Hello. This is Nada from Seito Medical School. This time it's about mathematics. When I think of mathematics, I don't know if anyone imagines an impregnable fortress, but it goes without saying that it is a very difficult subject. I have many fond memories of mathematics, and even though I was an amateur, I had been researching efficient ways to solve prime factorization.
・Mathematics is profound
・There will come a moment when it makes sense
・Maybe there really is a god of mathematics who controls the order of mathematics
・Mathematics exists only in the human head
・Knowledge of mathematics Perhaps all that remains are examples that worked well.The
order of this mathematics is beautiful.
Mathematics is deep. Mathematics is a study of assumptions, and it shines only under various conditions. For example, the integers 1, 2, 3, 4, etc. are obtained by adding the lengths of the intervals 1 one by one. 1, 1+1, 1+1+1, 1+1+1+1,...
I believe that everything in this world can be counted as 1, and that numbers such as 2, 3, and beyond do not exist. Because even if there are two cakes, they are not exactly the same in the real world. There are no two things that are the same down to the molecular or atomic level. By thinking of these as the same thing in your head and counting them, you can count different things as two or three at the atomic level.
The integer 1 is the first condition in mathematics, but I think you can add various conditions to it. If calculations under those conditions yield the same results as under another condition, then it can be said that the conditions that appear different on the surface are essentially the same.
For example, take a look at the following example: Suppose we have the formula A/B=C/D. a²+5a+6=0 becomes (a+5)/1=(-6)/a. In other words, A=(a+5), B=(1), C=(-6), D=(a). On the surface, this formula seems to mean a different formula from (A+C)/(B+D)=C/D, but it is actually calculated by substituting values for A, B, C, and D. When I tried...
(a+5-6)/(1+a)=(-6)/(a)
(a-1)/(1+a)=(-6)/(a)
(a-1)a=(-6)(1+a)
a²-a=-6-6a
a²+5a+6=0
In other words, although on the surface they should have been different formulas, they were essentially the same formula. Here, what conditions are required to find a? Probably AD=BC rather than A/B=C/D, so if we can find an expression like A+D=B+C, Variable a can be solved.
However, it is a formula close to A+D=B+C, so it turns out that finding the "correct formula" is not easy. Even if you simply substitute numerical values for A, B, C, and D, if the right and left sides are not equal, the formula is incorrect.
A/B=C/D is essentially the same formula as (A+C)/(B+D)=C/D. Because they are the same formula, the order of mathematics worked, and when we rearranged both formulas, we were able to derive the formula a²+5a+6=0. In this way, the knowledge of mathematics as an academic subject may be limited to well-written examples.
That is why we can say that order in mathematics is beautiful. If the equations follow order, in this case, essentially the same equations will yield the same result. I would like to conclude with a simple conclusion: perhaps there is a god of numbers in the science of mathematics, and that he controls the order. May the gods of mathematics smile on you. See you soon.
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