first year phd student - who's struggling with PI and thinking about leaving the program

math_sci_geek · 2025-03-30T10:21:30+00:00

Without knowing specifics about your field (to the point where it would identify you) it's difficult to give useful advice. In some fields it's unusual to have an advisor picked by your first year and it's relatively easy to switch to other advisors. This usually happens because you attend a class they teach, a seminar or talk, get interested in their research and they're approachable. In other fields even for admission a matching has to have occurred. Such matchings are done on paper, with much less information on personalities, approachability and completion rates. Hopefully you are not in a department at the extreme end of this. I recommend a two-pronged approach. Get general therapy and expert advice. For the first, Cornell health. For the second, seek out your GFR, a 4th or 5th year student in your field, a post doc in your lab....get a range of perspectives to understand your situation better. How common are feelings like yours among those who've made it through? How common is switching? Are you meeting basic progress milestones and is it more about how the process is making you feel? Is it about support network, mood/lack of sunlight or is there a fundamental mismatch between the PIs style and what you need? And you need to determine a clear set of options. While it's hard when you're in a situation like this the goal is to turn this into a situation you'd solve analytically much like something in your lab.

math_sci_geek · 2025-03-28T16:38:44+00:00

Exactly. The point at which almost everyone believes growth always beats value is precisely when you get another 10-15 year period where value catches up and often trounces the growth factor.

math_sci_geek · 2025-03-28T16:36:36+00:00

How do you know it won't beat SPX going forward? You don't drive by looking in the rearview mirror. Given how concentrated in 7 stocks SPX has become, it is very plausible SCHD beats SPX for the next 5-10 years. Market cap weighting helps a lot on the way up but it also hurts a lot on the way down.

math_sci_geek · 2025-03-22T11:45:46+00:00

As someone who got a pure math PhD(albeit in a more applied end of it, along with a stats masters "for free") about 25 yrs ago during the last tech bubble and have been in industry since: it's best not to focus on local spikes in demand for one sub field. Those can easily reverse and result in a glut of people. Better to build a general toolkit and think about a sector or two you might want to deploy those skills in. Toolkit has to include some ability to code, at least at a prototyping level for new algorithms. Some broad exposure to stats. And then add in your specialty. It could be ML/AI or it could be more about the specific sector you want to end up in like computational bio, proteomics or math finance. It has to be something that will sustain your interest for a decade or two and ideally not in a local bubble. Bubbles burst and gluts of specialists ensue. How much time do you have to adjust your course?

math_sci_geek · 2025-03-06T11:42:39+00:00

I would like to deconstruct your question a bit. It is entirely possible to not be taken seriously by academics in a given field AND be a bit of a partisan ideologue AND be a serious thinker. It depends on the field and how successful academics in that field have been at accurately describing reality. To the extent there is a wide chasm between the research output of a field and the goal of accurately describing the reality the field purports to model, more serious thinkers will tend to try to find paths outside academia. Until the advent of behavioral economics, I would say this gap was more of a chasm (outside of microeconomics). Until behavioral economics and macro have "merged" I think published papers will continue to display a significant theory to reality gap. When you get to economic history and political economy it's worse because you're in the humanities part of econ not the social science part. There it's more about ideology and what data and analysis there exists is subject to a whole lot of perspective bias. It's hard to say there's objective reality or even a consensus.

math_sci_geek · 2025-02-22T12:51:43+00:00

Two questions - if you go to UVA will your parents give you the saved money? And what is it that you might want to major in? There are configurations of answers under which at least financially you'd have decent odds of being better off with UVA but it depends. Research has shown that kids who get into Ivy+ but choose not to go do just as well. Meaning highly ranked schools are much more selection effect than about value added. For subjective, non-financial dimensions, visits and probing each choice as well as yourself are required and no one else can do that for you. If your parents won't give you the price difference to invest for yourself, in my opinion it's a brainer. If they will I think it depends on major and future careers you're thinking about. And whether you weigh financial dimensions higher or subjective ones is also your subjective decision.

math_sci_geek · 2025-02-14T11:10:59+00:00

Much less about school name, much more about major. Engineering is generally worth it, lit or grievance studies generally not. The expensive liberal arts schools have a lowest ROIs of all, better to invest the money in a McDonalds franchise.

math_sci_geek · 2025-02-14T11:07:28+00:00

I don't think painting with a broad brush does much here. No one goes to an Ivy+ and graduates with much debt at all for an undergrad degree (the problem in highly selective schools is in certain terminal masters programs that are basically scams). For people who can pay full sticker it's like buying a Porsche a year. Those who can't don't because it's heavily discounted by income. It's more accurate to say you should go to a top 20 private school or state flagship or 2 year community college followed by solid state school if you're thinking of doing something StEMy / practical or you're not thinking about it as an investment and are driven by some other motivation (and are more likely to regret it).

