation in future lives?

For children in kindergarten, elementary school students, and middle and high school students, how should they strive if they want to genuinely realize that 1+1=2? How should they perfect the causal conditions for proving 1+1=2? With a realization ratio of one in a hundred million, one in a billion, or one in ten billion—how likely do you think these children are to genuinely realize it in the future? How must they strive? Unless they are mathematical geniuses, there is almost no possibility. For the proof of 1+1=2, the most important part is the logical derivation steps in between; the result has already been given, but the intermediate proof process is missing and needs to be completed. In the course of the argument, one must forget the result and treat the result as unknown. As for the hardship of the argumentation process, just look at Chen Jingrun and you will know—the price was enormous.

There are also some Buddhist disciples who have practiced and encountered the Four Noble Truths and the prajñā and Yogācāra teachings, but they remain a very, very small proportion of all Buddhist learners. Among these people, there are varying degrees of knowing and understanding of the Mahāyāna and Hīnayāna teachings; most of the four kinds of wisdom belong to the wisdom of hearing, a minority belong to the wisdom of contemplation, very few possess the wisdom of cultivation, and those who reach the level of the wisdom of realization may be exceedingly rare—perhaps one in a hundred million. So for Buddhist learners who already know the principle of the Four Noble Truths and the prajñā emptiness teaching of the tathāgatagarbha but have not yet genuinely realized them, how should they go about realizing and personally verifying them? Or for those who have already understood the Buddha-dharma and comprehended it intellectually, how should they go on to personally verify and genuinely realize it? What causal conditions need to be perfected, and what effort must be made, to truly realize it? For those who have understood the Buddha-dharma and comprehended it intellectually, in order to genuinely realize the Buddha-dharma, they must forget everything they have understood and awakened to, treat the result as unknown, and not bring it into the process of investigation. This requires the wisdom of cultivation: actually practicing the thirty-seven aids to enlightenment, precepts, meditative concentration (samādhi), and wisdom, the bodhisattva's six perfections, perfecting the various conditions for seeing the Path, and investigating in accordance with the truth within profound meditative concentration. Therefore, those who have comprehended the Buddha-dharma intellectually need to forget what they have understood, let go of the knowledge and understanding they previously learned, abandon the desire for fame and gain, the competitive spirit, and vanity, and be willing to start over from the beginning—step by solid step, steady and unhurried. Only then is genuine realization possible. A great price must be paid along the way, and it is arduous, but every drop of sweat brings its harvest; no matter how great the price, it is worth it.