Securing Undergrad Research Experience - Maths at Cambridge

hey everyone and welcome back to the channel so if you're new here my name is ray and i just finished my second year studying physics here at cambridge and in this video we will be discussing what cambridge students are doing during the summer whether it's like internships research projects and stuff like that so here i have three of my friends who are going to be talking about some of the research projects they're doing and how they got it and everything like that but for now we'll probably do introductions so uh do you want to introduce yourself first yeah sure hi my name is georgie i'm a first year math student at st catherine's college and i'm from germany hi i'm xiang i just finished my first year at centron studying mass and i'm doing mass research this summer i'm from mainland china and hello everyone i'm manthas just finished my first year studying mathematics at cambridge um also as you're getting catherine's college and i'm from lithuania so that's

introductions for everyone so the question we want to like first address is what we're all working on during the summer yeah i'm doing a maths research project with a mathematician called emmanuel breach and we meet twice a week and discuss the topic which is something about group theory and computability theory it's about group freeness if you know what that means but it's not that's not that important um anyhow what we do is we read papers about the specific problem that no one's been able to solve since like the 60s and we're basically trying to take some techniques from some papers apply them to the problem see if we can find anything obviously we don't expect to solve the problem because people haven't been able to for a long time but we want to at least try and see what we can find out yeah so i'm also doing a math research project with mantis and we are doing something about graphs theory combinatorics and a little bit numbers theory and basically we are reading papers trying to fix it and trying to apply the method in it to other stuff that we want to solve so we set up a goal is a big conjecture but we found it very hard and then we just step by step just think of some small problems add more conditions we can that we are capable of solving and then we are in the process of writing a project writer and i guess the only uh part to add is that we're working with cambridge mathematician alec walker with which we meet um every week um and the interestingly enough the supervisions are actually led by us and it's all about asking the right questions that will get us through the next week that will keep us interested and have a sufficient amount of papers to read next week and it's quite a different uh feeling um as compared to studying internal time at

cambridge um yes so that sounds good um so i suppose the next question for all of us is that how do we go about getting this actual uh project that we're working on this summer i basically emailed a lot of professors and like who are working on the topic that i was interested in which was just group theory i had decided that i wanted to do something in group theory so i just thought about where would i like to go like obviously cambridge would be uh easiest but so i messaged like a few people in cambridge i thought maybe i want to do something in germany because that's where i live messaged some people in germany i japan just because i just thought that would be interesting but anyhow uh the key takeaways most of them ignored me also a very big portion just said no some of them were like ah covert probably not and like one person outright said yes so that's who i ended up with so yeah i think the key point is that just don't give up message many people and it'll work out at some point because i guess most people are interested in having a student of some kind okay so for me um i also want to get some research experience at an early stage so i can decide if doing research really suits me though if doing research is really the thing i want to do in my future life so initially i thought i want to apply for some undergraduate research program in usa because they make some application process for them and so i just wanted to apply for this for cambridge we have cms and cmp which is research projects for basically for second year and third year so it's very hard for first year to get in but then when i ask my director of studies to ask for a recommendation letter he just said yes i can write it for you for like for the american research opportunities but like i could also refer you to my colleague who's uh like our supervisor now um and my story uh for getting this some research placement is similar to that of georgie's um since we're from the same college i guess and i as well as georgie applied to many many specifically cambridge mathematicians um just looking uh on the cms website the center for mathematical sciences at cambridge website looking at the mathematicians working in the area i'm interested in and the you know finding out their email messaging them about the summer project um again um as gergie stressed um you only need one acceptance to have this project and i got um i guess ninety percent of people that either didn't reply to me or said uh no in like one sentence only but um you know having one positive reply is all you need so i guess you shouldn't at all worry that most people will say no or reject you or whatever and i guess if any of you guys want to do a similar thing in a summer to come then just apply to as many people as you can and don't worry about if they say no

