Introduction to ciphers and substitution. Alice and Bob and Carl and Julius: terminology and Caesar Cipher ; The key to the matter: generalizing the Caesar Cipher ; Multiplicative ciphers ; Affine ...

More than a century after Srinivasa Ramanujan scribbled his lightning-fast formulas for π in a notebook, physicists are finding that the same strange patterns help describe black holes and the fabric ...

For more than a century, Srinivasa Ramanujan’s uncanny formulas for the number pi have looked like pure mathematical fireworks, dazzling but detached from the physical world. Now a new wave of ...