“Does the barber who shaves all those in the town who do not shave themselves, shave himself?” This article explains Bertrand Russell's terrifying paradox that shook the foundations of mathematics, “set theory”, and changed the history of logic.
Even when we know that "cooperating with each other yields the best result", why do humans end up betraying each other? Through "The Prisoner's Dilemma", the most famous model in game theory, we will explain mathematically and psychologically the mechanism by which individual rationality creates collective irrationality.
Did you know that if you cut a single pea and reassemble it like a puzzle, it can become as large as the sun? We explain the bizarre world of the "Banach-Tarski Paradox", the most counterintuitive yet logically perfectly correct theorem caused by the "Axiom of Choice" in modern mathematics.
Can the swift hero Achilles never catch up to the slow-footed tortoise? The most famous of Zeno's paradoxes has troubled philosophers and mathematicians for over 2,000 years. We will mathematically unravel the trick of this logic using the concepts of the sum of infinite series and limits.
A TV show game where you choose a winning prize from 3 doors. Should you change your choice after the host opens a losing door? We thoroughly explain the "Monty Hall Problem", which caused a huge controversy involving mathematicians worldwide, from the perspectives of probability theory, Bayesian inference, and cognitive psychology.
Whether it is a school class or a company department, when just 23 people gather, the probability of two people sharing the same birthday exceeds 50%. We explain visually and mathematically using probability theory and graphs how easily human intuition overlooks this "combinatorial explosion".
Three guests pay $30, later $5 is returned, but the waiter pockets $2 and only returns $3. The guests pay $9 each, totaling $27. Adding the waiter's $2 makes $29. Where did the remaining $1 go? A complete explanation from the perspectives of mathematics, psychology, and accounting.
Two envelopes are in front of you. One contains twice as much money as the other. If you switch envelopes without opening yours, do you always gain in terms of expected value? Through the "Two Envelopes Paradox" where intuition and mathematics violently clash, we thoroughly explain the pitfalls of expected values and the concept of infinity.
Provides a thorough explanation of the background leading to the dawn of quantum computers, from the physical limits of classical computers and the end of Moore's Law to the barriers of quantum mechanical effects like quantum tunneling. This is Chapter 1 of the complete guide to understanding next-generation information processing technologies.
A thorough explanation of the 'double-slit experiment', known as the most beautiful experiment in the history of physics. We summarize the abnormalities of the micro world, where the common sense of the macro world does not apply, and the profound mysteries of quantum mechanics in a way that is easy for beginners to understand.
The prime factorization problem that underpins the security of RSA encryption. We thoroughly explain with formulas and conceptual diagrams everything from the mathematical mechanism of the strongest classical algorithm 'General Number Field Sieve (GNFS)' to why 'Shor's Algorithm' by quantum computers can break it.
Explains the basics of the 'quantum computer', which has the potential to exceed the limits of traditional supercomputers. It expertly and clearly unravels the mechanism of utilizing mysterious phenomena of quantum mechanics for computation, such as superposition, quantum entanglement, and quantum gates.
Public key cryptography faces the risk of being decrypted in the future due to the practical application of quantum computers. This article explains in detail the mechanism and importance of 'Post-Quantum Cryptography (PQC)', a next-generation security technology being developed to counter this threat (the Y2Q problem).
Explains how RSA encryption, which supports modern communication infrastructure, is threatened by the rise of quantum computers. Discusses the future of next-generation cryptanalysis and security, from the mechanics of Shor's algorithm to the current state of hardware in the NISQ era.
A thorough explanation with C++ implementation code of the mechanism of the 'General Number Field Sieve (GNFS)', a prime factorization algorithm used to crack RSA encryption. Must-see content for programming enthusiasts, approaching the abyss of calculation logic using the Boost library and algebraic number theory.
We explain the true mathematical structure of the General Number Field Sieve (GNFS), a prime factorization algorithm. We unravel the advanced mechanism for efficiently factoring huge composite numbers using 'homomorphisms' that connect the real world of integers with the world of algebraic number fields.
Explains the mechanism of 'General Number Field Sieve (GNFS)', humanity's strongest mathematics for breaking the RSA encryption that protects internet communications. Omits jargon to reveal the tricks of this magical algorithm, understandable with just junior high school math.
We explain the pros and cons of 'anti-vaccine' movements surrounding the COVID-19 vaccination and the lessons of epidemiology. We explore the importance of scientific thinking without being misled by media information, by understanding cognitive biases like 'confounding' and 'illusion of causality' in post-vaccination cases.
Analyzes the realities of soaring prices and an aging population behind the term 'Japanese First', which is gaining support in Japan in 2026. Eliminates emotional arguments to examine the true nature of social issues based on objective data and considers what future coexistence should look like.
We explain the correct cancellation procedure to prevent the 2,900 yen/month Google One membership from automatically continuing after the 1-month free trial of Gemini ends. If you are troubled by 'cannot cancel', please refer to the withdrawal method in this article.
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