Number theory and electricity development was/is very much paid from public funds, even dollars. For wheel there obviously was no money at all, let alone dollars.
For most science there is no obvious commercialization at least in any predictable timeframes. When there is, it's typically called R&D.
A distinction should be made between public funds from specific agencies with specific engineering goals in mind (department of energy, department of national security, NIST, etc. etc. etc.), vs "science is good we need science, health is good we need health, tell your local bureaucrat buddy how you will use science to fix health and collect your paycheck" funding (NSF, NIH).