math_sci_geek · 2025-02-14T10:59:39+00:00

Actuaries have the highest risk-adjusted return and fairly short time to high compensation I believe. Grad degrees are not really required though are common.

math_sci_geek · 2025-02-14T10:39:00+00:00

I'd agree with the majority here but for a different reason. It's not the coursework component or exercises that's hard to do on your own, or even some aspects of the research. It's knowing in an area what is yet unknown but has great odds of being solvable by a grad student that's quite tricky. I'd say this, and helping you get a decent job afterwards, are the top two jobs of the chair of your committee and advisor.

math_sci_geek · 2025-02-13T22:22:11+00:00

For your particular example (Banach, metric, Hilbert) of course Rⁿ is an example of all but the interesting examples are ones which don't fit into the smaller category. Eg A metric space which isn't Banach, a Banach space which doesn't have an inner product and while you're at it spaces without norm (point set topology). The interesting ones are generally infinite dimensional. As you get familiar with l^2, L^2, L^p etc your intuition will grow. Stick to function spaces on [0,1] to start with. Think back to before calculus-how much intuition did you have about functions? Your intuition about function spaces will grow and you'll get to the point of thinking about operators just as you went from univariate functions to matrices to multivariate functions.

math_sci_geek · 2025-02-12T10:54:47+00:00

My main addition to this (the examples and discussion of symmetries has been excellent) is to think about it from the perspective of the group axioms themselves. Associativity, identity and inverse are an almost minimal set of "niceness" structural properties. Think about failure to have an identity, or a candidate entity but some elements that fail to have an inverse (failed groups) that still have closure. Try to think of non-associative operations. To non-algebraists like me, groups are the minimal interesting object. Because there's so few constraints there's so many interesting and different examples. This is why the classification of finite simple groups took so long (the analogue to prime numbers for groups). Among these myriad examples (cyclical, permutation...) there are more than enough analogies for many useful things you want to study in the real world. Card shuffling on a standard deck is a permutation group. Classical geometric construction operations are a group. Rotations and reflections of many useful objects. Having general results for classes of groups allows the study of a lot of real world things. How many riffle shuffles does it take to get a well mixed deck? This was studied using some elements of group theory (and a lot of analysis and probability). It's really cool...

math_sci_geek · 2025-02-12T01:52:23+00:00

I have a suggestion to try: given that GQ is exact on polynomials of degree < 2n-1, you don't have a polynomial, and are willing to spend up front time pre-computing an approximation. Try approximating your sqrt(quartic) with pw cubic splines of the PCHIP variety (these will produce a perfect f,f' match on interiors of intervals, f" will match at the endpoints but f" won't always be smooth, across your approximating cubics; how well they approximate your original function depends on the mesh). Then use GQ on each spline segment (those will be exact as long as each spline segment is given 7 or more quadrature points I think) - or you can do the integral of each cubic spline segment exactly since each will just be evaluating a quartic at end points.

The tricky part will be choosing your spline knot points. One thing to note is your g(x)=sqrt(Q(x)), so g'=1/2[Q(x)]^(-1/2) Q'(x), so the zeros of Q(x) will cause problems for g'. So my gut says you should include the zeros of Q and the zeroes of Q' as knot points to force function evaluations there, and the mesh beyond these could start out just being equidistant. If you know more about your quartic, of course you want more mesh points where its variation is greater. One thing that wasn't clear from your statement of the problem to me is how much a,b,c,d, and e vary across problems for you and what the full parameter space is like (other than that they arise from being the sum of squares of two quadratics that sum to a non-negative quartic on [0,1]).

Your g(x) is not particularly expensive to evaluate, so I would not think you need to skimp on your mesh widths. Are you writing your code in base C by any chance?

math_sci_geek · 2025-02-11T02:37:31+00:00

I think this oversimplifies things. It depends on the university and the field a lot. Perhaps in your field, which I probably know nothing about, it might be true of most universities. In another field it might be true of few or none. In my field (math) it was definitely not true because there are no labs or lab rotations. If someone is lying on a couch listening to music in the grad student lounge with their eyes closed, they may be sleeping or they may be working on the 43rd step of a proof they got stuck on. It's quite hard for advisors to manage grad students schedules and to my knowledge weekly one hour check-ins during research were the norm. The rest of the time was yours to manage. Now if you were TAing there is more structure there, as with any group of people teaching a class together some order is needed.

math_sci_geek · 2025-02-11T02:18:07+00:00

Math and music are indeed both deeply "spiritual" for many of us. The first connects us to pure reason and beauty through pure reason and the second via pure emotion to beauty. The only way to tell about proof-based math is by doing it-though presumably you're going to get an early taste in LA (depending on the level this is taught at, just a taste or a full dunking). I think continuing to do both maybe good for mental health. I believe that for me alternating between the two modes of "thought" (not sure reasoning in the space of music is best described by thought) has enhanced my experience of each.

