Blog
Occasional Random thoughts from us.
The Math Behind Image Compression
A JPEG throws away most of a photo's data and you rarely notice. Here is how color spaces, the discrete cosine transform, quantization and Huffman coding make that possible.
The Math Behind Google Search
Google's original breakthrough was an eigenvector. Here is how PageRank turns the web into a matrix, why a random surfer model works, and what TF-IDF adds.
The Math Behind Google Maps
Every route you request is a shortest-path problem on a graph with hundreds of millions of edges. Here is the graph theory, geometry and prediction math that answers it in milliseconds.
The Math Behind GPS: How Your Phone Knows Where You Are
GPS is really a clock problem. A one-nanosecond timing error puts you 30 cm off, and ignoring Einstein would add about 11 km of error every day. Here is the math.
The Math Behind Bitcoin
Bitcoin's 21 million coin limit is the sum of a geometric series. Here is the math of hashing, proof of work, elliptic curve signatures and why six confirmations are "enough."
Why Prime Numbers Matter to Modern Cryptography
Researchers once broke tens of thousands of real encryption keys with nothing more than a greatest-common-divisor calculation. Here is why primes secure the internet, and what goes wrong when they are chosen badly.
The Mathematics of Public-Key Encryption
How can two strangers agree on a secret while everyone listens? A worked, small-number walkthrough of Diffie–Hellman and RSA, using only modular arithmetic.
The Mathematics Behind Cryptography
A cipher with 403 septillion possible keys was broken over a thousand years ago with simple counting. Here is how cryptography evolved from letter shuffling to modern mathematics.
The Mathematics Behind QR Codes
You can cover almost a third of a QR code and it still scans. Here is the geometry, binary encoding and Reed–Solomon error correction that make that possible.
How Error-Correcting Codes Make Digital Communication Possible
Every phone call, Wi-Fi packet and deep-space photo arrives with errors. Parity bits, Hamming codes and Shannon's theorem explain how the errors get fixed without anyone noticing.
What Is a Checksum and Why Does It Work?
Your credit card number, every book's ISBN and every barcode contain a check digit that catches typos. Here is the modular arithmetic behind Luhn, ISBN, UPC and CRC, and which errors each can and can't detect.
Hash Functions: The Mathematics Behind Modern Software
Hash functions power dictionaries, passwords, Git and blockchains. Collisions are mathematically guaranteed, so the whole game is making them hard to find. Here is the math, and what happened when MD5 and SHA-1 broke.