The statement of purpose, also known as research statement or letter of motivation, is a standard part of the application process for internships and doctoral programs. It is the most important part over which you have full control, since you are writing it yourself.
Unfortunately, many statements give no useful information, not because the candidate is unqualified but because they do not know what information they should include.
The target audience of a research statement is made up of scientists, thus you should write for scientists: stay concrete and support allegations with evidence.
Remember that scientists have varied backgrounds, and it is unlikely that all of your audience shares yours. In science you are expected to be neither overly bombastic, which comes across as egomania, nor overly humble, which comes across as self-hatred.
On the flip side, mention things that seem obvious to you but are not standard everywhere, such as having a full-time job during your studies, being a high-level athlete while maintaining high grades, and other such evidence of commitment, organization skills, and teamwork.
Your statement will be read alongside your CV and transcript, so restating their contents is a waste of space. Instead, your statement is an opportunity to elaborate on your past experience and future goals.
Your statement will be read by people with a limited time to review a pile of statements, so it must be short and to the point. The beginning especially needs to go straight to the point: if the reader finds it cliché and lacking specifics, such as “When I was little…”, they may not even read until the end.
Your application will be evaluated alongside hundreds of other applications, so you should focus on what makes you different, not on general facts that are true of most applicants. Your interest in research is not unique, but your experience and motivation may be. Your grades are not unique, but the specific projects you did may be.
The person reading your statement is trying to answer one question: would I want this person as a colleague? That is, will this person be motivated, competent, and nice to work with?
Your statement should start with a summary of your interests, past experience, and motivation. You should write this summary after writing the rest of the statement. The rest of your statement should convince the reader that you are motivated, competent, and nice to work with.
Describe your motivation: a specific challenge you want to tackle, a set of ideas you’d like to explore, the general area you want to dive deep in, and the reason why you are interested in these. Keep it focused enough that readers can see you as a good match, but not so focused that readers think they do not have the expertise to supervise you. Avoid looking like a “jack of all trades” by suggesting an overly broad range of subjects, since you cannot possibly have expertise in every topic. It is a good idea to use broad questions such as “How does a packet reach a server from my computer?” as a first question that you then refine into a specific interest. Mention specific pieces of work you find particularly inspiring, and explain why.
If you have research experience already, describe what problems you worked on, why they were interesting, and what you contributed. What approaches did you try and why? What did you learn? Would you want to continue working on this? Why did you enjoy doing research?
Paint a clear picture of you as a scientist and human being: what drives you, how you make decisions, how you resolve dilemmas, and so on. Convince the reader that you have some idea of what research entails and that you would like doing it, even if you’ve never done it before. Include experience that backs up your claims, such as leading a student club as evidence that you have leadership and management skills.
Finish by describing examples of work you like from the place you’re applying to. Are there specific advisors you’d like to work with? Specific work that particularly influenced you? This is not a commitment, only a way to explain why you are applying to that specific place. Such examples should not merely be one sentence stating names and paper titles. Explain why you want to work with specific people and what you found interesting in their work. This is not easy, but it will make you stand out. However, do not make your statement entirely about how you’d like to work on a specific project older than 3-4 years, as this risks dooming your application if the advisor is looking for people to work on something else, for instance because the student behind the project has graduated. Instead, you can say you enjoyed that project and would love to work on a similar topic.
Spend some time researching the challenges, ideas, and areas you mention. Avoid coming across as an amateur by using wildly incorrect terminology or describing challenges that are known to be either trivial or impossible.
Readers care about who you are now, not who you were in the past. Describe your current research dreams, not your childhood ones. Mention your past when it is relevant to who you are now, such as the experience you gained from past jobs, or a specific life experience that led you towards research.
Explain oddities in your record if possible. For instance, if you want to do research in operating systems but got a barely passing grade in your undergrad OS course, clarify what happened if there was a good reason.
Avoid abstract and unnecessary flattery toward your readers and yourself. Only praise your readers if you have specifics that make sense in the context of your application. Only boast about accomplishments that are impressive from a scientific perspective, not vague ones such as having been on many continents. Do not put down people, institutions, or entire research fields, no matter how much you dislike them.
Be specific whenever possible, illustrating with clear examples. Avoid unnecessary introductions, vague philosophical statements, and overly verbose descriptions.
Avoid subjective assessments and hyperbole. If something is “significant”, you can state it quantitatively. If something is “important”, it has some concrete effect you can point to. This is doubly true for soft skills, which are harder to provide evidence for. Better not say anything than make grandiose claims such as “I am a perfect fit” without evidence.
Aim for a high density of information in your statement. A one-page statement that tells a lot about you wins over a two-page statement stuffed with platitudes.
Use appropriate titles for people. If you’re not sure, use “Prof.” for everyone. Avoid accidentally calling someone by a lower title, such as “Dr.” for a professor. This can look particularly bad if you happen to only do so for members of underrepresented groups, even by accident.
Do not start the statement with an opening such as “To whom it may concern”, this is a waste of space. If you insist on having one, at least make it gender neutral and not “Dear Sirs”. Similarly, an end such as “Please feel free to contact me […]” is not useful as it is implicit.
Make sure your grammar is correct. Spell-check. Minor typos are fine, everybody makes those, but triple-check names such as the professors and labs you’d like to work with.
Ask people you know for feedback, especially if you know people who are already doing research such as former colleagues or advisors in internships. While not everyone may have the time to help, asking is free.