Hello there! I am Vijay and soon I will be embarking on a journey through space and time...and math; I will be going to ASU's Department of Mathematics and working with Dr. John Jones to attempt to solve the 3x3 Magic Square of Squares problem:
Construct a 3x3 magic square composed of distinct perfect squares or prove that such a magic square cannot be constructed.
This is certainly a very difficult problem; mathematicians have worked on this problem for quite a long time and still not solved it. However, bits of progress have been made over time and hopefully I can solve the problem or add some more progress. In addition to the 3x3 Magic Square of Squares, I will spend some time on similar problems such as 5x5 bimagic squares, 3x3 semi-magic square of cubes, magic squares of cubes, and add-mult magic squares. Mathematicians have solved similar problem of this difficulty, so I am sure that I can make some progress towards these smaller problems.
Anyways, enough about the project itself. As you probably know, I am Vijay and a senior at BASIS Scottsdale. My favorite subjects are computer science, math, and music. I plan on majoring in computer science and mathematics. In my free time, I like to listen to music, watch anime, and (please don't laugh) make computer programs. I know it seems clichéd, but I truly love designing programs. I have created a cycle decomposer, a rail-fence cipher decoder, a multiplayer video game and so much more. Maybe I will share some of my cooler projects with you. I also love jokes (By the way, What did the tooth fairy say to the lawyer? “I want the tooth, the whole tooth and nothing but the tooth!” and the lawyer responds “You can’t handle the tooth!”).
In 8th grade, I attempted to solve the 3x3 Magic Square of Squares problem. I independently proved that this magic square of squares must have either all odd entries or all even entries. Ever since then, this problem has haunted dreams for four years and my only goal in life is to solve it...well...maybe it's more like I have been thinking about and working on this problem from time to time. I really don't know what will happen at the end of my senior project. Will I actually solve the problem? or will I only know about the progress already made? One thing is for sure: I will do my best. Wish me luck!
Hi Vijay! I love magic squares. This is a great blog post. I hope I get to see many magic squares on your blog in the future. :) Also, I love the tooth fairy joke!
ReplyDeleteHello Mrs. Bailey! There will definitely be many magic squares with interesting properties on this blog.
DeleteSo Liam Neeson holds a super secret barbecue for famous people every year. Last year, he said "I have a very particular set of grills" and Julie Andrews replied "these are a few of my favorite wings."
Vijay, mathematics is more magical than I thought. How did you become interested in the 3x3 Magic Square of Squares problem? That seems so random for an 8th grader.
ReplyDeleteAnyways, I look forward to hearing about your journey and good luck!
Hello Nicole! In 8th grade, I took Math Investigations. In the third trimester of that class, all the students attempted to solve open math problems. It was then that I discovered and became absorbed by the 3x3 Magic Square of Squares problem.
DeleteHey Vijay, your project seems like the perfect match for you. It was fun to learn about magic squares, and I hope you're able to solve your magic square problem. I'm curious: what are some real-world applications of the problem that you are trying to solve?
ReplyDeleteHello Anthony! The 3x3 Magic Square of Squares problem's applications come indirectly; by solving this problem we may expand our knowledge in Number Theory and solve more complex problems.
DeleteWow, Vijay! This problem sounds really cool! Have you thought of any strategies or know of any strategies that mathematicians have previously used to try to solve this problem or similar problems?
ReplyDeleteHello Nathan! Much of the progress for this problem has been made through modding out the entries in magic squares to determine what kind of entries do not work. For example, by modding out by 2, we have found out that the entries in a 3x3 magic square of squares are either all even or all odd. Another strategy being used is generating magic squares and modifying the generation process such that certain conditions of the 3x3 magic square of squares is met. By repeating this process, all the conditions can hopefully be met.
DeleteHi Vijay! This seems like an extremely intriguing project. I can't wait to see if you will be able to solve it or make considerable progress on this extremely difficult problem. Of the advances made by other mathematicians, which one has helped you the most during this pursuit?
ReplyDeleteHello Jackson! I would say that the various ways of generating magic squares will help me the most. This is an integral part of trying to construct the 3x3 magic square of squares and I certainly would not have figured out how to generate magic squares on my own.
DeleteHello Vijay! This seems like a really interesting problem. I love math, but I have never actually heard of the magic square problem. However, thanks to you and your work towards this problem, I have been searching up equally interesting math problems on the internet for myself. Knowing that you have been working on this project since eighth grade makes me certain that you will make fruitful progress on this problem, and you and everyone on this blog will learn many interesting new things about math and magic squares. Also, what kind of math problems has Dr, John Jones made progress on and how will his progress help you?
ReplyDeleteLastly, keep up the good jokes! I can't wait to see what you have next!
Hello Gokul! Dr. Jones has researched many topics in number theory. Here's a link to his research: http://hobbes.la.asu.edu/research.html His background in number theory and his experience with unsolved problems should help me with my project.
Delete2 goats can produce 2 buckets of milk in 2 days. If farmer Joe needs 1 goat to produce 1 bucket of milk in 1 day, what does farmer Joe say?
"We're gonna need a bigger goat"
Hey Vijay! The senior project you have chosen seems very interesting as i too am a lover of math. Is there any particular reason why math and computer science are your favorite subjects? Thanks, looking forward to learning more about Magic squares.
ReplyDeleteHello Michael! If I had to give a reason why I like math and computer science, I would say that they focus on problem solving. Well... I guess all fields have some form of problem solving, but in those fields, people are limited in their power by the laws of physics and human behavior. With math and computer science, only logic limits your creative power.
DeleteHi Vijay. This seems like a very interesting problem. I have been intrigued since a very young age. I am looking foward to learning more about this problem in your future blogs.
ReplyDeleteHello Jack! I think that many of us are shown magic squares at a young age and then never shown them again, even though they have many interesting mathematical properties. I am glad that you haven't forgotten them and that I will have the opportunity to guide you around the world of magic squares
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