Fake it, do it, make it: a mathematician’s path through impostor syndrome.
I cannot tell you when it happened. There was no single moment, no paper accepted, no problem solved, no email from a senior colleague that flipped a switch. What I noticed, eventually, was that conversations had changed. My advisor would pause longer when I made a point. A visitor would ask me a question and actually wait for the answer. In a seminar, someone would push back on something I’d said and then, a beat later, agree. I was the expert for a moment. Then for several moments. Then, gradually, the moments stopped feeling exceptional.
Looking back, I had spent my early years in graduate school doing what almost everyone does: faking it. Nodding at the spectral sequence. Saying things in seminars that sounded like opinions. Performing a confidence I did not yet have any reason to feel. There is a piece of folk wisdom for this part of the experience, fake it till you make it, and it served me, the way it serves most people, until it didn’t.
I want to propose a better aphorism for the later part, and a phrase for the long stretch in between:
Fake it till you make it → Do it until you can show it → Make it until you believe it.
The first and last are endpoints. The middle is the mechanism that gets you from one to the other. Together, they describe something I think most mathematicians live through but rarely name: the slow conversion of borrowed confidence into earned belief.
Why “make it until you believe it” is the better aphorism
“Fake it till you make it” is about appearance. You project competence you don’t have, and at some unspecified moment, reality catches up. The trouble with the framing is that nothing in it tells you whether reality has actually caught up. You can fake your way to tenure and still feel like a fraud at fifty.
“Make it until you believe it” is about production. You do the work, prove the lemma, write the paper, give the talk, and let the accumulated evidence update your self-concept. The action is not performance; it is output. The belief, when it arrives, is backed by something.
In math, this matters more than in most fields. A proof either works or it doesn’t. The work itself adjudicates. You cannot fake a theorem. So the evidence you accumulate, when you accumulate it honestly, is unusually trustworthy.
The three phases
The phases below are epistemic states more than career stages. Most graduate students live the first; most postdocs live the second, often most intensely; most faculty live some version of the third, with residual visits to the second. But people move through them at different paces, and the boundaries are softer than years.
Phase 1 is fake-it territory. You don’t yet know enough to know whether you belong. There is no evidence yet about what kind of mathematician you are, because you haven’t done anything. Confidence, in this phase, has to be borrowed or performed. That isn’t a character flaw; it’s a rational response to the absence of data.
Phase 2 is do-it territory. You start producing real work, be it a finished proof, a clean writeup, a talk that goes well, a paper submitted. The evidence is arriving. But you discount it. You tell yourself the problem wasn’t really hard, that you were lucky, that anyone could have seen the trick once it was pointed out. Impostor syndrome is sharpest here, because the gap between reality and self-perception is widest. You are doing the work of a mathematician without yet recognizing yourself as one.
For postdocs, Phase 2 has its own particular weight. You are now expected to be independent, judged against a peer cohort scattered across the world, working on a clock that runs out. The phase is the same; the pressure on it is higher.
Phase 3 is make-it territory. The evidence has accumulated past the point where any honest accounting can deny it. The belief should follow automatically, but often it doesn’t, or doesn’t fully. The residual impostor feeling is mostly habit: old patterns of self-discounting persisting after they’ve stopped being accurate.
The transition between phases is rarely a single event. A specific moment may crystallize the shift, a paper accepted, a problem solved, a senior colleague treating you as a peer, but that moment usually just makes you notice a change that already happened.
What to do in each phase
The underlying logic is the same throughout: in each phase, the goal is to reduce the gap between reality and self-perception. What changes is which side of the gap is the problem.
Phase 1: Fake it till you make it
Show up to seminars you don’t understand, and stay through the parts you don’t follow. The goal isn’t to absorb the math, it’s to absorb the rhythm of how mathematicians talk. You are learning a culture before you are learning the content.
Ask questions even when you’re sure they’re stupid. The fake-it move here isn’t pretending to understand, it’s pretending you have the right to ask. Most “stupid” questions are shared by half the room.
Find one peer to be confused with. The fake-it phase is lonely because everyone is performing. Having one person you can be honestly lost with is structurally important. This is often the single most valuable relationship in early graduate school.
