Why would you need to experiment if it's pure mathematics? Don't you just spend your whole day writing down complicated computations using weird symbols and popping theorems out of your head? This talk is here to show you that pure mathematics is not always like this. We're going to explore some combinatorics questions like "how many binary trees of size 42 are there?" or "What does a random binary tree of size 1000 looks like?" and see how computer exploration plays an essential role in finding and proving new results. Doing so, we'll see what kind of code and structure we use and understand the aim of pure mathematical programming. All examples will be written in python using the mathematical software Sage. So this is also an occasion to discover about Sage through actual research based examples and demo. No previous Sage or mathematical knowledge is needed.