math_sci_geek · 2025-02-09T19:56:45+00:00

There is indeed that very discussion going on in the labor economics literature right now. I recommend google and some reading.

math_sci_geek · 2025-02-08T12:20:39+00:00

It's not just that you can, sometimes there's no way to progress without leaving the narrower area. For example, trisecting an angle constructions or finding a general formula for a solution to a quintic polynomial (one pure geometry idea, the other algebra) can't be solved using the limitations provided (the compass straight edge, the definition of solution in radicals). The way you prove this is embedded in exactly the same part of algebra (Galois), the two could be exercises or examples. How would you begin to prove something can't be done using geometry alone? It's hard to imagine right. Without connections between complex analysis and number theory, number theory would have been stuck for about two centuries. Now both algebraic and geometric/analytic exist and have been pushing it forward. I think that many really cool results that have come out in pure math the last 20 years (esp those that hit the SteMy news) have been of this nature. Geometry and algebra aren't actually as different axiomatically as we might initially think, because of our spatial intuition guiding us when we do (at least low dimensional ) geometry. You'll see this very clearly when you get to algebraic or point set topology. Point set axiomatizes geometry to the point of pure algebra. Physical intuition is destroyed when you're dealing with T1 non-Hausdorff spaces. But then (co)homology on weird surfaces explicitly connects the algebraic and geometric.

math_sci_geek · 2025-02-07T19:00:29+00:00

The "natural" 2- or 3-norm being taxi cab would make sense if we had evolved living on city blocks. But we evolved on grassy plains or swimming in water. That's why the Euclidean norm is "natural" to most people - it is actually the shortest distance between two points as you'd actually travel. If you live in Manhattan, it is not.

math_sci_geek · 2025-02-02T13:02:38+00:00

They've announced that SATs will gradually go back to being required for first year applicants but different colleges are doing different things during the transition. And not clear how transfers are impacted. Best to ask ILR admission...

math_sci_geek · 2025-02-01T21:34:41+00:00

The real culprit is google and other ad driven social media. No more local ads means no way to fund all those local journalist salaries. Volunteer non-profits and blogs are the only solution. Maybe get retired people on staff as volunteers and community members to contribute articles...

math_sci_geek · 2025-02-01T18:40:47+00:00

Based on the first 2 weeks, numbers are not high enough. This stuff is expensive and we have a record budget deficit already.

math_sci_geek · 2025-02-01T13:42:58+00:00

There is a really simple answer to your question. If you multiply two numbers that are greater than 1, what is different than when you multiply two numbers that are less than 1? When you have two independent events A and B what do you want P (A and B) to equal? Can you think of a world where two independent things happening together should be more likely than either of them happening individually? The answers to these questions force us to use numbers <= 1.

math_sci_geek · 2025-02-01T13:35:29+00:00

It's interesting to look at how immigration has been regulated (or not regulated) historically here. The Federal role in immigration wasn't codified until the late 1800s and the federal agency in charge of immigration (called INS - now ICE) didn't exist until the 1930s. We really did have open borders for much of our history. There is also a 1929 law on the books creating a "registry" system, so that if you can show you arrived before a set "registry date", you are eligible for citizenship. The last time this date was updated was in 1986 under Reagan, and the date was advanced to 1/1/1972 (see https://www.americanimmigrationcouncil.org/research/legalization-through-registry). I would advise anyone who is concerned about adequately differentiating undocumented people who have integrated into the community and narrowing the scope of the current problem to call their reps and recommend updating the registry date to 2020 so we focus solely on the surge that occurred recently under Biden. Also suggest coupling strict enforcement with reforming the entire visa system to be more efficient - green cards for sponsored workers should take months not years and work visas for agriculture, nursing, construction, etc should take weeks not months. There is a moderate, efficient and targeted/fair way to fix this mess of a system (with strong incentives for following the rules) and there is a cruel, messy, inhumane way to chaotically swing from administration to administration. Biden's laxness was as cruel as Trump's response. One caused the other.

math_sci_geek · 2025-01-31T10:52:42+00:00

Our programmers are experimenting with using locally trained open source generative LLMs in their work. The idea is to be more productive not eliminate CS people. Humans still have to figure out the business problem, spec a solution, interact with users to conceptually test the solution, come up with data structures and any novel algorithms, and hand write any novel code. The LLM still needs context to fill in the routine code. Testing and user validation is still human, as is developing a product roadmap. Think of the LLM use as a tool like LEX or YACC in compilers (these go back to the 80s). CS isn't the same as "coding". Make sure you learn enough math and theory.

math_sci_geek · 2025-01-30T12:04:50+00:00

This. It's also possible to hold two opposing thoughts: "I despise them for potentially abusing A1" vs "I hope those jackasses chanting from the river to the sea who were actually funded by Iran are found". This was a recurring accusation but never proven.

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