- #26

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We can go back to high school. There are pupils who just understand maths immediately, as soon as the teacher presents the material. And there are others, like the one I tutored today, who do not, who even have to spend a lot of money on extra tutorship and still get average grades or worse.

There is a clear innate ability involved here. Call it talent, call it intelligence. There are gaps you cannot cross with hard work alone.

I think it is more complex.

Do they still put effort into math? Do they really learn?

Are they still interested in math?

If the answer is no, then it is no wonder that they struggle.

What if the students had a bad teacher when they were in school?

What if they lack the elementary things of math?

If you lack the basics in math you will obviously struggle with the advanced stuff.

First of all, I never claimed that certain people do not understand math more easily than others (if you want to call that innate ability or talent, sure go right ahead). It's also worth keeping in mind that the understanding of mathematics is cumulative, so those who may not have learned the fundamentals at an early stage will have more difficulty in later years (all arguments for ensuring students receive the highest quality of math instruction and education at the earliest years).

That doesnotmean that (a) earlier obstacles cannot be overcome, nor (b) not everyone is capable to learn or develop an understanding of mathematics.

Exactly this is what I think.

If by 'good' you mean about the average at an average state university in the US, that's much more tenable, especially if you lax the requirement to 'only' be the basics needed for a major that 'only' uses applied math like engineering or physics.

Of course, I don't mean Field-Medal level since I said they have the talent to get there.

But I think talent only matters in this high-level area.

University level and a little bit above but under Field-Medal level is for everyone possible to reach. That is my hypothesis.