so i suppose the next question is that what your favorite parts of your projects are yeah i would just say it's interesting isn't that because the for example the topic i'm working on it's just like a very niche specific topic of group theory and it's not like you would ever learn about it and if you like normally progress to university like it's not only that this is advanced there's just like you wouldn't find a masters course on or like a bachelor's course or anything because it's just like this very niche topic so it just gives you a chance to like actually be able to engage with the topic which you would have never like even thought of thinking about so far and also you have a mentor which is really good because if you wanted to do this by yourself of course like it's extremely advanced and you wouldn't understand most of it but like it still turns out that i can understand most of it because often it's just like you have like one piece of background knowledge that you don't know so i just drop him an email and or like ask during our meetings and he just clears it up and then it's quite easy to understand so i would say yeah it's quite good that i got the chance to actually be able to deal with topics like these without like completely being overwhelmed even though i'm just the first yeah okay so my favorite part i would say is that i have a supervisor and i have a partner so having a partner the benefit is that you might make silly mistakes so your partner will point it out immediately and if he also makes a silly mistake i will point it out immediately so you will not waste a lot of time thinking about some like something that's not in the right direction and also i would say that because we are constantly changing our directions if we think okay we figured this small topic out or if they think oh we realize these topics very hard and then our supervisor will lead us give us new questions to think of or they can give us new hints or some big conjectures some big series that he can think of but we don't know so that's a good point about it yeah the way i would describe this research project is uh quite weirdly to compare it to this rabbit hole that you go on watching random youtube videos um i'd say that when we enter this project all of us are handed a question uh that we were supposed to answer in our case a conjecture raised in a recent paper but um we soon figured that either the conjecture is too hard or something about us too trivial or you know not that interesting whatever then from that you ask other questions which in turn make you ask a lot more of other questions not even that related to the first question you asked and you go on this random rabbit hole you learn so much of mathematics through this process and it's quite interesting that you don't even know what you're going to do the next day after you're done with work let's say on one of the days you're doing the project so i found this way of working where it's not following a textbook and it's not doing example sheet questions as during term time quite interesting because it allows you to sort of ask these questions at your own expense and really um enjoy them and learn a lot of maths while doing this so i think it's uh that's the main part i love about this

project so i suppose a follow-up question based on like what you've been enjoying so far is how do you feel it adds to your career progression in the future or do you feel like it's influenced your career decision in that you definitely don't want to do research or you potentially want to do more research in the future i mean to switch it up i might go first this time so for me i think that this project is just another way to try out something uh potentially that i want to i feel like this project is in some sense a way to try out a potential career opportunity for myself doing research that is i wouldn't say that you know that i'm either fully doing research definitely after university or i'm definitely not doing that um i'll say it's uh you know i need to try other things as well but what i do like about this opportunity um is that i realize that i really like this research mindset where um so even though you have a meeting every week with your supervisor the supervisor doesn't really you know schedule your day every day so you get to pick your your schedule to be exactly what you want and i really like this way of working being able to set my goals every day and be able to execute on them as i wanted not as you know my boss in like some company wants it i definitely want to try out working in different environments as well say some company or a startup or something similar and i definitely think that this is the sort of work-life balance that i do want to essentially um aim for in my future career i think i heard a similar opinion with mentors is that i try out what research will be and i think it's definitely will be a possibility for my future of doing research because you know i kind of like it it's very flexible i don't have there it goes i don't need to finish everything that i said set up for my in the morning because you don't know where you will end in the evening but then the things that if you have a brilliant idea and it's perfectly applies to your question the satisfaction is huge um and yeah i very much like it so the thing about research is that we have supervisor but if i really end up doing research i'll do go maybe post grads and something which you don't have very much connection with your supervisor but it's very much depend on your own and sometimes you don't have a partner so you might get lost so uh i think i'll have some backup plans for my future like i'll try maybe some companies but research is definitely one possibility for my future and i like it also an obvious thing to add is maybe that a research project like this is a good bullet point for your cv so it definitely doesn't hurt to have something like that to just show people that you have experience with research and um yeah for myself i had thought before that i would like to have done research after university and i think that's yeah confirmed it more or less but i've also become aware of many like hard things that they are in research like as mantis and sean said obviously you're very flexible which is nice because you don't have to do exactly what your company or a boss tells you to but also that means you can never really like turn off because with a normal job you have say nine to five so at five pm your job ends you come home and then you can just you know watch tv or do whatever but with research it's like the problem is always at the back of your head and you can never really chill so like most of the time you're just thinking about it which is nice because it's interesting and you enjoy the problem and you enjoy working on it but it's also stressful because you don't really get to calm down but as i say you can see that as a positive negative but it's definitely something i've learned yes i agree you know these days because we're currently writing a write tab we almost finish it and i remember yesterday morning when i got home i had a nightmare and it's like i'm in that dream it was like i'm asking myself is it results strong enough and i don't remember i didn't drink though for very stupid results and it was like in a dream oh i finished such a naive result such an easy result that's why every either writer and the morning i get up i think oh i actually did something the research did we get some trivia results that's something yeah i agree very much with the points in that it's useful to know whether you like being able to turn off and stop thinking about the problem for the day because we're very much nine well with 95 jobs or 95 internships you can just stop for the day and like chill for the rest of the day and it doesn't add as much stress whereas i feel like with research and even working for a startup because it's so flexible um or will not certain not really rigid in the hours you're working um it can become very difficult to take a break almost which yeah for some people they that's a huge concern for them other people not so much because they're enjoying it so uh so much but i don't i still don't know where i lie in that sense and whether i could sustain that for many months or even years right so i guess the final

