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I want to create a model using math without setting vertices by hand. Is it possible to use code to set vertices automatically?

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The simplest solution to being able to create a model via maths is to install the "Add Mesh: Extra Objects" add-on that somes shipped with Blender. Simply go into Preferences, Add-ons and search for 'Extra'. Enable "Add Mesh: Extra Objects" and you should have additional options within the 'Add/Mesh' menu for "Math Function".

The 'Math Function' option allows you to specify the details of the mesh surface to create by way of equations/variables. See What's the fastest and / or craziest way to model an arrow in Blender? for some examples.

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Yes, you can create geometry using python. However, you would have to learn python in the first place (if you don't know it yet) as well as understanding the API (if you don't know it yet). I'd suggest have a look into the docomentation and read about Bmesh which is the recommended way of creating meshes via python: https://docs.blender.org/api/current/bmesh.html

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