Does studying mathematics develop logical thinking skills?

What kind of skills do you acquire by learning mathematics? What are the "future-useful abilities" that you gain from studying mathematics?
A math teacher would likely say "logical thinking skills." However, I'm sorry to say, that is incorrect. Let me explain.
While we use the word "logical" in a single breath, its implications are diverse. In fact, "there are four types of logic." Mathematics is certainly a logical discipline. However, that is slightly different from the logic commonly referred to in society, or the logical thinking skills that are useful for the future.
This is because the logic referred to in mathematics is "100% correct logic." Correctness must be perfect. Even if it is 99% correct, if there is even a single exception, it is considered "false = incorrect." That is the logic of mathematics.
That point is decisively "useless" in the real world. Just think about it. In the real world, things that can be clearly divided into black and white are not issues to begin with. Problems that are actually thought about or debated are the kind where both sides have pros and cons, the results are unknown until you try, and even if you don't know, you have to decide.
What happens if you bring mathematical logic—that is, "100% correct logic"—into that situation? Both sides will inevitably be "not absolutely correct," meaning they will be "false." In the end, you won't be able to decide anything.
Alternatively, if you ask what is considered "mathematically correct" in that situation, it is essentially something that is "obvious" to anyone, and bringing that up will not solve the problem at hand.
Certainly, there is logic that you acquire through mathematics. And there is logic that you do not acquire through mathematics. The logic required in the real world is the latter. There is indeed logic acquired through mathematics, and it is not wrong to call it "logical thinking skills," but unexpectedly, that logic is not useful in the real world. The "logical thinking skills" that are useful in the real world are quite different from that.

So, returning to the beginning, what are the "future-useful abilities" that you acquire by studying mathematics?
I believe it is the "ability to use trial and error." Faced with a math problem, you think about various things: should I use this formula, or should I try that method I saw in the reference book, or is there an easier way to do it? And then, you try it anyway. If that doesn't work, you try a different method.
This process is trial and error. And this is extremely useful in the real world. To do this, you must have acquired various methods and ways of thinking. If you only have one method, it's over when you hit a dead end. Whether it's a math problem or a real-world problem, you have several options and try to solve it through trial and error. Studying mathematics serves as training and experience for that.
Solving math problems and tackling real-world problems are the same in terms of trial and error. However, the goals are completely different. What you get at the end of solving a math problem is a "100% correct answer," but that is not what you get at the end of tackling a real-world problem.
Real-world problems might be things like "how can I make a rocket fly straight?", "why is the organization not functioning well?", or "how can I win her heart?", but there is no perfect answer for such things. Even so, you try various ways in search of a better result. And if it finally works out, that is the answer. What is correct is something you don't know until you finally try it. Or, it is something you might not know even after you try.

By the way, I said that "mathematical logic" is "not useful in the real world," so what kind of logic is "useful in the real world"? For details, please see Chapter 2, "The Etiquette of Thinking," in my book "Business Thinking Lessons for High School Students," but here I will briefly show a sample.
The "logic useful in the real world" is the kind of logic I am developing in this article. I have not written anything in this article that is "100% absolutely correct." But if you are convinced by what I have written here, then this article can be said to have provided a "logical explanation." That is logic in that sense. And that is mathematically completely nonsensical logic.
Let's summarize here. What kind of "future-useful ability" do you acquire by studying mathematics? It is the "ability to use trial and error." It is not "logical thinking skills." You can cultivate some aspects of logical thinking skills through mathematics, but they are unexpectedly not useful in the real world.
High school students, let's study mathematics.

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~ We say logic in a single word ~　　
▷ There are four types of logic　　　　　　　　　　　　　
▷ People who try to solve things with mathematical correctness　　　
▷ Does studying mathematics develop logical thinking skills?