Why do I Love and Hate mathematics at the same time?

I love mathematics – because it is the only “language” that humans can communicate each other without the barrier of their native language; because it is as beautiful as art and you can really enjoy the joy of mastering a mathematical topic (just like playing a musical instrument or painting a picture); because it is both pure (“simple enough but not simpler” – to a mathematician) and applied (“anything you can do, I can do it better” – to a math-trained mind). I can only look up to the greatest mathematical minds in human history and thank them for revealing so many elegant concepts and theorems to their descendants. I do believe what Erdos call “proofs in the book” – mathematical reasoning represents the highest level of intellectual gymnastics and any humble mind cannot help wondering if the creator knows a simpler proof. I am grateful to my own creator that I am talented enough to appreciate the beauty of math even though at a level of lower than professional players because …

I also hate the mathematics. It is a language abused by some to disguise the truth; it is often used as “the emperor’s new cloth” (indeed it works even better because a mathematically-decorated paper can more easily fool less-mathematically-trained minds); it deals with mentally-reproducible objects only – if its connection with the physical world is cut off, one can inevitably get trapped in delusion. Abusing mathematical language is like pouring the paint to a cloth and calling it a creative art; legendary physicist Richard Feynman has warned us a long time ago the law of gravity can be derived from at least three different math formulations and they are all equivalent. So no mathematical topic/tool is more fundamental/important than the other (e.g., algebra vs. geometry). I still detest a probability course I took in my graduate study when the instructor claimed that I was “completely confused by the advanced notation of probability theory”. To me, if the depth of a topic has to be conveyed by the  mastering of some specific symbol system, it is no better than a dried meat/fish with good nutrition being gone already.

So how do I love and hate mathematics at the same time? For every piece of mathematical topic (e.g., definition, theorem, algorithm), I will find out its history and understand its context in the first time. I firmly believe good math is a long-living meme with a distinguished character from bad math. A mathematician does not need an apology as long as he/she recognizes there is no better mathematics (e.g., advanced probability theory has a higher rank than elementary probability theory). Meanwhile, for every piece of scientific topic (e.g., in physics, chemistry, biology and sociology etc.), I will look for the simplest mathematical model or language for communication. I will keep in mind “all models are wrong, some are useful” (George Box). I will not be fooled by better experimentally reproducible results (often on a highly limited test data set) alone but try to understand their implications (i.e., underlying models or hypothesis) in a mentally reproducible manner. I might never be a good mathematician or a good scientist but I will be happy to be the king of the middle-ground – maybe that is what a good engineer is about.

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