Category Archives: Uncategorized

“Embarrassing” open problems in maths

There are many open problems in maths, most of which have the decency to sound appropriately daunting. For example, is it the case that “every Hodge class on a projective complex manifold X is a linear combination with rational coefficients … Continue reading

Posted in Uncategorized | 20 Comments

Four paradoxes involving infinity

I recently read an entertaining thought experiment claiming to show that energy isn’t conserved in Newtonian mechanics. It involves a sneaky trick using an infinite sequence of balls of decreasing size. In this post I’ll discuss this and some other … Continue reading

Posted in Uncategorized | Leave a comment

Guessing polynomials

Consider the following game: Alice chooses a polynomial p with non-negative integer coefficients and challenges Bob to determine the polynomial. Bob is allowed to ask Alice for the value of p(n) for an n of his choice and upon receiving … Continue reading

Posted in Uncategorized | 4 Comments

A (fairly) interesting equivalent to the negation of the continuum hypothesis

I recently saw an interesting equivalent statement to the negation of the continuum hypothesis. The statement is essentially Freiling’s axiom of symmetry, presented in a very slightly different manner. It’s interesting in that it seems more geometric and less abstract … Continue reading

Posted in Uncategorized | 1 Comment