Prerequisites: Max out Matheo's level 1 friendship
Reward: None
Unlocks: Unlock Matheo level 2 friendship
Really? Yes, you can earn the respect of the ever-angry Matheo, and the process works the same as anyone else - though winning Matheo over is more annoying than with most other villagers. Matheo lives on the outskirts of Moonbury Town, south of Forrest's House and the Ranger Post, and he almost never seems to leave his house. This will force you to make the trek south whenever you want to boost your friendship with the witch doctor. Jumping to the first Meadow Range Fast Travel point is the quickest way to get to him.
Once you've earned Matheo's trust (at least to a tiny degree) he'll post a notice on the Bulletin Boards of Moonbury Town, asking for aid in finding something. You can find out what by going to his house between 8:00 and 19:00, from Monday to Sunday. Matheo isn't happy to see you, but he has no choice, so...
The item you're looking for is Matheo's Notebook. He said he lost it while wandering through Meadow Range, and unfortunately for beginners he lost it while exploring the latter half of the area. To get to the Notebook you'll need to complete Clearing the Landslide, as well as collect all the resources needed to sweep the debris out of the path. Once you can access the Heart of Meadow Range, travel northeast of the Fast Travel point, then look in the clearing to the north that's full of Feverfew plants. The remains of the Notebook are here.
Take what remains of the Notebook back to Matheo, at his house. He's none too pleased about the state of his notes, and will tell you to leave. Well, you tried. This will nevertheless unlock the second level of friendship with Matheo, and once you boost your friendship enough you'll gain access to the next quest in his questline, Research Papers.