Choices…

Studding mathematics is not as easy as everyone can think… there are so many subjects that there comes a point when you need to decide which one you like the most, and try to study everything about that subject, and only that one… And it’s hard to choose, very hard  especially when you start reading from books that cover general information from the most important subjects… and it becomes quite impossible to decide when you read a paragraph like this one :

“So far at least, it is not a serious difficulty not to know how to deal effectively  with the continuum hypothesis. No other important ideas in mathematics are dependent upon it. No engineer would design a machine one way if the continuum hypothesis is true and another way if it is false. (In fact, if mathematics is merely the manipulation of symbols, truth and falsity in the ordinary sense have nothing to with it). No one is going hungry because there are ideas that cannot be proved one way or another, and no sick person would become well if someone found an infinity lurking between the number of natural numbers and the number of real numbers. ” (“Mathematical Fallacies and Paradoxes” by Bryan H. Bunch)

After you read something like that you start to think in 2 directions: I want to study something that really helps the people around you, something that can be used in everyday life, or just in real life; and the other way: I want to study something that won’t help anyone at all… How can you choose between these two things? Because, stupid or not, you find both of them fascinating and you want to know more and more and more… and you cannot stop looking for new information… And then this happens :

“Few people other than some mathematicians and philosophers have taken seriously the results discussed […]. Among the two who have, the question has been raised as to whether or not these results indicate something limited about the human mind. Their assumption is that mathematics is a construct of the human mind. The limitations perceived in the construct must reflect limitations in the constructor. Others disagree with this notion very much. That axiomatic systems have limitations need not imply anything about the way the mind works, fir there is little evidence that human minds, even mathematicians’ minds, use axiomatic systems to create new ideas. Instead, the evidence is fairly good that new ideas come from looking at specific examples (nonmathematical induction), from a sense of form (it just feels right), and from sources deep inside that are poorly understood. The Indian mathematician Srinivasa Ramanujan claimed that a Hindu goddess passed along his ideas to him in dreams. (If so, she often made mistakes) Maria Agnesi claimed to do some of her work while sleepwalking. Poincare worried over one problem for months, getting nowhere. Then, while he was thinking about something else and, in fact, getting on a bus, the answer popped into his mind between the step up and paying his fare. No one has reported achieving really significant results simply by drawing then out of an axiomatic system. ” (“Mathematical Fallacies and Paradoxes” by Bryan H. Bunch)

So, the conclusion is the empty set… But I just need to wait for God to help me, or just pray that the next time I will travel with a bus everything will be clear in my mind… Until then I need to wait and read even more…

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