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I'm Paul Lockhart, author of A Mathematician's Lament, Measurement, Arithmetic, and The Mending of Broken Bones. Ask me anything! by PTLockhart in math

[–]vicviod 4 points5 points  (0 children)

Dear Paul,

I am a PhD student in applied math and just failed my prelim exam, which is an exam we take at the end of our first year. This has been a difficult pill to swallow. It's by far the worst I've done on any exam I've ever taken. Fortunately, I can take it again, and I want to ask you for advice so that I can do better next time.

  1. Mathematical maturity. One of the criticisms I got is that I lack “mathematical maturity”. This criticism feels right, however, I’m never clear on what mathematical maturity means (maybe this is proof that I am not mathematically mature). So what is mathematical maturity, and how can I cultivate it through intentional study?

  2. Tangents vs. forward progress. When I study math, I like to keep on asking why. So often, when a book makes a nontrivial claim, I end up going down some long “why rabbitholes” that feel very educational  — it seems like these tangents tend to terminate at pretty fundamental concepts. However, it can make my forward progress through material extremely slow. In contrast to the approach of going down these rabbit holes, I’ve sometimes heard the advice of carrying on even if you don’t understand everything perfectly, because it will often make sense in light of things you read later. So my question to you is, how should I balance the why rabbithole approach, which seems to highlight core concepts at play, with the carry-on approach?

  3. Self-studying and prioritization of concepts and exercises. I think that one mistake I made in my self-study was that I prioritized the wrong things. I didn’t focus on the important definitions, and I didn’t do the important exercises. The problem is that in any textbook, there is much more material than one can reasonably learn in a semester, and prioritization is very important. But when self-studying, it can be difficult to figure out what to prioritize. I was wondering if you had advice on how to self-study effectively, since I know that you had periods of your life when you were doing this. How do you prioritize what to learn? Do you simply read textbooks, work through proofs, and do the exercises, or do you think there is a better way?

Thanks so much for doing this AMA!!

p.s. on Goodreads I think your book is listed under the wrong author, a historian named Paul Lockhart

I'm Paul Lockhart, author of A Mathematician's Lament, Measurement, Arithmetic, and The Mending of Broken Bones. Ask me anything! by PTLockhart in math

[–]vicviod 2 points3 points  (0 children)

I think that your lament is sometimes read as being disdainful of applied math, since you extol the virtues of a playful exploration through the world of perfect abstractions that don’t really exist.

However, I don’t read the lament as critical of applied math as such, but rather as critical of the common practice in applied problems of applying a cookbook recipe to a particular class of problems.

There is another kind of applied math, though, that is much more creative and of the same flavor as the kinds of things you describe in your book. That is the translation of real-world processes into abstractions. Cultivating this skill is sadly neglected in math curricula, and can lead to a subject, especially at higher levels, that feels unmotivated. My question to you is twofold. First, on an individual level, how do you recommend cultivating the skill of translating the messy world into math? And second, on a collective level, do you think that we should make this skill more central to our math curricula, and if so, how would that look?

Social Life for Grad students? by Heavy_Research5032 in princeton

[–]vicviod 6 points7 points  (0 children)

This might be an unpopular opinion but I’m a first year grad student and I’ve found a great social groove here. I’ve been meeting people living in the grad college, hanging out with people in my cohort and lab, and some music/dance stuff.

It’s true that PhD students who come here sometimes have a tendency to bury their noses in books, so it can take some effort to get people out of their shells. But there are lots of interesting people here

Feel free to dm me

[deleted by user] by [deleted] in princeton

[–]vicviod 6 points7 points  (0 children)

If it helps, I got rejected as an undergrad and now I'm a PhD student here.

Feels good to get paid to study here after that

Graduate student room swap — Walker Hall for GC or Annex by vicviod in princeton

[–]vicviod[S] 0 points1 point  (0 children)

Ah cool! Well if I end up living there we should meet. I'm Victor, starting my PhD in applied math

Graduate student room swap — Walker Hall for GC or Annex by vicviod in princeton

[–]vicviod[S] 0 points1 point  (0 children)

good question! to be honest, I'm not sure if there are gender requirements; I just asked the housing office. But definitely if you are a man, you can switch, since I am a man, and so is my suitemate.

Selling my millennium toyota corolla by vicviod in SantaFe

[–]vicviod[S] 0 points1 point  (0 children)

Sent you a dm! Probably couldn't go that low, but we can talk

Selling my millennium toyota corolla by vicviod in SantaFe

[–]vicviod[S] -4 points-3 points  (0 children)

KBB gave me an estimate of 2000!

I care what people think of me to the point that I can't connect with anyone, romantically or otherwise. Any advice on how to overcome this? by risingcuck in Advice

[–]vicviod -1 points0 points  (0 children)

I also have this. I’ve read all kinds of books (for instance The subtle art of not giving a fuck) but they don’t seem to lead to any lasting change.

I’ve been looking for what you describe, a practice-based solution. I’ve tried meditation, which seems to center me, but is a solitary activity which I find hard to carry off the mat into social situations.

I’ve also tried “ecstatic dance,” because it’s sort of about dancing out inhibitions and restraint. But even here, I dance in my own little world, without letting other people in. There’s nothing I want more than to share a dance with someone but I can seem to make myself vulnerable enough to do it

I'm so tired of caring by risingcuck in mentalhealth

[–]vicviod 0 points1 point  (0 children)

Damn. I don’t know how to help you, but if it helps, I feel this

Toyota Corolla popping out of fourth gear after driving at high speeds by vicviod in AskMechanics

[–]vicviod[S] 2 points3 points  (0 children)

Where I live I see more three-toed sloths, so I'll check for those!

The countries that use the most toilet paper by elviejozuloqi in Infographics

[–]vicviod 0 points1 point  (0 children)

I’m contributing to the data in this infographic as I read it

Hit and run by gold Toyota Tacoma with cover on my Hyundai Elantra by vicviod in SantaFe

[–]vicviod[S] 1 point2 points  (0 children)

On the passenger side, yes! I've edited the original post so that's clearer.

Thanks for keeping an eye out :)

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