India's Mathematica Diplomatica

Modern India has a strong record in mathematics but it is yet to undertake a concerted national strategy for the coming technology revolution.

The working of the mammoth global economic machine, the sustenance of societal well-being, the protection of environments, the forecasts of climate, and the rationale of the military strategy depend on numerical fidelity. The maintenance of global order, the deterrence against chaos, and the bedrock of the war depend on a nation's strength in mathematics. However, mathematics is much more than these urgent pursuits. The architecture of our Indian civilization has built, the music we have created, the harmony we have attained with nature has underpinnings of mathematics.

Modern India has a strong record in mathematics; much of it has been a scholastic undertaking. Today, India's high-school students top the international mathematics Olympiads; our space and the nuclear program has made immense progress due to strong mathematical competence, our scientists are members of the International Mathematical Union and various domestic and transnational mathematical societies, including those for classical, applied, industrial, and other domain-specific mathematics. However, the mathematics taught in schools, used in industry, and pursued by research professionals, are rarely linked to India's strategic necessities.

Eastern European countries and Russia have been home to world-leading mathematics curriculum and research for more than a hundred years. Their curriculum played a crucial role in supplying mathematical talent that built the U.S. and Soviet space and nuclear programs. The Enigma cipher used by Allied Forces to decrypt messages of the Axis Forces or the Manhattan Project all have links to the mathematics curriculum of Eastern Europe. Over the years, the U.S. has benefited from the massive migration of Eastern European and Russian mathematicians to their universities and innovation ecosystems. Today, most of the Fields and Abel's Prize winners affiliate to western institutions, but they have Russian and Eastern European origins. Despite reaping the benefits of talented people migrating, the U.S. mathematics curriculum continues to languish. Therefore, many talented U.S. students join study abroad programs such as the Budapest Semesters in Mathematics in Hungary, or Math in Moscow, and those taking place in Poland's Jagiellonian University. India has a strong mathematics scholastic culture, with deep classical roots and applied mathematics competence, but we have experienced a fate similar to that of Russia or Eastern Europe when it came to talent attrition. This is because, India is yet to undertake a concerted national mathematics strategy for the coming technology revolution.

If an invention is the pinnacle of science, technology, and engineering, for mathematics, solving a 'millennial prize problem' conjecture, as is called by the Clay Mathematics Institute of the U.S., is the zenith. However, not many know the importance of these conjectures and their close relations with scientific discoveries and technological inventions and innovations.

The fourth industrial age offers a small window-of-opportunity to every country, including India, to execute high-end technology applications of novel scientific concepts, thereby holding its intellectual property rights and control over their global standards. However, with the earlier mentioned plans, the policymakers are putting the cart before the horse. They have grasped how to make a tool but are not planning what to make out with the tool. For example, 'millennium prize problem’ conjectures such as the Riemann Zeta Function, the P versus NP Problem, the Navier-Stokes Existence, and the Smoothness of the Hodge Conjecture, if solved, can bring great strides in quantum physics, fluid dynamics, astrophysics, particulate physics, pandemic mitigation, financial and weather forecasting, climate models, ecosystem modeling, orbital dynamics, space travel, blockchain, and other complex frontier sciences. However, solving them requires apt use of emerging technologies like big data, cyber-physical systems, artificial intelligence, and supercomputing.

In recent years, the Government of India (GoI) has formulated several national innovation plans revolving around emerging sciences (S), technology (T), and engineering (E), but mathematics (M), the last constituent of STEM, seems to be absent in these plans. The GoI's National Supercomputing Mission or the NITI Aayog's National Strategy for Artificial Intelligence do not explicitly aim to advance cutting-edge mathematical capabilities in the country. This lapse symptomizes the unfamiliarity of policymakers to the unmissable fact that 'mathematics is at the heart of the fourth industrial revolution and the subsequent technology evolutions and revolutions to come.' If our technocrats and policymakers formulate strong mathematics R&D with emerging technologies our overseas dependency for various applications, be it financial or weather forecasting, big data analytics, or predictive pandemic modeling, will reduce tremendously.

Mathematics is not superficial, its substance, like of science, technology and engineering, lies is logic, metaphysical wisdom, and philosophy. Providentially, India is home to various co-existing schools in these profound areas of knowledge. The knowledge from these schools can be used to decipher novel mathematical conjectures and hypotheses. In turn, these conjectures can spawn both inventive and innovative leads in science, technology and engineering if we are able to express them in algorithms, natural language processors, supercomputing models, quantum operations or tools yet unknown to us. This transmission of mathematics from philosophy to applications will be crucial in the fourth industrial age. Therefore, it becomes essential for India's various mathematical societies to brainstorm with the schools of logic, metaphysics, and philosophy in search of newer millennium problem conjectures and other grand mathematical challenges. The GoI can play a vital role by introducing mathematics-driven diplomacy.

The classical schools of Indic logic, metaphysics, and philosophy are not limited to India's reverence and practice worldwide. These Indic schools' influence spans from Japan in the East to the United States in the West. The GoI can create a mathematics' melting pot' by facilitating to bring practitioners worldwide to gather under an India-led 'global mathematics grand challenge' project. This conjecture-to-reality grand-challenge will not be a theoretical undertaking but an applied pursuit. Such mathematics diplomacy will be a win-win for all those countries participating in it. For instance, many U.S. high-end technology manufacturers such as Cray and IBM have been active in India's supercomputing pursuits for decades. India should invite U.S academic institutions and high-tech manufacturers to participate in this 'global mathematics grand challenge.' France and India, in 2018, signed a three-year agreement to build the BullSequana series of supercomputers as part of India's National Supercomputing Mission. As the agreement comes to a successful closure in 2021, India can invite French academic institutions and manufacturers to participate in this challenge. France's participation will be vital as French mathematicians have postulated many of the Millennium Prize Problems.

In the coming days, when India develops quantum computing and AI-specific supercomputers, pursues internet-of-things, and other outlandish technologies, there is a need for understanding that these technologies are nothing but carts. India may eventually do well for itself by engineering (E) these technologies (T), but if it has to stay ahead of the game, then it will have to put four horses before the cart; these are philosophy, metaphysics, logic of science (S), and mathematics (M).

This blog was published in the December 2020 edition of Science India magazine published by Vijnana Bharati.