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Every credit card number encodes a quiet mathematical guarantee. Here is the modular arithmetic that makes Luhn's checksum work — and the exact conditions under which it fails.
RSA has secured the internet for decades. Shor's algorithm, running on a sufficiently large quantum computer, renders it obsolete. Here is exactly how.
A rigorous but accessible introduction to differential privacy — what it means, why it matters, and how the mathematics actually works.
Elliptic curve cryptography offers the same security as RSA with dramatically smaller keys. Here is the mathematics that explains why.