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

All four wisdoms of hearing, reflection, cultivation, and realization know that 1+1=2, but the difference between kinds of knowing 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 knows that 1+1=2. How great, exactly, is the difference among them? 1+1=2 belongs to the difficult problems within the Goldbach Conjecture. Among Chinese mathematicians, only Chen Jingrun and Hua Luogeng ever set out to demonstrate 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 completely proved it. Those capable of proving 1+1=2 are fewer than one in a hundred million; those able to attempt the proof are no more than one in a hundred million; those able to ponder 1+1=2 are fewer than one in ten thousand, even one in a hundred thousand; yet those who can know that 1+1=2 are countless.

So all of us know that 1+1=2—how diluted, then, is this knowing? By the same token, many Buddhist learners have studied the principle of the Four Noble Truths and the dharma of the tathāgatagarbha, studying for several years, or only two or three years, or even just two or three months, and then claim they have realized and awakened. The dilution here is, of course, equally enormous. Most people have never reached the level of cultivation, lacking the conditions to practice genuinely and solidly; none of the conditions for seeing the path are fulfilled—how can there be any talk of the wisdom of cultivation and the wisdom of realization? To have even the wisdom of reflection is already 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, new karma will be added—how could there be liberation in future lives?

For children in kindergarten, elementary school students, and middle school students, if they want to genuinely realize that 1+1=2, how should they strive? How should they perfect the conditions for proving 1+1=2? With a realization ratio of one in a hundred million, one in a billion, one in ten billion—how likely do you think it is that these children will genuinely realize it in the future? How must they strive? Unless they are a mathematical genius, 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 is missing and needs to be completed. In the process of demonstration, one must forget the result and treat the result as unknown. As for the hardship of the demonstration, just look at Chen Jingrun and you will know—the price was enormous.

In Buddhism, there are indeed some Buddhist disciples who have studied and engaged with the Four Noble Truths and the prajñā and Yogācāra teachings, but their proportion among all Buddhist learners is still very, very small. Among these people, there are varying degrees of knowing and understanding of the Mahāyāna and Hīnayāna dharmas. Most of the four wisdoms belong to the wisdom of hearing, a minority to the wisdom of reflection, and only a very few possess the wisdom of cultivation; but 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 principle of the tathāgatagarbha but have not yet genuinely realized them, how should they proceed to realize and personally verify them? Or for those who have already understood the Buddha-dharma and attained interpretive awakening of it, how should they go on to personally verify and genuinely realize it? What conditions must be perfected, and what efforts must be made, for genuine realization? For those who have understood the Buddha-dharma and attained interpretive awakening of it, in order to genuinely realize the Buddha-dharma, they must forget everything they have understood and awakened to, treating 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, meditation, and wisdom, the bodhisattva's six pāramitās, perfecting the various conditions for seeing the path, and investigating in accordance with the truth within profound meditative concentration (samādhi). Therefore, those who have attained interpretive awakening of the Buddha-dharma need to forget what they have understood, let go of the knowledge and understanding they previously learned, abandon the craving for fame and gain, the competitive spirit, and vanity, and be willing to start from the very beginning—step by solid step, steadfast and unhurried. Only then is genuine realization possible. A great price must be paid along the way, and it is very arduous, but every drop of sweat brings its harvest; no matter how great the price, it is worth paying.