Comment by reikonomusha | Hacker News Reader

Comment by reikonomusha | Hacker News Reader

I watched the video and it definitely does not paint an accurate picture of mathematics. Additionally, there's a heap of misinformation (e.g., "fractals are scale invariant", "group theory is about groups [of things]", "Gödel's incompleteness theorem leads to a mystery of why math is even useful", all of which is not true whatsoever).

The most beautiful part of math wasn't explained at all, which is how the fields relate! How do geometry and algebra come together? How about algebra and topology? How about prime number theory and complex numbers? Many of the most influential, important, deep, and illuminating theorems of mathematics are precisely those that make such bridges.

Instead, the video gave extremely high-level mathematical "buzzword soup" with artificial boundaries and an explanation that seems to be derived after the fact.

I'm all for educating the masses on the magnificent landscape of higher mathematics, but I think it's a disservice to do it non-factually.

The video does mention that "how the field relate" can't be drawn properly on the same 2d map.

So maybe the next step is now to make other maps using different projections to show those relations ? Using the same pictograms would help people visualize better, and it would make an interesting collection of maps.

Indeed, it would have been better if they had one or more mathematicians in their team. I'm pretty sure that most mathematicians would have loved to support them, at least to proofread their script and to review their animations.

These are the things I found I would have known to be wrong at the end of high school:

The complex plane doesn't usually have the imaginary on the x axis.

Real numbers are not the only ones that have infinite digits, think 1/3.

e is not called 'the exponential'.

Also, why the hell is probability applied math?

1/3 is a real number, did you mean irrationals?

The video described real numbers (beyond rationals, hence irrationals) as ones with non-terminating decimal expansions.

I have not watched the video, but for people reading only comments let me clarify.

Numbers go naturals < integers < rationals < reals. Reals are the union of rationals (quotient of integers) with irrationals.

Rationals may have an infinite decimal expansion, like 1/3 has, but it has a repeating pattern at some point. Irrationals have an infinite decimal expansion and has no repetition of that kind.

This characteristic of irrationals does not depend on the base, it is always the same way. The finitude or infinitude of the representation of a rational depends on the base, but if infinite, there is a repeating pattern.

The video says the difference between reals and rationals is that reals can have infinite decimal expansions. But I concede you're right (if a bit pedantic), the complement of reals and rationals is irrationals.

Do you have a better source? I would love to see something that focuses on the relations, such as what Langland tried to do, in video form.

The book "Elements of Mathematics: From Euclid to Gödel" by Stillwell does this in terms of identifying what is considered advanced in a survey of elementary math topics and showing how they fit together or don't, like how Groups drop commutativity of multiplication from the ring http://press.princeton.edu/titles/10697.html

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