The answer is simple: there is no largest number. In mathematics, numbers are infinite. However, the largest known number is a googolplex, which is 10 to the power of a googol, or 10^(10^100). A googolplex has so many zeros that it cannot be written out in normal numerical notation. Put simply, a googolplex is the biggest number there is - and beyond!
This isn't to say that bigger numbers can't be theoretically created though. In fact, various other numbers have been coined in mathematics – many of which are much larger than a googolplex. Some examples include Graham's number, TREE(3) and Skewes number.
Though these numbers are mindbogglingly large, they are all finite. An interesting notion in mathematics is that there can be infinitely larger numbers than any of those previously mentioned – no matter how huge the number is, another one could always exist that is even bigger. This is due to the fact that numbers are infinite, so there is no limit to how large a number could be.
So in conclusion, the largest number in the world is a googolplex. However, it is important to remember that bigger numbers can always theoretically exist – no matter how big they get! The concept of infinity means that the sky is truly the limit when it comes to understanding numbers.