Is doing Calculus based on irrationality ? I have always used to think at Mathematics and Calculus as something based on pure logic and that is a logical deductive system. Then I tried to sit down and think a little bit over how Calculus is done and I got a bit surprised. If I do some Algebra, or if I solve some equitations I’m usually able to do so using some rules or some patterns that will usually lead to the solution (If it can be found.) If I should make a program that should solve any kind of mathematical problems (that I were able to write) the way it would work would to apply a set of rules in some “logical deductive pattern”. On the other hand, if I am solving some composite integrals, that will be difficult for me, but that might be easy for others, I observe myself working in a quite different way from just applying rules, the rules is applied, but not in a straight forward way. When you take a look at that “integral thing” there will normally be no straight forward way of solving it. First you go trough a set of basic integration rules to se if any of these basic logical structures will work. If this will not work you try some other logical structures like integration by parts, integration by substitution etc, etc. But what is this search of that logical structure that will fit the best for the certain task, does this search itself follow a straight forward logical pattern ? Can it be doubts that solving difficult integrals will involve some creativity ? What is then “creativity” ? Will the process of applying creativity on the problem involve some other tasks or methods than just applying straight forward logical deductive rules ? After applying some creativity, the next phase will typically be some “after rationalization” to check if the last logical model that were found will fit in, in a logical deductive patern. But what is this process of searching for the applicable logical model ..is the process itself managed using logical rules ?