Our alumns are going places! They've gone to MathILy (of course), Mathcamp, HCSSiM, the Ross program, and PROMYS in subsequent summers, and to UC Berkeley, MIT, the University of Chicago, Williams, Carnegie Mellon University, Hamilton, Rice, Stanford, Oberlin, Yale, Oxford... and more places, for college.

*Evan*: The subjects taught at MathIly-Er broadened my view of mathematics. Math has so many subtopics and branches that usually never get covered or even mentioned in a typical course. Something that was also curious to me was that I had thought about some of the ideas covered in MathIly-Er before, but I had never spent the time to actually explore those ideas and find out more about them. All in all, MathIly-Er has definitely been one of my favorite summer experiences and without question the most rewarding online program I have ever had the pleasure of experiencing.

*Emily*: MathILy-Er was a phenomenal experience for me, and I am so fortunate to have had the opportunity to spend five weeks with such a talented group of students under the guidance of fantastic instructors. I applied to MathILy-Er desiring a challenge, the opportunity to explore math that I had not studied before. Indeed, MathILy-Er fulfilled my expectations and more, and I left MathILy-Er even more enthusiastic about math. One of the highlights of my experience at MathILy-Er was definitely the people. Although MathILy-Er 2020 was on Zoom, the instructors did a fantastic job making us students feel connected. The instructors at MathILy-Er care deeply about each students' growth as individuals and mathematicians---they are also really cool and more than up to having some fun! Students at MathILy-Er are all eager to help each other---at MathILy-Er, I met a group of extremely bright and friendly people, and we still stay in touch!

*Jamin*: MathILy-Er has been a great experience for me to grow and learn more math, and working with my classmates has been especially helpful in striving towards a better understanding of math concepts. The wide range of math topics the program covered were very different from what I am used to in school and competitions. Most importantly, I love that Math is Infused with Levity!

*Lydia*: My biggest failures were things that later became some of my favorite successes (which is not a coincidence).

*Andreea*: Who knew that such a far-spread group of kids and people could become so close (from many many miles away) through a computer screen? I was nervous, at first, that it would be difficult to spend so many hours with practical strangers, but I proved myself wrong quite quickly. This program was, simply put, very awesome.

*David*: I liked math. Now, after MathILy-Er, I like math even more. MathILy-Er, most importantly, taught me how to express mathematical ideas in a clear, concise manner and how to be a better thinker and collaborative learner.

*Efe Inan*: When I came here, I wanted to learn about math that I wasn't taught in school, and I feel that it has been fulfilled beyond what I could have expected.

*Youbin Cho*: In general, I feel like I accomplished a lot of things I wouldn't have without MathILy-Er. Personally, it was my first time with inquiry-based learning, and I'd say it is the way I want to be taught for everything else because you get more out of it. It forces people to actively participate in a good way. I made good conjectures and proved many things. Seeing my name often on the problem set assured me that I have done a lot to contribute to the class, which made me proud of myself.

*Joeli L.*: My five weeks at MathILy-Er have honestly been great. [...] I feel like I've finally met the goal I set when I applied [...] : Make friends. Learn math. Have fun.

*Rory Erlich*: I feel that I overcame an initial lack of confidence to come to a place where I could find solutions that contributed to the class's overall progress. I was also proud of the times, however, when I pushed myself to struggle with and work to understand a concept despite knowing that others has already developed it or might come to it faster or more easily than me. ... in large part what I have actually taken away from my time here is that I want to pursue Math more seriously in the short term, perhaps through the Math club at my school or other extracurricular venues. [...] I know when I leave I will miss being in an environment that constantly fosters intellectual growth and encourages me to apply myself as a mathematician, both inside the classroom and out.

*Paola V.*: After realizing that I can in fact do what I didn't used to think I could do, I probably would reach for the problems that seem impossible more often.

*David Z.*: When I came to MathILy-Er, I was extremely resume-orientated. I thought that this would help improve my number theory (which it did) and I could do better in math competitions as a result. However, as time went on, I quickly realized that I didn't care about doing well in competitions nearly as much as learning about the wide variety of fields mathematics had to offer. By looking at how the instructors talked about their field of work, I saw and felt the passion they had for mathematics, and so I also wanted to have that same kind of passion for math.

*Max E.*: I can't believe it's already been 5 weeks and my time at MathILy-Er is over. During my time here I grew as a mathematician and as a person in so many ways. I had never experienced a teaching style like what we went through in Root and Branch class, but it was a style I thoroughly enjoyed and it really worked for me. Not only did the instructors expand my mathematical horizons, but outside of class they treated me as a peer, which is something I've never really experienced with adults before.

*Yuchen Fan*: When I asked Jonah the first day when our lectures would be, he looked at me and said that he wouldn't ever lecture. At the time, I wasn't sure how he would lead a class and teach us without doing so, but he, like all of my teachers, has never done so. ...allowing us to discover and prove conjectures is definitely worthwhile, even if it does make me want to tear my hair out sometimes.

*Steven Santos*: I've never called a teacher by their first name before so it was totally a new thing for me. It made me feel more welcomed than anything into the program... [My classmates] are the best group of people I have ever met in my life. They showed me that there are people that share a common interest with me in math and that I actually can have fun and make progress at the same time. There's no other group I'd rather be in.

