I have spent time working on almost every impossible problem there is. This is a lie, but it is rooted in a kernel of truth. I remember my very first impossible problem. When I was eight or nine, my dad gave me a word problem about firemen and houses or…

There's this longstanding observation that we live in a "fine-tuned universe," which is to say that several fundamental physical constants (e.g. strength of gravity, electromagnetism) appear to be set perfectly for us. If they were any different, even by one part in a billion, the universe would…

I discovered a new (to me) way of approaching the Goldbach problem; this is a brief overview. Scratch page [ HTML | PDF ] Trying to prove there are always primes %p, q% such that %p+q = N% for any even %N > 2%, where %p <= q%. N.B. Largely ignoring 2…