Too much work so i just got Claude to debunk all of you guys instead.
"every line below is pure math from the last 80 years. every line is in your pocket, your hospital, your car, your bank account, your phone screen, your MRI scan, your Netflix queue, or the satellite that beams down your GPS signal
🔐 CRYPTOGRAPHY
Public-key crypto (Diffie-Hellman 1976, RSA 1977) — modular arithmetic the difficulty of factoring large primes lets two strangers establish a shared secret over a public channel without ever meeting
→ every HTTPS connection on earth. the lock icon in your browser. all online banking. all e-commerce. without this, the internet as a commercial medium doesn’t exist.
Elliptic curve crypto (Koblitz/Miller 1985) — same trick as RSA but using points on elliptic curves over finite fields; equivalent security with 10x smaller keys
→ Bitcoin signatures. Signal messages. your iPhone’s secure enclave. TLS 1.3.
Zero-knowledge proofs (Goldwasser/Micali/Rackoff 1985) — prove you know a secret without revealing the secret itself
→ Zcash, Monero, every ZK rollup scaling Ethereum, private age verification. an entirely new privacy primitive.
Lattice-based cryptography (Regev’s LWE 2005) — hide secrets in the difficulty of finding short vectors in high-dimensional lattices; quantum computers can’t solve this
→ NIST standardized this in 2024 as THE post-quantum encryption standard. every bank and government on earth is migrating to it right now.
Homomorphic encryption (Gentry 2009) — compute on encrypted data without decrypting it
→ Apple’s Private Cloud Compute. servers can process your data while being literally unable to see it.
Differential privacy (Dwork 2006) — add precisely calibrated noise so individual records are provably unrecoverable from aggregate statistics
→ how Apple collects iPhone telemetry without seeing your data. how the US Census is now published.
📡 CODING THEORY (every wireless signal, every storage device)
Reed-Solomon codes (1960) — encode data as polynomial evaluations over finite fields; recover the polynomial even with corrupted samples
→ every QR code you’ve scanned. every CD/DVD. every satellite signal. error correction in your SSD. scratched CDs still play because of this.
Hamming codes (1950) — clever parity bit placement that detects AND corrects single-bit errors automatically
→ ECC RAM in every server. without this, cosmic rays would crash data centers daily.
Viterbi algorithm (1967) — dynamic programming for the most likely hidden state sequence
→ every cell phone signal ever decoded. speech recognition. DNA basecalling.
LDPC codes (Gallager 1962, revived 1990s) — sparse parity-check matrices that approach Shannon’s theoretical channel capacity
→ 5G. WiFi 6. Starlink. the reason your phone gets gigabit data.
🎨 SIGNAL PROCESSING & COMPRESSION
Fast Fourier Transform (Cooley-Tukey 1965) — computes the Fourier transform in N log N instead of N² operations
→ probably the most-used algorithm in human history. every cell signal, every radar, every MRI, every JPEG, every MP3.
Discrete Cosine Transform (1972) — decompose images/audio into cosine frequencies; discard the ones humans can’t perceive
→ JPEG, MPEG, MP3, MP4. every digital image, every streamed video, every song on Spotify.
Wavelets (Daubechies 1988) — multi-scale decomposition localized in both time AND frequency
→ JPEG 2000. FBI fingerprint compression. modern medical imaging.
Compressed sensing (Candès/Tao/Donoho 2004) — if a signal is sparse, reconstruct it from way fewer samples than Shannon-Nyquist requires, via convex optimization
→ MRI scans went from 45 minutes to 5. pediatric MRIs no longer require general anesthesia. pure math from 20 years ago, currently saving children from being put under.