She received a lot of flack about it and made a second video.

A mathematician came to her defense and called the teen’s questions “profound.”

I wouldn’t call her questions profound or stupid, but do call them naive.

Three related questions the teen asked are: 1. How did people come up with algebraic formulas?

2. How did they know what they were looking for? 3. How did they know they were correct?

Maybe Gracie could answer these herself if somebody asked her leading questions the way Socrates did the slave boy about geometry in Plato’s

*Meno*. I won’t do that here, but what follows could guide the leading questions.

I’ll take the second question first. Why does she believe somebody has to be

**looking for**something in order to find it? Suppose Gracie is walking on a sidewalk and she sees a $5 bill that somebody else (no longer present) dropped. Did she need to be looking for a $5 bill in order too find it?

Suppose she walks further and finds a $1 bill that was also dropped by somebody else (no longer present). She may have been more on the lookout for money this time, but was she

**looking for**$5 + $1 = $6?

The roots of algebra can be traced to the ancient Babylonians. It was formalized later, especially by the Greek mathematician Diophantus and Persian mathematician al-Khwarizmi. Both men have been regarded as "the father of algebra" (link).

I suspect some people before Diophantus and al-Khwarizmi were

**implicitly**doing algebra. Maybe they used a question mark, not X. Suppose a farmer acquired some more land and wonders what amount of wheat seeds he needs to plant. Suppose he knows he used four 50-lb sacks per acre last year and he has 80 acres now. His neighbor just gave him 300 pounds of seeds to pay him for something. So how many more 50-lb sacks of seed does he need this year for planting? 50*X = 200*80 – 300. So X = (200*80 – 300)/50 = 26. That is an answer to question #1. After he plants all the seeds and finds he had the correct amount, he has an answer to question #3.

An Australian math or stats lecturer says Gracie’s questions are “insightful” (link).

*imaginary*numbers aren’t

*real*numbers. Maybe Gracie will make a video about imaginary numbers some day.

*i*

^{2}= −1 looked pretty unreal to me when I first saw it. I later learned it is also a

*really*powerful concept.

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