A Crash Course in Applying to a Math PhD - Applying guide

Sep 13, 2026

A rough, practical guide to what applicants should do and expect when applying for a PhD in mathematics, with guidance structured across key phases before, during, and after the application cycle. It focuses on decision-making about fit, preparation steps such as professors, coursework, research, the GRE, CV materials, and funding topics, then moves into completing applications with essays, recommendations, transcripts, outreach, timelines, and interview preparation. Advice is grounded in sincerity and integrity and can also help applicants to PhD programs in other fields.

LanguageEnglish

CategoryGeneral

FormatPDF

Pages23

Reading Time8 min

AccessFree to download

Introduction

Deciding if a PhD is right for you

Before the application opens

Beginning the application

Application is complete! What now?

What to do if things don’t go according to plan

A CRASH COURSE IN APPLYING TO A MATH PHD GREGORY BORISSOV Abstract. A rough guide on what to do and expect when applying for a PhD in mathematics. Goes over broad topics before, during, and after the application process. Advice in this paper can still help people applying to PhDs in other fields as well. Contents 1. Introduction 2 2. Deciding if a PhD is right for you 2 2.1. You can apply for a PhD right out of undergrad 3 2.2. What to expect 3 2.3. Mastering out 3 2.4. Take care of yourself 4 3. Before the application opens 4 3.1. Professors 4 3.2. Go to class 5 3.3. Research 6 3.4. Graduate classes 8 3.5. GRE 8 3.6. CV 10 3.7. NSF 11 3.8. Extracurriculars 11 4. Beginning the application 11 4.1. Deciding where to apply 12 4.2. Personal statement essays 12 4.3. Letters of recommendation 17 4.4. Fee waivers 18 4.5. Transcript 19 4.6. Outreach 19 5. Application is complete! What now? 20 5.1. General timeline 20 5.2. Keep outreaching 21 5.3. Interviews 21 5.4. Getting an invitation to visit 22 5.5. Making a decision 23 6. What to do if things don’t go according to plan 23 6.1. Master’s 23 6.2. 5th year 23 Date: January 2026 . Fifth version (first released June 2024) . Website: [gregoryborissov.wordpress.com](gregoryborissov.wordpress.com). 2 GREGORY BORISSOV 1. Introduction Applying to grad school is no easy task, and it is very difficult to even know where to begin. This guide is specifically catered to current math undergraduates applying for a math/applied math/statistics PhD, but I am sure a good chunk of this will apply to other majors as well. I have learned a lot throughout my whole application process, and I wish I had some sort of general guide to follow while applying. You absolutely do not need to follow everything I say in this guide. For example, research (section 3.3), graduate classes (section 3.4) and outreach (sections 4.6 and 5.2) are definitely not needed to get into a program, but I stress them heavily in this paper as they are all very strong ways to give your application a significant advantage. Also, I am saying what worked for me and what I found effective when I applied. There is a good chance this will not work as well for you, so adapt and ask others for guidance. Throughout this crash course, a lot of the advice I give involves handling and speaking with others. You only have one brain; if you work with others you can have so many more brains working your application. Because of this, I am going to recommend you read the book How to Win Friends and Influence People by Dale Carnegie, which teaches you how to speak with people effectively and be a more sincere and affable person. This will help greatly in nearly all sections I wrote in this guide. You definitely don’t need to read it, but it has helped me so much that I had to include it: I do not think I could have gotten into grad school without the knowledge I gained from this book. It is very popular and is most likely in your school’s library. Regardless, all recommendations given here are meant to be followed with sincerity and respect. The key to success is genuine interest and enthusiasm for the field, dishonesty will only hurt you in the long run. When you tell a professor you would like to work with them, say it because you mean it. Don’t lie to someone just to gain an advantage. Collaboration is a big part of academia and everyone appreciates people who work with integrity. I must say that I am not an international student, so this guide does not contain any pointers on things that are unique to international students, like applying for a visa or taking language proficiency tests (e.g. the TOEFL or Duolingo) . If you are looking for any resources which touch on this, Shintaro Fushida-Hardy’s document Grad School Application Advice has some tips on applying as an international student (and he also has some other good resources on his website too!) . I

FAQs

How can applicants decide whether a math PhD is the right choice?

The guide emphasizes that a PhD demands sustained effort and strong motivation, but also stresses that lack of “intelligence” should not be treated as a limiting factor. It recommends talking with professors and trusted people to assess fit and making a choice by trying it.

What preparation should be done before the application opens?

Preparation includes engaging with professors, attending classes, developing research experience, considering graduate-level classes, and completing components such as the GRE, CV preparation, and understanding related topics like NSF and extracurriculars.

What steps come after the application is submitted?

After submission, the guide outlines general timeline expectations, the importance of continued outreach, how interviews typically work, how to handle invitations to visit, and how to make a final decision based on the process outcomes.

Sep 13, 2026

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