A substantive body of Hindu philosophic and mathematical thought, pertaining to the classic Mahayana school of Buddhism and known as Vijnanavada or Yogacara, can be seen as an early attempt at filling in some of the more elusive notion gaps while bridging the obscure later elaborations to their original legacy (Nagao, 1991, pp. 53-62).
More importantly, it borders on the forefront of the Western thought as in positivism, neo-positive, phenomenology studies, and their interplay with ontology discourse. Dating back to 4th-11th centuries CE, the school remains highly influential and increasingly relevant in treating some of the finer residual debates in the modern mathematics, as diverse as the classic versus the intuitive or constructivist schools, and reduction of these to formal logic along the lines of completeness and complexity dilemmas.
Thesis One: The stunning variety of Buddhist approaches to science could be reconciled in a parsimonious fashion based on a handful of core principles.
Whereas vijnana could somewhat loosely be construed as either the ultimate knowledge or indeed the threshold of consciousness short of irrelevance, the host of operational readings ranges anywhere in between the all-phenomenology and ontology-only extremes (Tagawa, 2009, pp. 21-22). The very notion of dharma takes on the seemingly dual connotations as either the optimum path or the perceived reality, with experience striking a careful balance with an eye on both. The two are at times opposed as the citta-matra versus the vijnapta-matra perspectives stressing the complete potentiality versus pragmatic representation (cf. Pingree, 1970, pp. 45-55). In other words, the wise could benefit even from the less ontologically reliable paradigms or instruments, insofar as that secures faster or more sustainable progress toward the ‘coveted’ objectives, the enlightenment and nibbana.
In effective terms, then, it is of lesser relevance to decide between the objective versus subjective idealist standpoints. Pure mind may or may not be the ultimate reality, and the subject versus the object may or may not be inseparable, let alone prove asymmetrically so. Suffice it to know exactly which stance acts to best accommodate the particular mind or the particular purpose, while rendering shunyata (emptiness or ultimate potentiality) the more economical and transferable instrument, if only based on the Occam razor criterion.
Thesis Two: The vast variety of mathematics schools of thought in Japan, China, and India apparently fit into experientialism in Zen as well as instrumentalism in Buddhism at large.
The very observation that Japan has maintained as much of an isolationist approach as it proved open to very distant technological traditions, applies to its mathematics as represented by a large body of schools while responsive to the distinctly Western approaches, as well. For one thing, Zen does cultivate practical verifiability and personal relevance as a cut-off criterion, thus setting few if any downright priors or biases (Dumoulin, 2005, pp. 61-63).
On the other hand, largely the same is posited in classical Buddhism (Needham, 1954, ch. 7), despite the cornerstone assumptions on the delusions and the limited ex-ante avail to delving in-depth on the interplay of the various manifestations of maya or even dharma.
Thesis Three: Although renowned as by far the more involved and arcane body of Buddhist thought, Vijnanavada in actuality captures many of the core complementarities evident in the Western legacy (Garfield, 2001, pp. 154-155), while making the interchange more tractable within each as well as between the two.
Apparently, the positivist notions of hypothesis refutability and experiment replicability leave out the issue of ultimate reality as though of second-order if unattained relevance. However, vijnanavada and neo-positivism alike look into the role of language and self-consciousness, in appreciating the missing links of coherent perception and apperception of reality as a whole (Yamabe, 2004). Arriving at the ever more general theories or elegant equations in physics could be explained along the lines of psychic processes that are similar to a conjectured ultimate patter design in the nature at large. Rahman (1972) and Bhargava & Chakrabarti (1989) have presented some common points that can be traced to the Hindu and non-Hindu impacts on the mathematical and adjacent thought. Kapur (1992) presents some new evidence on the mutual and cumulative West-East transferability.
Bhargava, P., and Chakrabarti, Ch. (1989). Of India, Indians, and science. Daedalus, 118(4), 353-368. [Presents some counter-intuitive accounts on the timelines and history, with an eye on how the earlier and subsequent ideas are interrelated.]
Dumoulin, H. (2005). Zen Buddhism: A history. Bloomington, IN: World Wisdom. [In retrospect, a close connection between the Chan/Zen tradition and the earlier yogacara is traced.]
Garfield, J. (2001) Empty words: Buddhist philosophy and cross-cultural interpretation. Cambridge: Oxford University Press. [An account of the oriental terms as bridged to their Occidental counterparts.]
Kapur, J. (1992) Development of mathematical sciences in India during the twentieth century. Indian Journal of History of Science, 27(4), 389-408. [An insight into the more recent West-East interchange building on the cumulative history.]
Nagao, G. (1991). Madhyamika and Yogachara. New York: SUNY Press. [Comparing and contrasting the close legacies.]
Needham, J. (1954). Conditions of travel of scientific ideas and techniques between China and Europe, in Science and Civilization in China, Vol 1. L: Cambridge University Press. [On some early precursors of the eventual Scientism paradigm.]
Pingree, D. (1970). Census of the exact sciences in Sanskrit. Philadelphia: American Philosophical Society. [The work addresses some mathematical and notional evolution with an eye towards the Sanskrit body of Hindu literature.]
Rahman, A. (1972) Trimurti science, technology & society: A collection of essays. New Delhi: People’s Publishing House. [Some overlapping instances of Arab, Persian, and Hindu influences.]
Tagawa, Sh. (2009) Living Yogacara: An introduction to consciousness-only Buddhism. New York: Wisdom Publications. [A highly readable background in the starting sections.]
Yamabe, N. (2004) “Consciousness, Theories of,” in Buswell, R., Macmillan Encyclopedia of Buddhism. New York, NY: Macmillan Reference. [The section dwells on some of the more critical mind-world correspondences.]