I want to buy a desk top UPON which I will run word processing programs and mathematical computer algebra including  Mathematica . I do not want to connect  this computer to the internet EVER. I plan to use thumb drives to tale files from it to my laptop  when I want to use the internet.

This is to try to avoid malware, cookies, virisus etc.

I see a weakness in my plan. The thumb drive could BECOME infected or if i download software onto the laptop and then copy it to the desktop.

Is my plan silly, IMPOSSIBLE and doomed to failure?

Thfayyour idea has merit if you are paranoid about security and 'Big Brother' and all that...
but sadly in the real world, although not impossible, it is silly and doomed to failure.
for one thing, as you point out, the USB stick will be the weak link and the day will come where someone gets careless and pow - malware time.
then there's software, Windows, drivers etc that will benefit from updates - not mandatory I agree - but nice to have.

plus it HAS to be on the web sometimes simply for Windows and new software install activations.
a healthy respect for security is good and these days a layered approach works best.
for example, Windows 10 inbuilt AV called Defender, a modified HOSTS file by MVPS, a browser ad-blocker and real time malware protection is as close to perfection as is humanly possible.

sure, things may still GET through but so will they with your USB approach.
Mark is right. The USB is the weak link.
Otherwise, almost any modern desktop PC can do what you want.