They have been giving out grants for Checking security of open source software. I think that in the past projects such as Rust and curl have gotten grants to make a review of the code.

Certainly, but how large was the budget?

Then compare it to the 10-100 billion euros spent annually on scientific research [1].

I'm not saying that the budgets should be equal, but there should be some proportionality.

I also think it should be easier for universities to have scientific programmers (who would write open source software) on their payroll.

It's especially important for Europe as more research on open protocols means that the internet can become less dependent on large US corporations. And for this type of research you'd need developers.

[1] https://www.nature.com/articles/d41586-019-01566-z

Traditional grants are a poor fit for OSS development. The application process adds a lot of overhead and results in payouts for those that optimize the process rather than write good software.

The best implementation I can see is for government institutions to vote on the most useful OSS software with awards for the winners.