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                 Philosophy and Math

"Axiomatic" means no constrain. you don't have to care much about the physical reality. The proposition or axiom has no constrains, not any statement. And if any statement is true depends on what kind of logics you are following, so with the same subject, there are different math statements, for example, we have many geometries, Euclidean or non.
Have we ever seen a young successful philosopher who at least built a phi-structure of understanding? How many young math men have we seen? The history performance tells that we have considerably less philosopher than any other professions, why? And a successful profession become a philosopher in some way because they have to think that way. The ambiguity of the job is the logic dead-corner, which baffles mathman.
Yes, any one can have his life philosophy and can challenge the pillar, that makes a success more difficult because there are limitless examiners around to attack you from all directions. As a mathman, the only thing you care is self-consistency. You can assume the sun is made up of gold as a mathman, but if you do so as a phi-man, you become everybody's laugh stuff. That is what we say depicting a ghost is easy but a cow is far more difficult. Not much life experience or wisdom is needed to start math. A lot of math assumptions come as the abstractions from reality, or physical model, at least at the beginning of its construction of any system, so you can not say that physical world has nothing to contribute to math, otherwise math become ghost depicting completely. Without physical evidences any statement remains as assumptions.
Philosophy serve many purposes. Paradox is a kind of training tricks, or help thinking, not necessarily true to reality. But phi-statement is "meant" to be true, even though there is no guarantee. But a math statement is not meant to be true to reality, only to its only math system.

And the philosophy which denies reality actually means non-reality is the reality.

Math uses formula or symbol to argue or reason, philosophy uses language to do so most of the time because the case can not be generalized into a set of simple symbols and equations or > or <, that does not mean no reason or structure at all.

Remember how the word "philosophy" comes from? A man with wisdom can do a better job in any profession.
Math is reputed as mind agility demanding. A laborman can not afford it. But mind agility is not enough for philosophy, transforming mind agility into wisdom needs other properties along like the sense of responsibility, being balanced emotionally, that is, dancing gracefully between subjectiveness and objectiveness, etc.
Yes a philosopher will not be easy to adapt to any profession, not because of the difficulty but the professional glossary and the same is true to any one. I think a philosophy concept is far more difficult to grasp than a math one since they are "axiomatic".
How much effort is dependent on how much you want to gain, not the subject. With a math concept is that you define the concept first, then try to identify the extension of the concept, physical or philosophical understanding is the other way around, the extensions come first. That is why math tend to be analytical and philosophy synthetical. That is why we call it like ghost-depicting, because the concept comes ahead of the extensions.

Difficulty exists in any profession and can deter any one, for instance, walking is simple but can you walk on hands, on one hand? on a finger? The same is true with math or any other profession, you can build a math maze that no one can solve or simply there is no solution to it, but this is not an indication of wisdom. With the subject held the same, the efforts by different people are different to achieve the same degree of understanding. With the same effort, or studying hours if you agree and same subject, the degree varies.

Difficulty cause impossibility.  No one has ever comes up with a complete success one till now, but we have some great attempts worth of examing.

When I can solve a math problem, I have no idea of philosophy, not to mention to answer a question.

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