How could I replace Mathtype in a mathematic document with Catalina?
I had the same dilemma with Adobe CS5 and CS6. Ended up buying a refurbished 2018 Mac Mini directly from Apple. Came with Catalina preinstalled. Used the following steps to install Mojave.


Download Mojave from the link on the Apple website How to upgrade to macOS Mojave.
Use the Disk Utility application to create a new APFS volume in the existing APFS container.
Boot to macOS Recovery to allow booting from external media. You will only need to perform this step, if your Mac has the new T2 chip.
Used a flash drive to install Mojave to the new APFS volume. The instructions are given on the Apple website How to create a bootable installer for macOS.


You can now install your 32 bit applications. Basically, you will have a dual boot arrangement. When MathType 8 is released, you can install to the preinstalled Catalina. Mojave can be removed by using the Disk Utility to delete the APFS volume containing Mojave.

Before purchasing a refurbished Mac, you should confirm that the model was early enough to run Mojave. The website everyman.com is a good place to get this information. If for some reason the purchased model can not be downgraded to Mojave, Apple does have a 14 day return policy.

I should note that under Mojave I do get a error message when quitting an Adobe CS5 or CS6 application. Other than the message, the applications appear to function properly.