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Platonism today refers to the belief in the existence of abstract objects – that is, unchangeable objects that exist outside of time and space, regardless of a person. Such objects can be considered numbers, qualities, and so on. �
The ” world of ideas “in this case is a metaphor for” where ” the number three exists, for example – regardless of any three objects and whether someone has thought of the number three.
If I start giving a list of platonists among philosophers and mathematicians, it will stretch to the size of the average Wikipedia article-these are people from Godel to Badiou.
It is always relevant, whether we know about it or not. The ideas or Eidos of which Plato spoke are self-existent. It is these eidos that create all of nature and the entire universe in the end, are so to speak the primary foundations of everything. And a person standing on the scale of his evolutionary development can develop a mindset that can reach out to these much more perfect ideas (Eidos), and therefore make a person better, giving birth to grains of this perfection in us. And this world of eidos is not absolutely perfect and perfect, it also develops and grows further, because the development of everything in the cosmos is boundless.
I don't quite understand your question – do you mean the relevance of the world of Ideas itself, or are Plato's ideas relevant in today's world?
Justin called Plato, along with Socrates and Heraclitus, Christians before Christ, and all because they to some extent voiced the ideas that Christ revealed in His time-revealed more fully and most importantly authoritatively. So the world of Plato's ideas ,or the ideal world according to Christ, is the Kingdom of God, which is distorted by descending into our world due to human vices, illusions and delusions. By the way, the same can be said to some extent about Plato himself – he aspired to an ideal world, but did not quite understand what this world was, but he still understood the very idea of distortion.�
Everything comes into the world from the spiritual – as it is said, the visible comes from the invisible. However, the spiritual world is divided into two worlds – the world of light and the world of darkness, the world of Angels and Demons. Therefore, not all ideas coming from Plato's world of ideas are homogeneous – they come from different sources.
1 Beloved ones! Do not believe every spirit, but test the spirits to see if they are of God, for many false prophets have appeared in the world.
(1 John 4: 1)
I apologize for going beyond the limits of philosophy in my answer.