*Cam Harrington*: MathILy-Er has been a great experience for me. I am glad that I had the chance to meet everyone here. I have enjoyed learning about numerous topics like slinkys, SOZOMs, graph theory, staircase number, combinatorics and much more. The teachers here are gifted and truly furthered my knowledge in areas of mathematics I had not previously encountered. I was also amazed at the talent of the students who were adept at problem solving and were all very creative and approached problems in multiple ways... Classes here were not something I had been exposed to prior and it was a fascinating new way of learning.

*Andrew K.*: I can't, no matter how hard I try, express how much I have enjoyed these past five weeks... I have learned more than I could have ever expected here, from donut-man generating functions and forbidden colorings to cake-cutting and balanced numbers. But what I'll treasure the most are the experiences I have had ...and I couldn't have hoped for a better summer.

*Lola Seibert*:
Overall, I have grown tremendously as a math student and as a person. I have become more independent and view math in a new way. I am especially proud of all of my work in class and how hard I work. I have made friends who I have laughed with until my stomach hurts and my eyes are tearing. I have learned so much in as little as five weeks.

*Aaron Mesa*:
I think one of the most valuable things MathILy-Er has taught me is that it is possible to actually be a mathematician and that if I work hard it is something I am capable of doing. ... I have a much better sense of how to explore mathematical ideas on my own and what to look at if I am exploring a problem.

*Lindsey*:
I've learned a lot about learning and how to learn how to learn. So, after this program, I feel significantly more prepared and confident in doing math, and it has been a truly valuable experience as I look into studying math in the future.

*Saraphina F.*:
This has shown me a whole other kind of math I had never seen before, so I feel like it opened the door to something I never thought possible in a math class. I can't wait to do many more problem sets like the one in class, and just think about all of the other cool math!! Just the way we do things is really what makes such a difference---building them ourselves, letting the problems teach us concepts instead of being told them, and the instructors are just incredible.

*Karol M.*: I can't even begin to express how important MathILy-Er was for me. I built so many wonderful relationships with people, and I had so much fun! Throughout the school year, it is easy to drown in schoolwork, so this was an amazing break where I could actually interact with a lot of nice and funny people. Along with that, I learned so many cool ideas which I will probably remember for a long time. Last but not least, this style of learning was so amazing! I have never been in class where it was so student led and people got to build off each other's ideas and go up to the board so much.

*Shardul C.*: Along with the mathematics itself, I learned a lot about how mathematics actually works (if asked to compress that understanding I would put it as "free yet focused foraging coupled with continuous collaboration").

*Stacy Godfreey-Igwe*: These 5 weeks have given me some of the best moments of my life. It's surreal. I learned so more math that I ever imagined, took long walks in the morning and explored the city, made some awesome shots in ping pong, played the best game ever... and was able to create memories that will last me a lifetime.

*Milleno Pan*: I came here expecting math that would be much less interesting, and instead got problems and solutions that were quite surprising to me. Before coming... I think I had a much lower interest in studying math in the future, where it was, to me, just something I was kinda good at compared to the small group of people around me, and something I didn't completely hate... I am very sure that I will be continuing math in college.

*Julia T.*: There's something wondrously beautiful about being in a room full of people who do mathematics purely for indulgence, and I will never forget the joy and love and laughter that I felt in our classrooms.

*Nathan*: I've been able to experience mathematics I had never heard of while immersed in a mathematical community, the likes of which I could never encounter at home. I've learned much not just about different fields of mathematics, but the nature of learning and expressing mathematics itself. Before this program, my work was incomprehensible and full of technical symbols. I had difficulty explaining math to my friends, or helping them understand why I found joy in exploring it. Now, I feel more whole in these respects. I've really learned how to treat mathematics as a study, not simply as a set of numbers and definitions.

*KaiYuan Chi*: It feels very satisfying when we were the ones to create the rules instead of having someone telling us directly, and I believe that is the most important academic skill I gained in the past month.

*Alice Wei*: Overall, the relationships I've created in this program with people who appreciate math like I do helped expand my interest in math! Being surrounded by friends everyday made classes and activities an enjoyable environment.

*Pirooz Fereydouni*: MathILy-Er teachers use a quite different and more affective teaching strategy than other schools. After a brief introduction to what we are doing, the teachers stand aside and the students do all the work. Just when you think you have reached your mathematical limits, you can head to the dormitories and challenge your brain with card games, board games, or even engage in communications with other mathematically motivated students.

*Mia Taylor*: I knew that I was going to have fun when I came, but I was still surprised at how much fun I had.

*Stephen*: I've met fun mathematics-oriented teenagers, which are quite scarce where I live, so this has been one of the most interesting experiences of my life!

*Clarissa X.*: I felt that because the environment was very open and you were able to discover things on your own, I was able to look at concepts in a different way, and hence my problem solving abilities improved.

*Emma Y.*: MathILy-Er is like a big family, and I'm so happy to be a part of it.

*MathILy, MathILy-Er, and MathILy-EST are projects of the nonprofit organization Mathematical Staircase, Inc..*