Graph theory, eigenvalues, and applications to PageRank. Uncovering the structure and dynamics of networks algebraically.
The fascination of a theory applied from physics to finance and AI.
Mathematical proofs using randomness, and its connection to Ramsey Theory
Derive the FFT for finite DFTs and implement a complex-valued Python version. Distinguish FFT algorithms from the DCT and MDCT used in audio and image coding.
An in-depth explanation of the mathematical principles and information theory behind error-correcting codes, such as Hamming codes and Reed-Solomon codes, that protect digital data.
Expandable to topology, DNA, and quantum computing.
Delving deep into the Kakeya conjecture, starting from Soichi Kakeya's intuitive problem statement, to the discovery of Besicovitch sets, and the high-dimensional Kakeya conjecture in modern mathematics (harmonic analysis and partial differential equations).
Explaining everything from convenience stores and hospitals to server loads with a single mathematical theory.
Exploring the mathematical background of aperiodic tiling, from Penrose tiles and Shechtman's quasicrystals to the 2023 discovery of the 'Einstein (Hat)' tile.
Exploring 50 years of technical innovation and history in home video game consoles, from their birth to the present day.
Looking back at the evolutionary history of map projections, we explore deeply how humanity has perceived and represented the Earth's space, from the Mercator projection to the latest Equal Earth projection.
An in-depth guide to SI prefixes, from milli and mega to the newly added quetta and ronto, exploring the physics and scale of our universe.
A comprehensive explanation of the history of human timekeeping, from the isochronism of the pendulum to atomic clocks, time dilation by the theory of relativity, and the latest optical lattice clocks.
From the MS-DOS era to .NET, and into the age of cloud and AI. Unraveling the evolutionary path of Microsoft Visual Studio, which has shaped the history of software development.
A comprehensive guide covering the history and evolution of OpenGL starting from Silicon Graphics' IRIS GL, details of the graphics pipeline, fundamentals of matrix transformations, and practical implementation examples using C/C++ and GLSL.
Wasan is an advanced form of mathematics that developed uniquely in Japan during its isolation period. We explore the footsteps of genius mathematicians like Seki Takakazu and the mystery of 'Sangaku' dedicated to shrines and temples.
A thorough explanation of 'On the Origin of Species' and the theory of natural selection proposed by Charles Darwin, from historical background to modern population genetics and simulation implementation.
From the history of the moving sofa problem to mathematical approaches and the latest research results, we approach this unsolved geometric problem.
Drafted by 17 technologists gathered in Snowbird, Utah in 2001, the "Agile Manifesto for Software Development" revolutionized the industry. This article delves deeply into the historical background, the sense of crisis at the time, and the philosophy and essence that modern development organizations should truly learn from Agile.
An in-depth exploration of the 'Brain in a Vat' thought experiment and the Simulation Hypothesis from the perspectives of philosophy, quantum mechanics, and information theory. Is the world we live in reality, or a highly advanced virtual reality? A detailed reflection on humanity's ultimate question.
![Featured image of post [Behind the Agile Manifesto] The Trajectory of a Revolution that Laid the Foundation for Modern Software Development](/p/philosophy-agile-manifesto/eyecatch_hu9217002861231043496.jpg)
![Featured image of post [Brain in a Vat and Simulation Hypothesis] Is Our Reality Real?](/p/paradox-brain-in-a-vat/eyecatch_hu2136396691569261844.jpg)