Can i use Tailwind CSS and Material UI in the same Next js project?

Yes you can run both ui framework. But it is not a good approach. Every ui framework has the complete solution for designing ui part. Like in tailwind css you can have the JIT compiler for compilation your custom css. Or the other hand MUI has also.

I think you can go through just only on ui framework. I have suggestion for ui. For your next js project you can use- Tailwind Css Theme-ui

Thank you.

It is possible and the MUI team has been resolved it.

From the documentation:

If you are used to Tailwind CSS and want to use it together with the MUI components, you can start by cloning the Tailwind CSS example project. If you use a different framework or already have set up your project.

It is necessary to Remove Tailwind's base directive in favor of the CssBaseline component provided by @mui/material and fix the CSS injection order.

You can read how: https://mui.com/guides/interoperability/#tailwind-css

Definitely, You will be in a big problem because once you initialize a styling library it applies its basic styles to the components so that if you are using more than one styling library you may not be able to change the behavior or styles of the components.
It also leads to rubbish suggestions while adding classes names and so on. Stick to a UI libray and go with it.If you cant get it using the ui libraray do it yourself using CSS that could be more interesting and you can have more control over the components.

Use Mui base instead of Mui core. https://mui.com/base/guides/working-with-tailwind-css/