*Due Sunday, Sunday, September 13 at 11:59pm*

Contents

## Background

#### Gracie’s questions

Gracie Cunningham is a student who went viral on Twitter a few weeks ago when someone tweeted her Tik Tok and said, “this is the dumbest video ive ever seen.” (That person’s Twitter account has since been suspended btw.)

After catching a lot of hate on Twitter, Gracie made a follow-up video and tweeted it herself. (I like both videos but I think I prefer the first one tbh.)

Alongside all the critical comments calling her dumb, Gracie got a *huge* outpouring of support from mathematicians, physicists, philosophers, and teachers, who *loved* her videos. Like, really, really loved them.

#### Dr. Cheng’s answers

Eugenia Cheng is a mathematician who is very good at explaining math to non-mathematicians. She’s published a few popular books about math for a general audience and is very active on Twitter. She’s even appeared on the Late Show with Stephen Colbert!

Gracie’s questions are mostly about the history and philosophy of math (which is a real academic discipline that people can study and get PhD’s in!). Some of her questions have concrete answers and some of her questions just lead to more questions. When Dr. Cheng saw Gracie’s videos and the critical comments on them, she tried answering Gracie’s questions one-by-one on her blog.

## Assignment instructions

None of us are experts in the history of math or in the philosophy of math (unless there’s something you’re not telling us in your OpenLab introduction post from last week!). But we all have studied math and encountered math in some form in our day-to-day lives…which means that we’ve all spent time *thinking about math*, so we can ask questions about it.

For today’s assignment, think about math in the big picture of the human experience, not just the math you see in your math classes.

- Watch both of Gracie’s videos above and read Eugenia Cheng’s blog post.
- Choose one of the following prompts:
- What are you curious about? Have you ever had any questions like “Is math real?” or like Gracie’s questions that you’ve thought about before? What is one of your questions and what have your thoughts been about it? Was there something in particular that made you have question? Was there something that changed your mind about how you think about it? Do you have any possible answers for your question, even if they contradict each other?
- Which of Dr. Cheng’s answers is the most interesting to you? Why? Did you agree with everything she said or do you have a different idea? How would you have answered this question?
- Imagine Gracie is your friend. What would
*your*answers to her questions be? Which of her questions would you ask her more questions about? What would you ask her? How would you engage with her ideas in a supportive way? - What’s something mathematical that you have encountered in your life that had nothing to do with the math you learned in school? Was there a problem you had to solve on your own? Did you have to look up how to solve it or did you figure out a way to solve it yourself? How do you know what you did counts as math instead of as something that’s not math?
- Look up the history of a mathematical fact, formula, or idea. What problem were people trying to solve when they discovered it? How did it solve the problem for them? How did they know they were right and how did they use it? What is the
*story*of this fact, formula, or idea? (I’m not sure how reliable it is, but the website the Story of Mathematics might be a good place to start). - Make your own video (on Tik Tok or anywhere else that’s public) asking your own questions about the history and philosophy of math.

- In a comment below, respond to the prompt you chose in at least 5-7 sentences. Make sure to tell us which prompt you chose so we know what you’re responding to! If you are making your own video, include a link to it in your comment.

You will receive participation credit for your comment.

If you want to write more than a few sentences, you are certainly allowed to! If your response is too long for a comment, you may submit your own OpenLab post. Select the category *Gracie* under *Document* in the settings on the right-hand-side of the screen.

I will be answering prompt 1. I know that math is real but like Gracie, I question myself sometimes about some math concepts. I have always been confused about how those mathematicians come up with some of those math symbols. For example, we have the infinite, integral, square root, the sum of, theta, pi, and summation symbols. How do they even think about coming up with them? What were the process and the purpose of it all? What do they even need all those symbols for, it’s not like people were going to school to learn about them during that period. I think that the answers to some of my questions have to do with the construction, and buildings that they were doing during that period. They might need those symbols to figure out some dimensions and measurements to do the construction. Even though people weren’t learning about them back then, we are learning about them now and it helps us find the answers to our question in school but also in life.

A. Though I have never thought about why math existed, I do understand its applications in in Pythagoras days. Infrastructure needed to be built without machinery we used today. Astronomy was prominent during these times. In fact, certain ancient cities built before Pythagoras aligned with the stars.

