Thread: Philosophy of Plato

Was curious if anyone would be willing to give me a terse synopsis on Plato's philosophy? I.E, main points, where he was wrong/right, etc. I have searched wikipedia... but as usual find their summaries a bit long and incoherent. Would also rather not sort through another philosophy book. Thanks to anyone who helps, and my apologies for burdening anyone.

I posses zero qualifications, consequently take the following with a grain of salt.
Most mathematicians maintain that mathematics is discovered and not invented. This is my own position. I understand that this position is in line with a "Platonic" perspective.
I can't say that I understand exactly what the Platonic perspective is. And the following is my least sure statement, I suspect that Platos ontology is best summed in his work "The Allegory of the Cave", which is a section in his larger work "The Republic".
Roger Penrose provides his interpretation of Platonic thought and it's significance to mathematical thought In sections 1.3 and 1.4 of his book "The Road to Reality". The relevant section is available for preview on Amazon.