What does "mathematics be consistent" mean? Imagine you graduated as a math teacher and one day some very curious students, as it is not hard to find because they exist regardless of the current level of our high school, ask you: "Teacher, does mathematics really work?" "Do you guarantee that I can trust her?" "Why will we never find absurd conclusions?" "Why does it work well for physics and why does physics trust it so much?" "Why is it said that evolved science is one that already knows how to use mathematics?" "Why do people tell so much lies in our daily lives?" "Why is it so common for people to hold on so strongly to strange beliefs and illusions?" "Why in Brazil is so small the number of Brazilians who dedicate themselves to Science and especially to Mathematics?" At a time like this you will feel all the responsibility for you and we hope you will not regret being so "shy" or so free of "noble intellectual ambitions" or so accommodated by the "ease" of your Mathematics course. .
Surely you will miss fundamental knowledge. Perhaps, at such a time, you will discover the quality of the math course you have attended. For example, it was crucial to have learned that consistency means that in mathematics, two statements in the form "A is true" and "A is false" have never and never will be demonstrated. In fact, contradictions have already happened, called paradoxes, that were discovered early in the investigation of various theories. It is an essential part of your basic mathematics background to know that the known paradoxes have all been fixed by generations of mathematicians. A student who has never been exposed to this information has yet to appreciate what fascinating mathematics is. What chances will your prospective students have?
It is very common for a student to come across a subject called "Fundamentals" which, under the guise that "students come to college without foundation," is merely a cover for the convenience and ease of a "junior high school" lesson. and high school ". In some colleges even the refinement of toasting the student with "Fundamentals II"! The college student has his precious life time occupied with "junior high and high school topics". The student of Information and Knowledge Age Mathematics would take up his time better if he seriously considered Mathematics, for example by asking himself, "How do you get literate in Mathematics, how do you learn to read with I benefit from the good books of mathematics, how do you begin a study of mathematics without deception, without subterfuge, without half truths, without omitting the delicate but fundamental questions of logic and set theory? Is it done to end the fear some teachers have of recognizing that their knowledge is anachronistic and outdated for contemporary science, and because of that they hide under the motto "Our students today are so weak!" Is it wrong to recognize that the best thing a teacher has to do today is roll up his sleeves and study with the young students? The game is tied because if on the one hand many students have serious shortcomings, for example in their ability to read and interpret texts, to express themselves clearly and intelligibly in the mother tongue, on the other hand, we teachers need to start over because our knowledge is obsolete and for the most part useless into the Information and Knowledge Age.
The student should be immediately aware that the axiomatic study of mathematics is inevitable and is the only way for those who are tired of fallacies, circular reasoning and empty sentences of meaning.
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