B. Dr. Cheng most interesting answer was when she said math was about making up your own rules. I think she is partially right. I think there must be an empirical way to go about it. I do think when it comes to theorems that proofs are important, in order to establish a commonly accepted principle. I would ask her about her blood pressure because she used a whole stick of butter. Her quirkiness is interesting and has the ability to teach complex ideas through simplistic means.

c. I think the questions that Gracie ask are interesting because they give light to first principle thinking, which was introduced by Aristotle. I think we must first ask the questions we don’t understand. However, I do not agree with the Idea that math isn’t real. I think that you must understand a little more about history to understand why and how Math was developed. For example, why they needed it and what they weir looking for. I would Encourage Gracie to continue to question everything. I think that is how we began to better understand things that we previously had no answer to.

d. In 2018 I was building a home recording studio and I had to buy lumber. I had to decide whether or not the base of a recording cabinet can support a particular load; but rather than use a statics formula to determine this. I just reinforced the base so I would not need to do math. However, If this was a commercial product and I needed to mass distribute and sell this, I would have properly calculated the max principal stress, bending stress, torsional stress, max load and etc. I do believe that

My answer is to prompt a and b.

Yes, like Gracie I used to question myself about math being real. At first, I thought of math to be just like abstract art, as if it came out of nowhere. I say that because I took a space science class in school and when concepts such as magnetic field strength would pop up it would link to the pythagorean theorem many times. It made me wonder: magnetic field strength can be found using this theorem, then how can we be so sure this theorem is right? I wouldn’t have just said, oh c^2=a^+b^2. What made someone think of it? Just as Dr.Cheng said in her blog, these formulas are not absolutely true but that they are in a particular type of geometry.

Dr.Cheng’s answer to question #1 is most interesting to me and I agree with it. Formulas are made when patterns are noticed. When we see a series of events, realize certain similarities, it makes us ponder about why is it the way it is. And yes, nowadays it has become so easy for one to just relate to what someone else thought, as it has already been figured out.

My comment is for prompt a: Well it is well known that math is used in mostly everything and is really required, I’m talking about basic math (addition, subtraction, multiplication and division). More than that of course math is really important in our daily lives, thus math is real. Now, just like Gracie I’ve always wondered about it being real, and the need of advance math for our daily lives. When I was in high school and was introduced to algebra I really start to wonder many things which were linked to why we need to learn all of this? My whole idea was that we would’t be using all of those formulas/solutions in our lives. We used to joke with my friends stating that when we go to a store we don’t need anything besides knowing basic arithmetic operations. However, after investigating and getting more knowledge about why math is soo important it became interesting to me. I think we as human being will always have questions even about obvious things, which can take us to learn even more.

Prompt B: I found the first answer interesting because I have heard that mathematicians are lazy sometimes so spotting patterns and making formulas out of them is an efficient way to get things done. I agree that starting from scratch each and every time would get pretty tedious. It’s also interesting how she said that we are taught math out of context. I always wondered why the philosophy behind math is never taught in math classes. Sometimes I forget that math is just more than numbers and equations…there’s a whole philosophy behind it. I honestly would not know how to answer Gracie’s question but say that these people probably had a lot of time on their hands to just sit around and think about the world around them and how it works. Without the people who asked those question’s I wonder how far our society would have evolved.

Ever wonder how we got the word algorithm? Algebra and algorithm both stem from the same word, a name actually, Muhammad ibn Musa Al-Khwarizmi. Al-Khwarizmi was a renowned scholar from Baghdad who lived in the late 700’s to early 800’s CE. While not much is known about him, his books have been incredibly influential. He gained much of his knowledge from the vast library known as the “House of Wisdom” where he worked and studied. He is known as the father of algebra and the first person to treat it as an independent discipline. He pushed for the standardization of the Hindu-Arabic number system (0-9), introduced the decimal, established the balancing of both sides of an equation, as well as countless contributions to astronomy, geography and of course, math!

What I think is really interesting about Al-Khwarizmi is that he took works from other cultures and mathematicians and unified it. He took specific ideas and generalized them and created standards for how we describe math that we still use today. These things we tend to take for granted. Partly because, it happened over a thousand years ago, but also because it seems so simple. Duh, of course, if you take x + 7 = 12, you can solve for x. For Al-Khwarizmi it was a balancing act that he had to prove through language and many examples. He wrote a whole book about it! Gracie wondered how mathematicians knew what they were looking for while theorizing formulas. Al-Khwarizmi might have wondered the same thing. He studied and expanded upon the ideas of those before him. We use the term basic to describe algebra, but someone had to come up with it, define it, and prove it so that others could go on and expand upon that “basic” work to discover bigger and tougher principles of math and how the world works.

