I’ll add to this to give an example of someone who I feel is doing a great job of satisfying this very request in the field of mathematics: Timothy Gowers.

His yt channel is an excellent resource of theoretical understanding through numerical methods.

Here’s my favorite series where he confirms/elucidates a “strange” theoretical fact with an explorative numerical style: https://m.youtube.com/watch?v=byjhpzEoXFs

Simply superb content.