# Category Archives: Foundations of Mathematics

## Are Real Numbers Real?

Undoubtedly, real numbers are the most fundamental things to describe literally everything we know about our physical world, so questioning if real numbers are real may appear to be as silly as questioning if our world is real. But seriously, … Continue reading

## Can $1+1$ be $1$?
$1+1=2$ is often quoted by laypeople (in mathematics) as an epitome of the absolute truth. Those who know a bit of mathematics know that that is not the case. For example, there is a number system where $1+1=0$. It is … Continue reading
## $1+2+3+4+\cdots=-\frac{1}{12}$?
No, folks! I am not drunk nor I am pot-headed. Yet, I am about to discuss the crazy identity $$1+2+3+4+\cdots=-\frac{1}{12}.$$ No, I am not joking either. This is actually pretty serious mathematics and is also pretty serious stuff even to … Continue reading