Is it possible to call a well-read person smart, and a person who knows algebra, physics, etc. erudite?

The author does not understand what he is talking about at all.

Let's start with the fact that mind and intellect are completely different things.

He talks about mathematics and physics, claiming that those who are well versed in these sciences, they are smart.

But in reality, they can be absolutely stupid. Because the mind is not intelligence, but a more mundane quality, usually (but not always) associated with the ability to earn money and provide oneself with a comfortable environment. Well, in any case, this is what is meant when they say "if you are so smart, why are you not so rich."

In general, the mind is not only intelligence, but also the ability to avoid difficulties balance of the psyche, which does not allow making sharp impulsive and harmful actions. In short - the mind is a combination of character traits and thinking that allows you to go to your goal in the most optimal way.

But the goal is different for everyone. The funny thing is that people often do not understand their purpose. An academician may be downright brilliant in the field of science, but his REAL goal - to marry and raise descendants, he may not understand (at least consciously). And in the end, he remains a fool that everyone makes fun of.

There are other nonsense in the article, for example, that intelligence is not associated with knowledge. The author clearly does not understand that the brain is not a computer in which the memory is separate, and the processor is separate. It is knowledge that forms the process of perception and processing of information. And the more knowledge, the more ways the brain finds to solve non-standard problems using the analogy method.

Intelligence, erudition and erudition are not strictly defined terms, but rather subjective assessments of a person. But this does not mean that they can be used in any way, it means that there is no strict division when erudition begins, and when intelligence begins.

Erudition is deep knowledge in any area. Erudition is closely connected with a person's memory, with his ability to memorize and reproduce information from memory. We are talking about a person with great knowledge - an expert, an erudite person. Reading many books it is quite possible to become an erudite person in the field of literature - to know the writers, the books they wrote, the plot and the heroes of the books. An example of the use of erudition is a quiz game. But the winner of the quiz cannot be said to be a very smart person. Yes, he remembers a lot, but that is not the mind yet.

Reading is also connected with memory. It differs from erudition in that being well-read gives side bonuses in the field of language proficiency - the so-called congenital or acquired literacy, the ability to easily express one's thoughts and a large vocabulary. But if you just swallow books without thinking about their content, then this will not add to the mind. Well-read and smart are not synonyms.

Now I want to talk about thinking. Thinking is what helps a person solve problems. This is a simplified definition. The simplest example of using thinking without reference to memory is the game of sapper. Or sokoban if the level is unknown. A person who quickly copes with a solution to a new problem is quick-witted. But smart is not smart yet.

And the final touch to the picture of an intelligent person is perception. This is a grasp of what is happening around in the form of images. It is closely related to attention, thinking, memory and the mental state of a person. About a person who is doing well with perception, we say: "grasps on the fly."

The combination of perception, thinking and memory gives the intellectual level of a person. He can be tall, then they say that the person is smart. High intelligence = mind.

You can read many books and be a well-read person, but not be able to draw conclusions, i.e. not be able to think. A well-read person may not have a great mind. A person who knows physics and algebra may well grasp on the fly, effectively solve problems, relying on knowledge from memory - to be smart. And at the same time be well-read. Or not be.) That is, well-read, erudition and intelligence are not mutually exclusive concepts.

Erudition is the knowledge of a large amount of information about the surrounding world, culture, history, etc. An erudite person is one who knows a lot (respectively, reads a lot, watches, etc.)

A person who knows exact sciences well can be called an intellectual. Intelligence is the ability to think, erudition is the knowledge of a large amount of information from various spheres of life.

And the word "smart" is generally relative and evaluative. A cat can be smart too.