It's not unusual that original scientific works are more clear than the later works of people trying to explain them.

The original author has to persuade people, and convince people who aren't familiar with them. The "pedagogical" author later is in a more clear position of authority and doesn't need to work as hard.

> The original author has to persuade people, and convince people who aren't familiar with them. The "pedagogical" author later is in a more clear position of authority and doesn't need to work as hard.

Or perhaps: The "pedagogical" author can assume that by the time of his writing, we live in a society where it is accepted that there is nothing mysterious about the material (e.g. imaginary numbers are nothing mysterious) and can concentrate on explaining the material in the best possible way.

The problem is that many students come from a background where they were taught a deeply anti-scientific attitude.

EDIT: To put it more concisely: It is a different job to convince someone of a scientific result (here the other side is distrusting) than to teach it (here the other side gives you credit of trust (but a lack of understanding) and you have to teach them so that they understand it). Unluckily many students who attend lectures have an attitude where they need to be convinced instead of taught.

>Unluckily many students who attend lectures have an attitude where they need to be convinced instead of taught.

Isn't this backwards? If you're just accepting the lecturer's word as dogma, I would argue you're not really gaining an education at all. The process of being convinced and having doubts about the material resolved improves critical thinking and improves understanding of the underlying material as well.

> Isn't this backwards? If you're just accepting the lecturer's word as dogma, I would argue you're not really gaining an education at all. The process of being convinced and having doubts about the material resolved improves critical thinking and improves understanding of the underlying material as well.

Maybe I think differently from you because I come from Germany. But I don't think this is backwards. I openly admit that I cannot stand "critical thinking" gospel.

Before you can start thinking critically, you have to understand the material that is there (that you want to criticize). Explaining the material so that you hopefully understand it is the role of the lecturer/teaching assistent. Why are you enrolled in the degree course if you are critical of it instead of wanting to learn the material? So one can assume that the students want to learn the material.

> Why are you enrolled in the degree course if you are critical of it instead of wanting to learn the material?

Maybe you want to learn why it is true?

Since Euclid, mathematics is about proof i.e. being convinced. If you really understand the material, you see it must be true - and need not blindly accept it.

What is taught in high school and many university courses is not mathematics, but how to use it. Like how to use Word, not how to write Word.

When you understand something, it becomes yours. You remember it longer, and can adjust and generalize it.

Unfortunately, it can be many times as much work to understand some mathematics, even some from early high school, and requires higher mathematics. So you can't understand til after you've understood it... It makes sense mathematics is taught the way it is... especially when most people are users, anyway.

But bad luck for those who need to understand and be convinced, which was so important to the developers of mathematics. i.e. mathematics filters out mathematicians.

> Maybe you want to learn why it is true?

> Since Euclid, mathematics is about proof i.e. being convinced. If you really understand the material, you see it must be true - and need not blindly accept it.

I agree. Learning mathematics means learning the proofs. This is pure learning and has nothing to do with critical thinking (at least to me and I am a mathematician).

Maybe we mean different things by "critical thinking"?

To me, an essential part of a proof is checking that it is correct yourself... as opposed to "learning" it i.e. taking it on faith, believing it is correct because someone said it was. (Of course, in practice you can't verify everything yourself... but nonetheless that's the idea of mathematics, in theory).

Is that not the purest form of critical thinking?

OTOH I suppose when a proof uses a clever change in perspective, to show that it must be true (such as non-constructive proofs), it refutes many possible objections without ezplicitly considering them. So formulating those objections (or "criticisms") isn't needed.

> (at least to me and I am a mathematician)

Please keep in mind that you therefore have an inevitable non-zero amount of survivor bias there, and may have some trouble seeing why everyone else had trouble with the material.

The lectures of the old 4 semesters of calculus at UT Austin consisted almost entirely of the proofs of why the material worked.

Less than entirely helpful if you wanted to use it.

That's how you become the annoying student in the algorithms class who interrupts the professor all the time and ruins the class.

And probably doesn't understand all that was required to see and prove the theory. Making his message narrower.

too easy, last night I went to Gilbert De Magnete (original in latin no less) http://www.gutenberg.org/ebooks/33810?msg=welcome_stranger

You joke (and cool find), but Maxwell's writings one the subject of electromagnetism are indeed a lot easier to grasp than some modern textbooks

I don't doubt it