question is uh what advice would you have for future students who want to be working the same project as you are or just any lessons you've learned that you are willing to share with them yeah and don't be afraid of writing 30 emails at once that's really not an issue just try as much as you can there's really nothing that can go wrong just remember to change the name when you do it because i have a friend who accidentally wrote an email asking for a research placement but the name of a different professor in the header line so try to not do that besides that do you get a reply i don't know actually i assume not i assume not but yes anyhow um besides that uh i think it's there's really nothing you can do wrong so just it's a good experience i would recommend to just if you have nothing else going on in the summer then there's really no harm in doing it it's good looks good for your cv it's good to get experience and research know if that's what you want to do with your life yeah so just add a few point is that um many people would say why while you're doing research at undergrad you can't make any like world class achievements to the society but i think the things that um because it's more competitive to get a phd you're entering master schools so you really need to get to them more about research at your early stage so you can maybe get more familiar with doing research and you can become stronger when you really become a phd student and regarding finding a research opportunity i would say uh it's the easiest if you can find some someone you know like your connections like uh your lecturer your supervisor for your like normal courses and asks and maybe uh to refer to someone they know that's the easiest way because you can secure this place and if not you can just email loads of people and i think definitely you will get some replies and there are some official ones research opportunities but uh because it's official because it's online lots of people will apply for it so some of them are very good you should definitely apply uh but beware that there are other ways they are definitely not only restricted to this official research opportunity yeah i definitely agree i think the thing that i would like to add um and maybe this mostly applies to mathematics but i think many other fields as well is that especially if you're an undergraduate student applying for summer research placement i wouldn't care so much about the specific topic of the project that you're applying for especially if you don't know that much about the field as an undergrad which i guess mostly is the case for most undergrad students it would be super nice if you didn't hate the subfield that you're applying to but other than that i think uh for everyone um that has done a research placement i think they would say that they've learned so much in that field that they didn't even imagine they would end up learning as they started the project so i think treat this as a opportunity to learn and uh also i guess to add more onto desean's point um it's not only good for your cv i think it's also good to you know always be in contact during the summer with a working either mathematician or a person in any other field so that you build up those uh connections so that next year you can so you can next year drop them an email and do expect a response recommendation to either another project or to work with another mathematician and so on so i guess um doing some placement like this can only be a good thing in the end you will gain a lot of experience learn about yourself and also um create these opportunities for yourself in the future yeah and something that we should add would is probably funding so if you're worried about funding uh there are like many opportunities many things you can apply to i for example applied to the department in cambridge just to the maths department and they gave me money so and it not only covers my living costs it just it's even more than that so it's like more than enough and i don't know like if your home university has something like that i'm sure they will you can ask there you can ask the university you're studying at if it's a different university there are like even lots of independent stuff at least in the uk independent organizations which will give you money to do summer research so that mostly isn't an issue yeah so that's

basically for the video hopefully you learned something useful about how you can do undergrad maths research and find these opportunities for yourself and i guess we'll see you next time bye