Ramanujan and AI

Context:

• In early 2021, a team of Israeli scientists announced The Ramanujan Machine
• It is a software tool that creates mathematical conjectures i.e. equations without proof. Mathematicians then prove or disprove these conjectures, thereby establishing theorems.
• Conjectures in mathematics shed light on newer frontiers that otherwise lurk in tenebrous corners.
• Srinivasa Ramanujan was famous for such conjectures.

Srinivasa Ramanujan (1887-1920):

• Born in Erode, Tamil Nadu and died in Kumbakonam, Tamil Nadu.
• In 1911 Ramanujan published the first of his papers in the Journal of the Indian Mathematical Society.
• In 1913 he began a correspondence with the British mathematician Godfrey H. Hardy which led to a special scholarship from the University of Madras and a grant from Trinity College, Cambridge.
• In 1918 he was elected to the Royal Society of London.
• First Indian to be elected a Fellow of Trinity College, Cambridge University.

Contributions to Mathematics:

• Conjectures – From 1904 till his passing in 1920, Ramanujan, recorded more than 3,000 equations that were mostly conjectures because he did not supply proof.
• Most of Ramanujan’s conjectures are correct as established by the proofs provided pari passu with their generalisation in the last 100 years.
• Game Theory: He discovered a long list of new ideas to solve many challenging mathematical problems, which gave a significant impetus to the development of game theory. His contribution to game theory is purely based on intuition and natural talent and remains unrivalled to this day.
• Ramanujan’s Book: One of Ramanujan’s notebooks was discovered by George Andrews in 1976 in the library at Trinity College.
• Hypergeometric series, the Riemann series, the elliptic integrals, mock theta function, the theory of divergent series, and the functional equations of the zeta function
• Formulas and Equations: Ramanujan compiled around 3,900 results consisting of equations and identities. One of his most treasured findings was his infinite series for Pi.

Applications of Ramanujan’s work:

• Artificial Intelligence(AI)– AI makes things happen faster because they imitate cogitation.

• Due to findings of infinite series like fundamental constants of Pi – the artificial intelligence machines can lead to more frequent mathematical advancements.

• “Invincible originality” – Ramanujan could connect different mathematical domains deeply, leading to remarkable technological applications.
• Encryption – He developed certain equations called class invariants which generate elliptic curves suitable for encryption and this led to Elliptic Curve Cryptography

• It is an efficient cryptographic technique, in 1985 to make computer network communications secure.

• Discovery of mock-theta functions–  Ramanujan might have discovered it by starting from hypergeometric series whose consecutive terms form ratios that follow a pattern.

AI- enabled technologies:

• Latest advancements in AI technology have attempted to “create”, mimicking human intelligence, such as:-
• ChatGPT (Chat Generative Pre-trained Transformer) is a software tool that can answer questions on almost any topic, carry on conversations with humans, write poems, computer programs and perform many more complex tasks that require intelligence.
• Google’s LaMDA (Language Model for Dialogue Applications) that is similar to ChatGPT and other sophisticated products (Dall E) that can create image from verbal descriptions.
• Industrial Metaverse – Digitalizing processes of frontline workers, estimated to make up about 80% of the global workforce, have just started and there is enormous potential in the same.
• Augmented Reality/Mixed Reality – By linking these devices to data and workflows, industrial enterprises can create a new platform built around the needs of shopfloor workers.

Indian initiatives on AI:

• National Task force on Artificial Intelligence 2017 launched to explore possibilities to leverage AI for development across various fields.
• NITI Aayog’s  ‘National strategy for Artificial Intelligence’ identifies five core areas for application of artificial intelligence
• The PM-STIAC’s Artificial Intelligence (AI) mission 2018 focuses on efforts that will benefit India in addressing societal needs in areas such as healthcare, education, agriculture, smart cities and infrastructure, including smart mobility and transportation, academia-industry interactions on developing core research capability – creation of new knowledge and in developing and deploying applications.
• Centre of Excellence in Artificial Intelligence (CoE in AI) has been established by National Informatics Centre (NIC) in 2019.

Way forward:

• AI is playing an integral role in transforming the way businesses have been conducting operations across numerous industries.
• The pandemic and remote working models have pushed companies to embrace using remote experts to create genuinely seamless end-to-end customer experiences, as 80 per cent are deskless workers.
• #AIforAll will aim at enhancing and empowering human capabilities to address the challenges of access, affordability, shortage and inconsistency of skilled expertise and technology leadership for achieving the greater good.

Source: The Hindu