Prompt A, In my perestive, Math is real because it is learning the language of logic. It would give us a strong foundation upon which we deal with the problems with efficiency and critical thinking. it expresses a way of understanding many situations at the same time. most of mathematics can be applied in real life. When I started to learn geometry, I was curious about the concept of Pythagorean theorem. It is associated with the right triangle that the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. Like Gracie emotions that each subject developed across time by people agreeing about what a good framework would be for that type of question. For math the framework is logic, and math results are proved using careful logical steps. On the other hand, the non-Euclidean geometries have allowed new ideas on the conception of the universe.

I will be commenting on prompt A. I do ask myself why some math is necessary when I highly doubt I will be using it for my future career. I don’t see how y=mx+b, antiderivatives, and other advanced math in the near future. I also did question who invented mathematics and how did that person know if he/she was correct when they first thought of an equation, formula, rules, etc. I also questioned if there was any careers that did involve antiderivatives, chain rule, polynomial equation, etc., aside from math instructors obviously. To this day, I still ask myself these questions.

I am going to be answering prompt 1. I know that math is real is real to a certain extent. But I do ask myself about some math topics. I always wondered on how certain topics came to be, such as pi, how did they determine the value of pi, or the Pythagorean theorem. I would be confused on how these mathematicians could come up with these formulas or symbols. As Gracie stated, how do they know they are correct. what did they do to confirm their formulas are correct. With the symbols how did they come up with each symbol, did they use reference from the past, draw random symbols and decide which fits best. I do wonder things like this but as times go by, new formulas are created and is used in sometime in our lives

My answer will be to prompts a/e. I will be discussing the famous mathematical formula E=mc^2. Let me start by explaining what this formula means. Energy, E, of a system is equal to its mass, m, multiplied by c^2, the speed of light squared. Can you believe that the relationship between energy and mass is summed up in this simple equation? After learning about this formula, I had many questions similar to what Gracie had. How do you even measure the speed of light? How can you measure the speed of something that’s not physical? Why do we have to square the speed of light and how did we figure out we needed to do that? Astoundingly, the speed of light is 186,000 miles per hour. We multiply the mass of an object by the speed of light to determine how much energy is inside it. The reason is that whenever you convert part of matter to pure energy, the resulting energy is by definition moving at the speed of light. But why did we need to know this? It has a lot to do with physics which is another huge topic of discussion. To think about the amount of mathematics that we have come up with is insane.

I will be commenting on Prompt A. My question is not “Is Math Real?”, it’s more why do certain topics of math exists. For example, how do I apply definite integrals into my daily life? The only time I use definite integrals is in school. All these math topics and knowledge being taught to me but none of them has been used outside of my math classes. Maybe certain occupations may need definite integrals but why does everyone need to learn it? When is a chef going to use the chain rule or product rule? When is a marine biologist going to use trigonometric substitution? Shouldn’t we learn certain math topics based on our future occupation? I do not have any answers to my questions but I would love for Dr. Cheng to answer them for me.

I will be answering prompt A. I did had questions about math back in high school, but the questions were not about the whole concept of math. My questions were about certain topics. Now that I’m trying to become an engineer I have a better understanding of why we need to learn math and some formulas. For people that are in a science major, these questions really sound silly. In the science, math prevents a lot of trial and error time.

I will respond to prompt D.

One mathematical thing I have encountered (even it is not math I learned from school) is the weather forecasts I have watched several years ago. I have learned how to recognize high/low temperature patterns. Since I was able to recognize these high/low patterns for the 12-month period, I noticed that the high/low patterns have a sine wave. I wasn’t formally introduced to sine waves until 11th or 12th grade. In this case, it counts as math, because it involves measurement and data.

Another mathematical thing I have encountered is the “square root” function on my calculator. Starting in 2nd grade, I explored the repeated usage of the “square root” function, and noticed that whatever number I put in the calculator, it just approaches the number “1” each time. In 6th grade, I also noticed algebraic and trig functions such as sin(), cos(), tan(), log(), ln(), however, at that time, I had no idea what are these functions are. At 8th grade, I started to explore trigonometric functions, and graphed those trigonometric functions (sin, cos, tan) on paper to know a little bit about these functions.