1. the math and arts which we make with discussion club

2. the math and arts which we make by discussion club
3. the math and arts with discussion club
4. the math and arts discussion club
[Which names are suitable (and grammatical) for a club name? In this club, students learn math and arts together with discussin. They discuss math and arts in this club.]

I think all are too wordy. Try this:

Math and Arts Discussion Club

All four options you provided can be considered suitable and grammatical for a club name. However, each option slightly varies in terms of meaning and emphasis. Let's break them down:

1. "The math and arts which we make with discussion club": This option suggests that the club members actively create math and arts projects using the discussion club as a medium or tool. It implies a collaborative approach where discussions lead to tangible creations.

2. "The math and arts which we make by discussion club": This option also highlights the creative aspect of the club, indicating that math and arts projects are generated as a result of discussions within the club. It emphasizes that the discussions play a pivotal role in the process.

3. "The math and arts with discussion club": This option emphasizes the role of the discussion club as a platform for engaging in math and arts activities. It suggests that the club is a setting or environment where students explore both subjects with the help of discussions.

4. "The math and arts discussion club": This option is more straightforward and concise, directly stating that the club focuses on math and arts discussions. It implies that the club is primarily centered around discussing these subjects.

Ultimately, the choice depends on the specific brand or image you want to create for your club. Consider the club's goals, values, and target audience when selecting a name.