Don’t compare your insides to other people’s outsides. Other students who seem confident are also faking. The ones who seem to follow everything in the seminar are following maybe forty percent, same as you, just performing better.
Phase 2: Do it until you can show it
Finish things, even small things, and write them up properly. A two-page note proving a small lemma, fully written, beats a vague sense that you “basically understand” a big result. The act of writing produces evidence in a way that thinking doesn’t. You cannot argue with a finished document.
Keep a log of completed work, proofs, talks, calculations, papers refereed, students helped. Not for your CV. For yourself. The middle-phase mistake is constantly resetting your self-assessment to zero. The log fights this. When the impostor feeling spikes, you read the log.
Submit things before you think they’re ready. Papers, talk proposals, fellowship applications. The middle phase generates an infinite supply of “not quite ready yet,” the thing one polish away from being submittable. Submit anyway. Rejection is information; acceptance is evidence; perpetual polishing is neither.
Pay attention to what feels easy now that didn’t a year ago. The middle phase has a strange property: the things you’ve mastered become invisible. You stop noticing that you can do them. Looking back at old notes, old problem sets, old confusions is how you make this visible again.
Phase 3: Make it till you believe it
Notice when people start listening to you differently. The pause before they respond gets longer. They wait for your answer instead of moving past your question. They push back on a point and then, after a beat, concede. This is often the earliest external signal of the phase shift, and it usually arrives before you feel it internally. You are the expert for a moment. Then for several moments. Eventually the moments stop feeling exceptional.
Take credit for your work in concrete language. Not “I was lucky to stumble onto this” but “I proved this.” The language you use about your own work shapes what you believe about it. The make-it phase requires a willingness to use accurate language, even when it feels presumptuous.
Mentor someone earlier in the pipeline. Nothing collapses impostor syndrome faster than watching a first-year struggle with something you now find routine. You see your own progress reflected in their confusion. Their progress, in turn, becomes evidence of your competence in a way that’s harder to dismiss.
Notice when you disagree with senior people and turn out to be right. This will happen; a referee report you push back on, a conjecture you doubt, a proof technique you think is overrated. The first time you are confidently right against someone you used to defer to is a phase-shift moment. Mark it.
Say no to things, to the extent your position allows. Saying no to a referee request, a committee, a collaboration, and having the world not end, is evidence that you are a person whose time has value. Earlier-phase mathematicians say yes to everything because they’re not sure they can say no. Some Phase 3 capabilities are gated by job security; the security itself is part of what you are building.
Ask what you actually want to work on. The earlier phases are dominated by what your advisor wants, what is fashionable, what gets you a job. The make-it phase is where you can start asking what problems you actually find beautiful. This is the deepest signal that the belief has arrived: you trust your own taste.
A note for advisors
If you are reading this from Phase 3, you are also someone’s Phase 1 or Phase 2 guide. The framework is useful in two directions. The advice you give to a student in fake-it territory is different from the advice you give to a student in do-it territory. The first needs permission to belong, the second needs help recognizing what they’ve already done. Most advisor-student frustration I have seen comes from a phase mismatch: an advisor giving Phase 3 advice to a Phase 1 student, or expecting Phase 2 output from someone still in Phase 1.
Knowing which phase your student is in does not require deep insight. Ask them what they’ve finished recently. The answer will tell you.
It is also worth remembering, as an advisor, what you signal with the small things: how long you pause before responding, whether you wait for the answer, how you handle a student pushing back on a point you made. Your students are watching for the moment when you start treating them as an expert, even briefly. You are part of how they discover they have arrived.
A piece of advice for all three phases
Re-read your own old work occasionally. Old notes, old papers, old emails to your advisor. Mathematicians tend either to avoid this (cringe) or to do it nostalgically. The useful version is comparative: what did past-you struggle with, what does present-you find obvious, what does present-you still struggle with? This produces a calibrated picture of progress that neither pure self-criticism nor pure self-congratulation provides.
The point
You will probably not notice when it happens. There will not be a single conversation, a single result, a single recognition. There will just be a slow change in how you are listened to, and eventually a slow change in how you listen to yourself.
Keep producing. Keep noticing what you’ve produced. The belief, when it arrives, will be backed by something.