It's certainly not hard to see imperfections in a 4K picture, let alone "mathematically and scientifically impossible". Most obviously, you can simply lean closer, and you will see pixels. All claims to "invisible pixels" assume you're at least a given distance away, with average sight.
High contrast makes pixels more visible; anti-aliasing can smooth that, though if not done carefully (with good hinting) it can make font edges look softer. ClearType can also help, though also at a cost of a slight coloured fringing. More resolution definitely helps, as does just leaning back a little.
Then there's all the other ways pictures can look bad. Video compression can introduce blockiness, ringing, and other artefacts that are clearly visible even at 4K. Grain, noise, poor filters etc add their own problems, or exacerbate others. Colour and frame rates differences can cause obvious effects, or a much more subtle sense that something is not right; all of which can make a display look less than gorgeous, despite their resolution - and it can often take practice and experience to spot exactly what the problem is.