Which of the Four Types of Wisdom—Śruta, Cintā, Bhāvanā, and Sākṣātkaraṇa—Does Knowing 1+1=2 Belong To?

The four wisdoms of hearing, contemplation, cultivation, and realization all know that 1+1=2, but the difference in this knowing is immense. A one-year-old child can know that 1+1=2; even a well-trained dog can know it. A university professor knows that 1+1=2, and a mathematician also knows that 1+1=2. How vast is the difference between them? Proving 1+1=2 belongs to a difficult problem within the Goldbach Conjecture. Among Chinese mathematicians, only Chen Jingrun and Hua Luogeng once attempted to demonstrate and prove it, but Hua Luogeng and other mathematicians did not succeed in providing a valid proof. 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 who can even begin to attempt the proof are no more than one in a hundred million. Those who can contemplate 1+1=2 are fewer than one in ten thousand or even one in a hundred thousand. Yet, those who simply know that 1+1=2 are countless.

So, since all of us know that 1+1=2, how much substance is there really in this knowing? Similarly, many Buddhists study the principles of the Four Noble Truths and the Dharma of Tathāgatagarbha for a few years, or only two or three years, or even just two or three months, and then claim they have realized or awakened. Naturally, the "water content" here is also quite substantial. Most people have not even reached the level of cultivation; they lack the conditions to practice truthfully and diligently. None of the conditions for realizing the path are fulfilled, so how can they talk about cultivating wisdom or realizing wisdom? Having the wisdom born of contemplation is already quite good. Therefore, the path of Buddhist study and practice is not so easy to walk. Do not overestimate yourself or underestimate the Dharma. Otherwise, with old karmic obstructions unresolved and new karma added, how can liberation be attained in future lives?

For children in kindergarten, elementary school, and middle school who wish to empirically prove 1+1=2, how should they strive? How can they perfect the conditions and causes for proving 1+1=2? With an empirical success rate of one in a hundred million, ten billion, or a hundred billion, how likely do you think it is for these children to achieve empirical proof in the future? What effort is required? Unless they are mathematical geniuses, there is almost no possibility. For proving 1+1=2, the most crucial part is the intermediate steps of logical deduction. The result is already given; the intermediate proof process is missing and needs to be filled in. During the process of argumentation, one must forget the result and treat it as unknown. To understand the hardship involved in the proof process, one only needs to learn about Chen Jingrun – the cost was immense.

Among Buddhists, there are also some who have studied and encountered the Four Noble Truths and the Prajñāpāramitā and Vijñānavāda teachings, but their proportion among all Buddhist practitioners is still very, very small. Among these people, there are varying degrees of knowing and understanding regarding the Mahayana and Hinayana vehicles. Within the four wisdoms, most belong to the wisdom born of hearing, a minority to the wisdom born of contemplation, and very few attain the wisdom born of cultivation. However, those who reach the level of the wisdom born of realization are probably exceedingly rare – perhaps one in a hundred million. So, for Buddhist practitioners who already know the principles of the Four Noble Truths and the emptiness principle of Tathāgatagarbha Prajñā but have not yet realized them empirically, how should they proceed to realize and directly perceive them? Or for those who have already understood the Dharma, who have comprehended the Dharma intellectually, how should they proceed to directly perceive and realize it empirically? What conditions need to be perfected, what efforts must be made, to truly realize it empirically? For this group who have understood and comprehended the Dharma intellectually, if they wish to realize the Dharma empirically, they need to forget everything they have understood and comprehended, treat the result as unknown, and not bring it into the process of investigation. This requires the wisdom born of cultivation, the actual practice of the Thirty-seven Aids to Enlightenment, the Threefold Training (precepts, concentration, wisdom), the Six Pāramitās of a Bodhisattva, and perfecting the various conditions for realizing the path. It requires investigating according to principle within profound meditative concentration. Therefore, those who have intellectually comprehended the Dharma need to forget what they have comprehended, let go of the knowledge and understanding they previously learned, abandon minds of fame, profit, competitiveness, and vanity, and be willing to start anew, step by step, steadily and surely, without haste or impatience. Only then is there a possibility of empirical realization. The process demands great sacrifice and is arduous; every drop of sweat yields its harvest. No matter how great the cost, it is worth it.

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