For our 6.5610 (Applied Cryptography) final project, we present an backdoorable DRBG based on Dual EC DRBG that, unlike Dual EC DRBG, is a true DRBG under suitable assumptions. Our algorithm, which we call the Twisted Dual EC DRBG, involves iteratively multiplying points on an elliptic curve or its quadratic twist.

The introduction contains background on how the NSA and NIST initially worked to backdoor a DRBG; LOL.

Ben Sparks explores hidden depths of a seemingly simple game.

Tic-tac-toe on a magic square. Hella neat, and hammers home how important representation is in mathematics.

Tony Padilla does a ‘magic trick’ with Fibonacci numbers and talks about Zeckendorf decompositions.

Nice set of videos on the theory of ordinals and their application to Goldstein sequences.

Interesting math relevant to compiler optimization.

Let m and n be positive integers. For the quantum integer [n]_q = 1 + q + ... + q^{n-1} there is a natural polynomial addition such that [m]_q \oplus_q [n]_q = [m+n]_q and a natural polynomial multiplication such that [m]_q \otimes_q [n]_q = [mn]_q. These constructions lead to the construction of the ring of quantum integers and the field of quantum rational numbers. It is also shown that addition and multiplication of quantum integers are equivalent to elementary decompositions of intervals of integers in additive number theory.

Very beautiful exposition. I hope all of my mathematical communications can be as clear as this.

via: https://www.youtube.com/watch?v=Fkc0pti6I3E

Mathematicians cannot determine whether multiplying pi by itself repeatedly might produce a whole number

A twin prime is a prime number p such that either p+2 or p-2 is also prime. For example, 11 and 13 are a pair of twin primes. The twin primes conjecture posits that there are infinitely many such pairs, but as of 2024 this conjecture remains unproven. This combo creates a board state where the outcome hinges on this unsolved math problem.

Funnest game ever!!