Srinivas Ramanujan
Context:
- According to English computer scientist Alan Turing, a machine successfully simulates human intelligence (i.e., may deceive others into thinking it is a human-like intelligence) if it responds to a question like a human mind does. It assesses a machine’s ability to behave intelligently in a way that is either similar to or hard to distinguish from human behaviour.
Machines with intelligence (IM):
- Artificial intelligence, in contrast to animal and human intelligence, describes the perception, synthesis, and inference of information displayed by robots.
- According to Plato, who recognised mimesis (representation) as the fundamental principle of art, “the key to AI has always been the portrayal” (Jeff Hawkins).
Man vs Machine:
- In the case of extended representation, can a machine “create” new things? Recent technical advancements have attempted to “create”. Artificial intelligence may “create” as seen by the recent buzz surrounding ChatGPT (Chat Generative Pre-trained Transformer), a piece of software that can talk with people, write computer programmes, compose poetry, and carry out many other complicated tasks requiring intelligence.
- The AI research firm OpenAI has developed a dialogue-based prototype chatbot called ChatGPT that can comprehend actual human speech and generate incredibly sophisticated written content. It is trained using a machine learning technique known as Reinforcement Learning from Human Feedback (RLHF).
- The same is true for Google’s LaMDA (Language Model for Dialogue Applications), an advanced technology (Dall E) that is akin to ChatGPT and can generate graphics from voice descriptions. In general, the aforementioned objects develop their creativity by learning to combine pre-existing information, such as conversations, documents, and photos.
Machine-based analysis:
- When these capacities are increased, can a machine conduct research? In the beginning of 2021, a team of Israeli scientists unveiled the Ramanujan Machine, a piece of software that creates equations devoid of supporting data. Mathematicians then confirm or disprove these conjectures to produce the theorems. If not for mathematical theories, tenebrous crevices would conceal more recent frontiers.
- Such theories were Srinivasa Ramanujan’s area of expertise. Between 1904 and 1920, Ramanujan produced more than 3,000 equations, the majority of which were conjectures because he offered no proof. According to American mathematician and Ramanujan specialist Bruce C. Berndt, the proofs that have been provided alongside the generalisation of the majority of Ramanujan’s conjectures during the past 100 years provide evidence that they are correct.
The “unparalleled ability” of Ramanujan:
- How does the Ramanujan Machine resemble Ramanujan? To comprehend this, think about Ramanujan’s formulas on (22/7 is merely an approximate approximation to).
- In general, a modular equation is an equation in x that is identical to the same equation in powers of x, or x n. In 1914, Ramanujan published a series of equations that used this equation to compute; the equation’s solutions were modified to yield decimals with remarkable accuracy.
- However, the Ramanujan Machine employs a different technique to construct equations for numbers like e, and others. This is done by using an equation with two unmatched sides and a mathematical structure on one side, such as a continuous fraction, and a mathematical constant on the other. The software then repeatedly matches both sides using sophisticated algorithms and computing power, which results in the identification of a conjecture. In recent years, many of conjectures have been found using this strategy.
A wise move:
- It was insight on the part of Ramanujan to foresee the ramifications of these connections between mathematical abstractions, which have been unravelling for more than a century and have led to incredible technological developments.
- For instance, elliptic curves are a hot issue in number theory due to the potential applications of their properties to secure computer network communications.
- Ramanujan, who developed a system of equations known as class invariants that result in elliptic curves suitable for encryption, made significant contributions in this field. Elliptic Curve Cryptography became widely accepted as a secure cryptographic technique as a result decades after his passing, in 1985.
- Another illustration of his inventiveness was the discovery of mock-theta functions, which served as his swan song. Ramanujan might have discovered it by starting with hypergeometric series whose succeeding terms develop ratios that adhere to a pattern.
- Only seldom have equations including fundamental constants like been found throughout the history of mathematics. The machine can lead to more frequent mathematical successes by making such discoveries automatic and more prevalent.
Conclusion:
- The prevailing expectation is that artificial intelligence technologies will speed up operations because they can currently mimic cogitation. Ramanujan is exceptional even in the age of artificial intelligence.
