Here are four clear bullet points summarizing the article: • Terence Tao predicts AI will bring about an era of "Big Mathematics" where humans and machines collaborate on complex problems. • Historically, mathematicians derive joy from understanding and solving abstract mathematical problems, driven by a sense of accomplishment and beauty. • AI systems are making inroads into bypassing the slow process of human mathematical reasoning, with some systems already achieving Ph.D.-level research results independently. • The future of mathematics is uncertain, with the potential for AI to sideline humanity completely or create new opportunities for collaboration between humans and machines.

Here are four clear bullet points summarizing the article: • Researchers from the MIT Hardness Group have found that determining whether Super Mario can reach his goal is at least as complicated as decoding financial transactions' encryption. • The team, led by Professor Erik Demaine, created levels in the game using fan-made editors and Super Mario Maker that are undecidable, meaning it's impossible to write a computer program that always correctly predicts if Mario can reach the castle. • The findings pushed Super Mario into the RE-Complete complexity class, which contains undecidable problems, contrary to previous assumptions that the game belonged in the PSPACE complexity class. • The proof relies on a reduction technique, where the team breaks down the video game using localized parts of Mario's path called gadgets, making it impossible to write a computer program that always correctly predicts if Mario can reach his goal.

Here are four clear bullet points summarizing the article: • Determine monthly installment amounts for loans, including mortgages and personal loans. • Calculate returns on Systematic Investment Plans (SIPs) to track investment growth. • Estimate maturity amounts and interest earned on Public Provident Fund (PPF) and Fixed Deposits (FD). • Use a Mutual Fund Calculator to estimate pension corpus accumulation under National Pension Scheme (NPS).

Here are four clear bullet points summarizing the article: • Determine monthly installment amounts for loans using a calculator. • Estimate returns on Systematic Investment Plans (SIPs) with a calculator. • Calculate maturity amount and interest earned on Public Provident Fund (PPF) and Fixed Deposits (FD). • Estimate pension amounts and corpus accumulated under National Pension Scheme (NPS) with a Mutual Fund Calculator.

Here are four clear bullet points summarizing the article: • Determine monthly installment: Calculate loan payment amounts with ease. • SIP returns estimation: Forecast investment returns through Systematic Investment Plans (SIPs). • Maturity and interest calculation: Know maturity amount and interest earned on PPF and Fixed Deposits (FD). • Pension and corpus estimation: Estimate pension amount and accumulated corpus under National Pension Scheme (NPS).

Here is a summary of the article in 4 clear bullet points: • The TOI Science Desk is a team of journalists dedicated to covering scientific news and discoveries. • They curate articles from various fields, including genetic engineering, space exploration, and artificial intelligence. • Their goal is to make science accessible and engaging for readers of all backgrounds by demystifying complex topics. • The TOI Science Desk aims to tell scientific stories in a way that brings readers on a journey of discovery and enlightenment.

Here are four clear bullet points summarizing the article: • Mathematicians conjecture that in a group of runners jogging around a circular track, every runner will end up "lonely" (far from everyone else) at least once, no matter their speeds. • The "lonely runner" problem is equivalent to various questions in number theory, geometry, and graph theory, making it a challenging and complex mathematical puzzle. • Recent breakthroughs by mathematicians Matthieu Rosenfeld and Tanupat Trakulthongchai have proven the conjecture for eight and ten runners, respectively, after a long-standing stalemate. • The problem has been reframed and solved using computer-assisted proofs, demonstrating that the speeds of the runners must be highly constrained to prevent at least one runner from never ending up alone.

Here are four clear bullet points summarizing the article: • Researchers from Peking University developed an AI framework that bridges the gap between natural language reasoning and formal machine verification. • The framework successfully solved an open problem in commutative algebra and automatically formalized the proof with minimal human intervention. • The AI performed mathematical tasks faster than human mathematicians, including working independently on complex problems that typically require collaboration. • The research demonstrates how AI can substantially automate mathematical research, with potential to accelerate scientific discoveries.