I will discuss some ideas about mathematics on which it broods for a while 'time.
I think I will need a few posts, to put everything down.
Ten or more years since I Lauer, I started to study mathematics. Only now have much less time, and perhaps the brain is also more difficult to do very abstract and complex reasoning.
This is a disadvantage on the one hand, but on the other allows you to realize a number of very interesting problems that I had at the time the University completely ignored.
picking up some manuals (text relatively simple things to say two years of mathematics), I felt a growing sense of unease.
Not in the sense that the demonstrations did not understand, or definitions. No, maybe I difficulties, but it was a difficulty that could be overcome.
Then I realized where it came from the discomfort: those manuals, compelling in their logic, in their series of demonstrations were complete nonsense. A true triumph of the absurd.
Take a traditional manual. How to start? With a definition: "Given a set V on which an application is defined with the following property ...." and so on. This approach is' absurd.
We are, in a completely arbitrary definition, without a shred of justification in their choice. But, as it happens, then pull out the theorems that are working perfectly. They look like sleight of hand: as it happens, the objects we have exactly defined the properties we need to define our theorems.
E 'this absurdity. The manual is deceiving the reader into thinking that this is a path that runs through spontaneous, logical, obvious, but that is not understood to the reader.
The basic question to be answered is what, but why? Not what I choose, but why choose a set with certain properties? Why choose a demonstration to go in a direction which, coincidentally, leads me to exactly find the solution? Where is the sense?
sense there obviously. Only that the manual makes it incomprehensible, because it is spelled backwards. Mathematicians, despite what they tell themselves, they are human like everyone else and think just like everyone else.
Where are the clues? The definitions hidden within the proofs of the theorems. The math you encounter while trying to prove something: find an object with some properties, and cut them off from trying to define prorietà they saw that they need.
The definitions come from the practice of mathematics. I understand that talking about practice, about a mathematician may seem ridiculous, but the fact that the brain activity of the mathematician is not the practice makes it less of a mason. The tools he uses are different, but still practice.
And then things start to make sense: we define an object from the use we make of it. That the object itself is very abstract is a marginal. We understand how a mathematical object when we see it in operation, in a demonstration.
To understand how a mathematician, one should be able to rummage in his trash can: search all the demonstrations that have not discarded because they worked all the trials that led nowhere. Then things would highly respect, and become, at that point, even interesting.
This is extremely interesting, because it is very related to my work as a software developer. But this deserves another post.
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