Due Monday, September 12 at 11:59pm
Contents
Background
Gracie’s questions
Gracie Cunningham is a student who went viral on Twitter a few years 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 this week’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 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; comment here with a link to your post so we can find it later.
The prompt I picked was prompt A.
From watching the videos I must say that at some point in time Iāve also thought of questions that were similar to the ones Gracie mentioned in her videos. One question that was on my mind was why is math so difficult? From the videos alone I wouldnāt say there was something that changed how I think about it. But rather it reminded me of the questions Iāve asked myself in the past. If I had to make a guess, the answer to my question would be that the advancement of technology increasingly relies more on accurate calculated numbers so math gets more difficult as it tries to adapt to the changes.
I picked prompt A. Sometimes I would be like why are we learning this, are we ever going to use it again. After a while of thinking I just say to myself if we are learning it, we are going to use it eventually. I feel like everyone thinks about it, it not just math, it other subjects too but eventually we are going to use it. Sometimes I be thinking to my self when are we ever going to use antiderivatives
Prompt B: When Stephen Colbert was having trouble multiplying the obscene amount of layers on the puff pastry he eyed Dr. Eugenia Cheng to cue in for her to help him as he wasn’t able to solve it. Dr. Eugenia Cheng doesn’t answer it because she doesn’t know it right off the bat either, but he expected so since she was a mathematician. She replies to Stephen Colbert by saying, “I’m not a mathematician, not a calculator”, which is a very good point people expect people who are good at math to be good at calculating, being good at math involves thinking outside of the box and critical-thinking. Calculating on your own is a good skill up to a certain point where numbers get too large, as there could be room for inaccuracy when you calculate, and using devices to calculate for you helps mitigate miscalculating. If I was in the position of Dr. Eugenia I would have responded the same exact way after watching this clip of her baking with him.
I picked Prompt A.
I’ve had many questions on why so many types of mathematics are necessary or useful, especially since I have found learning math difficult in the past. The more I learn about math and science, especially physics, which is basically completely math in itself, the more I see that every formula, theorem, category of mathematics, etc has a point and a real application. I have learned how to every facet of the universe is made up of mathematics. When learning something new in math by just looking at gibberish formulas and symbols, it’s hard to understand it, because I’m not looking at it with the right perspective, seeing how it’s actually used and where it comes from. My professor in Physics II explained something very amazing; that there are entire fields of mathematics that have no application, they are theoretical. Really, they have an application, we just don’t know what they are yet.
prompt A: Math is one challenging subject, so there is no doubt that I asked why math exists and why are we learning this, and how we use this in real-life scenarios. I have always loved math growing up, but it’ll a subject where a lot of memorization is involved so it definitely gets more difficult to the point you’re in a position to sit there and ask yourself “why does math exists” or “is it even real”. On the other hand, there are definitely questions that contradict those questions. Math is such a broad subject, from algebra to calculus, and it all varies in difficulty.
I chose Prompt A. I chose prompt A because ive had questions that are kind of similar to the questions Gracie has. I ask questions like “Why havent I used y=mx+b yet? What made me question when will I ever use y=mx+b is because we learned it in school for a reason but I have yet to use it outside of school. Yes I do use math to add stuff like buying things online, going food shopping or even getting a certain amount of clothes but thats just simple math. I havent used none of the complicated math that ive learned outside of school. Im a computer engineering major and I can see why they require math classes in order to graduate in this major because maybe in a real computer engineering job we might use math to solve problems or build something. But in reality, I dont think they will use every type of math at those jobs. For example, will calculus be used in a real job?, I personally dont think so but the only way to answer my questions is to first graduate and then hopefully get a job in this major and see if I get proven wrong.
I choose prompt A and yes I always was curious on how something that we have in theory can be put in a practical world. Until I got introduced into vectoring with it comes to airplanes navigating in the sky. With vectors you can have a 2d model moving in a 3 dimensional space. Which includes, GPS as well!
PROMPT A
Okay so math or “is math real?” I have similar thought to Gracie question as I asked “what is math?” recently. We all learned Basic Arithmetic (Add, Subtract, Multiply, and Division), then more complex equation and new symbols and new math languages that we see through out our education. But, this hits me when I notice something and others as well, “when are we gonna use this in real life situations?” Math has its limit to some degree that we really need to use it: finance, time, and measurement. Math is like a 2nd language, but seeing it could let us theorize the answer.
For example “The Math Equation That Broke The Internet”
8 / 2 (2+2) = ?
I pick prompt A,
I been curious about several things in multiple subjects, including math and science, for example I’m not a big fan of chemistry, so I would ask how do we know that’s the exact number a mole? and things like that. The reason why I asked does that types of questions is because sometimes this questions come up because we are not actually able to see the things, mostly in my case, in science. Yes there are things that had change my mind, not exactly about the question I mentioned before but yes for example the question “is math real?” I believe to have an explanation, I believe that as humans be have evolved according to our needs, yes its not and answer how?, but rather why?. Why do people develop this thing? I read before that for example arquitecture has evolved like humans, things are built according to the peoples need and desires, and I believe this same analogy can be use for math, for example maybe in history there was someone that need it to add the same number multiple times and develop multiplication, yes for more advance math it becomes hard to understand what was need it, but I believe its possible
Prompt A: One thing I’ve always been curious about is, when will I ever use this kind of math in my day to day. I know we use math everyday for everything but there’s a few math concepts that I never see myself using. I feel like most people never use the complicated math terms once in their life. Things such as addition, multiplication, subtraction and such are needed but with todays technology, you carry around a calculator with you everywhere which is your phone. So what I wonder is, why is all this math needed when most people will never use it in the first place? Some people will definitely use it due to the career they want to go into but others will go into careers that will never need math. It should be more of a decision than a requirement.
