According to Kant our empirical experience is synthesized from sensations through categories. Apparently, unconscious "productive ability of imagination" mediates the process using the schemes of space and time. Curiously, Kant's examples of this (mental) synthesis come from scientific reconstructions, such as Euclidean geometry or Newtonian mechanics. So it seems that Kant identifies mental synthesis of knowledge with its reconstruction in sciences, where indeed some mathematical structures are a priori necessary to make empirical claims meaningful (like notions of geometry and calculus in mechanics). 

In hindsight, Kant's identification was clearly wrong, but could he still be right about the mental part? Our spatial intuition is still entirely Euclidean, so it would seem that "mental a priori" are Euclidean as well. In science, on the other hand, the mathematical structures (according to Cohen, Cassirer, Reichenbach, etc.) are only relatively a priori, they evolve over time. But if science can evolve, and the unconscious mental synthesis can not, there is a problem.

**QUESTION:** Was Kant right that our minds use space and time to synthesize perceptions, if so is that space Euclidean? If empirical experience is synthesized according to a priori schemes how do we manage to extract something from it that does not conform to these schemes? 

This is not specific to space and time or Kant, whatever mental schemes or categories are used to synthesize perceptions they can not keep up with evolving scientific descriptions. If categories are "conditions of the possibility of knowledge" how is it possible that scientific knowledge eventually violates conditions of its possibility?

**EDIT:** jobermark's answer gives a nice example of a priori in color perception, which should not be controversial. But this highlights the issue: neither color nor space perception evolved since ancient Greeks, or even since prehistorical tribes, while science did. If Kant was right about mental a priori then he had to be wrong about something else, like the acquisition of knowledge. Perhaps, reason can take from perceptions more than it put there itself after all. That would require a mechanism for forming new schemes/categories, which are not hard wired (and listed in Kant's table), but are extracted from perceptions somehow. 

If we do have such a faculty how does it work?