Objective Mathematics
Objective Mathematics is an ongoing project which aims to make mathematics objective, by connecting it to reality. This is being done by painstakingly going through each math concept, and thinking about the concrete, perceptual data to which it ultimately refers. If a math concept is not reducible to perceptual concretes, it is invalid; it is a floating abstraction. Objective Mathematics rejects Platonism: math concepts are not Platonic forms inhabiting an otherworldly realm, but rather they refer to physical, perceivable things. Objective Mathematics rejects Intuitionism: math is not a process of construction, but rather a process of identification. Objective Mathematics rejects Formalism and Logicism: math is not a meaningless game of symbol manipulation, but rather its statements have semantic content (just like propositions about dogs, tea, beeswax, or anything else).
What is wrong with standard mathematics
Standard mathematics is often useless.
In standard mathematics, what work is considered valuable is, to some extent, decided by the subjective whim of mathematicians.
Standard mathematics is often boring.
In standard mathematics, there is a disconnect between proof and explanation. [TODO]
In standard mathematics, it not always clear what constitutes a proof. People say it's a proof if it can be reduced to deductions from the ZFC axioms or something, but in practice, almost no one actually tries to do this. As a result, different communities in math have different standards of proof. For example, there is a disconnect between analysts who work on Fukaya stuff, and topologists who work on Fukaya stuff; there is stuff that the topologists consider proved, but the analysts consider unproved. For another example, consider the controversy over Mochizuki's proof of the abc conjecture.
What is right with standard mathematics
Standard mathematics has high standards of proof.
Standard mathematics does not use many undefined terms.
Standard mathematics is more conceptual than perhaps any other field.
Standard mathematics contains a lot of knowledge about the world.