Prompt C:
I would immediately start by telling Gracie that I do understand her confusion because I am currently taking one of the most confusing math classes I’ve ever taken. There are moments where some rules apply, some don’t, you have to know where to apply these rules and if you don’t guess which rule is the right one, you get the complete wrong answer (but how would you know until you get your graded test back?) I would ask Gracie when she realized she had this question, “is math real?”. If it was when letters and graphs started getting involved, I would have to nod solemnly and agree because that is about the time math started feeling a little make believe to me as well. I would attempt to answer her questions by reminding her that we didn’t learn math starting with the Pythagorean theorem so obviously there was a natural progression of mathematical discoveries. Her idea that “they didn’t even have plumbing” also ties in with the idea that no, they didn’t, therefore they had to come up with mathematical answers to find solutions to their “modern day” problems, the same way we do now. For example, a curve on a graph would just be a function to us but to people living in that time, it was probably how they figured out things like time, the natural progression of the seasons, or how big a given wheel should be.
Prompt B
The most interesting answers were definitely to questions 1 and 2. The reason behind my choice is simply because I too wanted answers. I understand that everything runs on logic and how they used letter to replace numbers but why? I know it’s to make everything easier but did it ever occur to them that it just might makes thing more confusing? I like how she explained how y=mx+c is the only equation for a line and how over the past years they have been coming up with more to confuse us great. I wouldn’t be able to answer these questions if anything I would just make it more confusing.
The prompt that I choice is A because I question myself whenever I am in class. A question that I always ask myself is, would I ever use math in the real world. The reason I question myself is because learning hard equations and memorizing them just to use it for one semester and never again. Nothing has changed my mind yet but I am still open to learning and hoping that my mind can be change. I do question math most of the time but at the end of the day is always nice to learn something new.
I picked prompt A.
Is math real? A great question that I have always asked myself, Why do I need this?,Who came up with this equation?, Why did they come up with this equation? As a Construction Technology Major you can see why I always ask this question, endless math classes that all seem to hold no purpose. Two key classes help me to understand the need for math and why it was created. The first was Calculus 1 (1475) and CMCE 1115, whilst some careers u might not need anything from Pre calculus and beyond these classes showed me the importance of math in our everyday life. One example that I can give is the floor we walk on every time we step into the classroom, someone counted and measured how much dead load (desk, chairs, etc) the floor could hold and how much live load (people) it could hold all at once. Math is the structure of our lives and is everywhere around us. Gracie made a good point on asking how did they even discover such complex equations in such primitive times, Me all I am is grateful they did the work so that our lives could be a little easier today.
I chose prompt A
Back in high school, I was struggling through Pre-Calculus and Geometry towards the end. During very difficult periods, I would start asking similar questions to Gracie’s. Why would I need this? In what way am I ever going to need or use this? Most of these questions came from working with Algebra and Calculus. Geometry was a little easier to understand as it can be used in real-life situations such as buildings, structures, and the like. The others… not so much. I was slowly able to understand the importance of them when it came to things such as graphs, but admittedly, I’m still having trouble seeing why it is necessary. Maybe it’s also the reason why I’m still having trouble with Calculus in general.
I feel similar to grace, when thinking if math is real she gives good points, who thinks about math and numbers at a time when it wasn’t necessary? when thinking if math is real you can’t think of it as just basic math like what 1+1, her opinion goes further on only basic math and that’s why people criticized her, they weren’t really thinking further beyond basic arithmetic, soon moving forward in life new types of math will be invented. In short, math is both invented and discovered.
Prompt A. I am confused by how Colbert did 2*3^7 in his head that fast. He was off by 2 but it is still impressive. Here’s how I would do it:
2*3^7 = 6*3^6 = 6*27^2 = 6*729 = 6*(730 – 1) = 4380 – 6 = 4374
This way is mental-math friendly but I doubt I could do it in under 30 seconds, and that is even after knowing a trick to square two-digit numbers. So either Colbert knows the trick as well and is really good at it, or he is secretly a mathematician. I mean, calculator.
The trick: (a+b)(a-b) = a^2 – b^2. Add b^2 to both sides. Let a = 27 and b = 3, so 27 squared is 30*24 + 3^2. Much easier to do by bringing the 0 over so it’s 3*240.
This trick is an example of math that is not very useful but comes up day to day. Math taught in school is the opposite, useful but rarely necessary for everyday life (as Gracie says). Personally, I would rather learn the latter.
I chose prompt A: What are you curious about? Have you ever had any questions like āIs math real?ā or like Gracieās questions that youāve 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?
I’ve wondered at times what the purpose was of some equation or problem I’ve had to solve. And a lot of the time, those problems had little, if any, direct applicability to my life. I’ve never needed to prove the congruency of triangles, or find the asymptote of a line, in my everyday life. But as an engineering major, these things have had an indirect application in my life. I haven’t had to find an asymptote, but I’ve needed to be able to understand them in working with concepts that I do need.
Prompt B:
The answers to Questions 1 & 7 are quite interesting to me because it gets to the core idea of mathematicians and their psychology. Question 1 speaks about pattern recognition and efficiency, which are the fundamentals of math and the fundamental ideology of mathematicians. It’s very interesting because it really can be applied to every discipline. From a personal point of view, I love learning new skills and things, and I also love being really good at it, but I donāt want to spend an eternity mastering it, which is where āmathematicians are lazyā (in a sense) comes in: being efficient is the goal to shorten the amount of time it takes. I just found that interesting because she explained something that I subconsciously knew, and basically reaffirmed that Iām majorly a STEM kid. Question 7 was also interesting because of the psychological point of view, but this answer is far too long to expand.