research11 min
The Riemann Hypothesis: A 2026 Status Report
The greatest unsolved problem in mathematics
The Riemann Hypothesis, proposed in 1859, remains unproven. We survey recent progress, computational verification to...
Akhilesh Yadav
All Articles
Deep dives into mathematical beauty, research frontiers, and the equations shaping our world.
Showing 1–6 of 12 articles
ai-ml9 min
The Mathematics of Self-Attention: Deconstructing the Transformer
Inside the equation that powers modern AI
The Transformer architecture revolutionized AI with a single mechanism: self-attention. We break down the linear...
Akhilesh Yadav
essay8 min
The Most Beautiful Equation: Why Euler's Identity Captivates Mathematicians
A meditation on e^{iπ} + 1 = 0
Euler's identity unites five fundamental constants in a single, breathtaking equation. We explore why mathematicians...
Akhilesh Yadav
ai-ml10 min
The Geometry of Gradient Descent: Curvature, Saddle Points, and Loss Landscapes
Why optimization in deep learning is a geometric problem
Gradient descent navigates high-dimensional loss landscapes shaped by curvature and saddle points. We explore the...
Akhilesh Yadav
history7 min
Ramanujan's Infinite Series for 1/π: Genius Without Proof
The extraordinary formulas that arrived in letters from Madras
Srinivasa Ramanujan produced formulas for 1/π of staggering complexity and beauty — with no formal proofs. We trace the...
Akhilesh Yadav
applied7 min
Spectral Methods for Solving Partial Differential Equations
When Fourier meets computation
Spectral methods transform PDEs into algebraic systems using global basis functions. We survey how Fourier and...
Akhilesh Yadav
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