Anyone following the news knows about the major breakthoughs that have taken place recently in $3$-manifold topology. These have come via a route whose big-picture I find to be conceptually ...
Which parts of mathematics are objectively true or false like finite arithmetic and which are only true, false or undecidable relative to a particular axiom system such as Euclidean geometry? ...
I remember attending a lecture given by an ultrafinitist who denied that curves are a set of points, he would only say that any particular point may or not be on the curve. Similarly for algebraic or ...
What are the relations between logic as an area of (modern) philosophy and mathematical logic. The world "modern" refers to 20th century and later, and I am curious mainly about the second half of ...
This post is partially about opinions and partially about more precise mathematical questions. Most of this post is not as formal as a precise mathematical question. However, I hope that most readers ...
Are there precise definitions for what a variable, a symbol, a name, an indeterminate, a meta-variable, and a parameter are? In informal mathematics, they are used in a variety of ways, and often in ...
In a thought-provoking answer to this MO question, Kevin Buzzard and several commentators have described a multitude of ways in which number theory is related to other parts of mathematics. It seems ...