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Featured Articles on: ALGEBRA
The ‘STEM-Quant’ Module: A New Optional Add-on for Engineering Applicants
Master the STEM-Quant Module GRE with our comprehensive guide. Explore technical details, strategic benefits, and how this optional add-on helps engineering applicants stand out for MIT, Stanford, and beyond.
Viral 9 ÷ 9 Math Puzzle: Technical Analysis of the 2026 Trend
Explore the technical logic behind the viral ‘9 ÷ 9 = 9 × 9’ puzzle. A deep dive into operator precedence, syntactic ambiguity, and computational parsing.
Terence Tao Solves Erdős-Herzog-Piranian Conjecture via Aristotle AI
In a 2026 breakthrough, Terence Tao uses Aristotle AI and Lean 4 to solve the Erdős-Herzog-Piranian lemniscate conjecture. Explore the technical details of this AI-math collaboration.
Masaki Kashiwara 2026: Closing the Analysis-Topology Gap
Explore Masaki Kashiwara’s groundbreaking 2026 paper on the Riemann-Hilbert correspondence, D-modules, and its impact on quantum technology and mathematical physics.
2026 Global Math Proficiency Crisis: The Case for Phone-Free Schools
A technical analysis of the 2026 global math proficiency decline to 41.7% and the legislative push for bell-to-bell cellphone bans in schools.
Fields Medal 2026 Predictions: Rumors and Betting Markets Peak
Explore the surging betting markets and expert predictions for the 2026 Fields Medal ahead of ICM Philadelphia. Analysis of Hong Wang, Yu Deng, and more.
DeepMind AlphaProof 2.0: Alien Matrix Multiplication Algorithms Discovered
DeepMind’s AlphaProof 2.0 discovers ‘alien’ matrix multiplication algorithms in Nature Physics paper, marking a new era of autonomous mathematical discovery.
Functional Equations: Solving f(x+y) = f(x) + f(y) + 2xy
A technical analysis and step-by-step solution for the advanced functional equation f(x+y) = f(x) + f(y) + 2xy with the boundary condition f(1) = 2.
Calculating Root Power Sums: Viete’s Formulas and Symmetric Sums
A technical guide to using Viete’s Formulas and Symmetric Sums to calculate the sum of squares for roots of cubic equations, including Newton-Girard identities.
Infinite Geometric Series: Detailed Solution and Convergence Analysis
A comprehensive technical guide to solving infinite geometric series with detailed proofs, step-by-step arithmetic, and historical context.
Solving Absolute Value Inequalities: A Technical Guide to |3x – 4| ≥ 11
A detailed technical walkthrough of solving absolute value inequalities using disjunction logic. Includes step-by-step algebraic resolution and theoretical deep dive.
Complex Number Evaluation: Solving ##z^3 + 8 \text{ for } z = 1 + i\sqrt{3}##
A technical guide to evaluating complex expressions. Learn how to compute ##z^3 + 8 \text{ for } z = 1 + i\sqrt{3}## using De Moivre’s Theorem and binomial expansion.
Functional Equations: Solving ##f(x+y) = f(x) + f(y) + 2xy##
Technical Specifications and Variable Analysis Formal Problem Definition The mathematical operation under investigation involves a classic challenge in Logarithmic Equation Solving where the primary variable is embedded within multiple transcendental terms. We are taske…
Systems of Linear Equations: Solving Solving ##3x+2y=16 \text{ and } x-y=2##
A technical guide to solving systems of linear equations using substitution and matrix methods, including detailed proofs and historical context.
Solving Quadratic Equations ##x^2 – 7x + 10 = 0##
A professional deep dive into solving quadratic equations using the factoring method. Step-by-step analysis of ##x^2 – 7x + 10 = 0## with technical proofs and historical context.