[HN Gopher] Advice to Young Mathematicians [video]
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Advice to Young Mathematicians [video]
Author : Anon84
Score : 97 points
Date : 2024-06-30 23:47 UTC (3 days ago)
(HTM) web link (www.youtube.com)
(TXT) w3m dump (www.youtube.com)
| ksd482 wrote:
| This one really stuck for me: "focus on something special, then
| expand from there".
|
| I have time and again fell victim to fulfill all the
| prerequisites before I begin to attempt to understand a topic.
| This is a mistake I have made repeatedly. I now understand why
| this is tempting to do and why it is a mistake.
|
| It is tempting to do so because you feel things will come easier
| to you if you fulfill the prerequisites first. But the problem is
| that there is just not enough time. AND, it actually may not be
| even necessary.
|
| It is a mistake to do so because you are wasting time and
| ultimately it may not be necessary after all.
|
| Even in a field such as pure mathematics (I have an MS in pure
| Math), it is okay to skim through some of the background material
| and understand it intuitively or even non-rigorously, while
| focusing on what you want to actually learn.
|
| It took me a while to learn that and I am glad it is being
| repeated here by such an accomplished professor.
| sage76 wrote:
| > It is tempting to do so because you feel things will come
| easier to you if you fulfill the prerequisites first. But the
| problem is that there is just not enough time. AND, it actually
| may not be even necessary.
|
| I think this is a lesson I am learning. I am going through the
| book PRML throroughly (which means attempting every single
| exercise) and writing out the solutions.
|
| I also did the prereqs somewhat rigorously.
|
| It has been incredibly time consuming.
| DecayingOrganic wrote:
| I really resonate with this. I've also struggled with
| perfectionist mindset when it comes to learning, especially in
| mathematics. Recently, I tried to meticulously add math
| problems to Anki for better retention, only to realize the time
| cost was too high. This perfectionist mindset often maximizes
| one variable (retention in my case) at the cost of all others
| (time as the most important one).
|
| I've grown to really like this Richard Feynman quote: "Study
| hard what interests you the most in the most undisciplined,
| irreverent and original manner possible." It feels like I've
| been finally granted permission to embrace my natural, messy
| way of learning.
| senderista wrote:
| If you take the time to learn everything relevant to your
| research then you will never have time to do your research.
| JustinSkycak wrote:
| I agree with this advice once you get to a sufficiently high
| level -- like, working on research problems.
|
| HOWEVER I think there's more nuance: there is tremendous value
| in having a baseline level of foundational knowledge in
| whatever domain you're in.
|
| For instance, if someone hasn't learned math to an
| undergraduate level, and they try to sink their teeth into a
| math research problem, then they're probably going to spend all
| their time flailing around and being confused. Waste of time.
|
| A better use of time would be for them to develop a baseline
| level of mathematical knowledge through a structured
| curriculum, and then take the leap once they've got their
| fundamentals down.
|
| Same thing with machine learning. If you want to work on a
| research problem and you have your ML fundamentals down, then
| yeah, go ahead and jump right into the research problem. But if
| you don't even know how gradient descent works, or what an
| eigenvalue is, how to work with continuous probability
| distributions, etc., then you're woefully underprepared and
| you'd be better off just shoring up your foundations first.
| lallysingh wrote:
| Meh? I think a more mercenary approach to learning
| prerequisites is fine, and frankly better. Use Mathematica or
| Alpha to show you how equations get from one place to another
| - those tools are great at the fundamentals. You can skim a
| calc book, use Mathematica/Alpha to fill in your gaps, and
| play with toy problems to convince yourself well enough to
| continue.
|
| The basics are the ones with the most different approaches
| developed to teach/use them, so they can most easily be
| skimmed by with cheap modern trickery.
| JustinSkycak wrote:
| There are some people who can pull that off, and you might
| be one of them, but they're extreme cases. For the vast,
| vast majority of students it's not a viable approach.
| Davidzheng wrote:
| I have a different advice for aspiring mathematicians. Learn in
| the way you want. If you enjoy learning the prerequisites or
| feel like you need to, by all means learn it carefully. There
| are enough mathematicians on either side of this advice and
| indeed of most advice. Don't take other people's opinions too
| seriously. Other people only know what worked or didn't for
| themselves, they have no idea what will work for you.
| gxs wrote:
| Yeah I did a similar thing.
|
| I was a math major and I used to be adamant about reading the
| chapter perfectly before starting my problem sets.
|
| I mentioned this to my math professor and he'd always say to
| not be afraid to jump into the problems, that my time was
| better spent that way.
|
| My take on it is that a) it's true and b) it works because
| reading with a purpose is very different than reading as a way
| of surveying something before you jump into a problem.
| vinnyvichy wrote:
| Passions, feeling special, finding the special one. Do I dare
| suggest that identifying (or equating(!!!)) these are not just
| urgent issues for young mathematicians, but young people in
| general? Or maybe even every one?
| markus_zhang wrote:
| Not a Mathematician myself, but I totally agree with him
| regarding the benefits of choosing Mathematics as the career.
|
| My father is a Mathematician with small fame. He was obsessed
| with Mathematics when he was a kid. In fact, Mathematics was the
| single thing that helped him to move through the political
| turmoil during his first 30 years of life.
|
| I'll also quote a paragraph from Cixin Liu's "Ball lighting".
| It's related.
|
| > "Of course I know!" Dad took another half glass of wine, then
| turned to me, "Actually, son, living a wonderful life is not
| difficult. Listen to Dad: choose a universally recognized world
| problem, preferably a mathematical one that only requires a piece
| of paper and a pencil, like the Goldbach Conjecture or Fermat's
| Last Theorem, or a pure natural philosophy problem that doesn't
| even need paper and pencil, like the origin of the universe.
| Dedicate yourself entirely to it, focus solely on the process,
| not the outcome. In the unconscious focus, a lifetime will pass.
| What people often refer to as a 'pursuit' is just this. Or,
| conversely, make earning money your sole goal, always thinking
| about how to make money without considering what to do with it.
| By the time you die, you can, like Grandet, hold a pile of gold
| coins and say, 'Ah, so warm...' Therefore, the key to a wonderful
| life is what you can become passionate about. For example, me--"
| Dad pointed to the small watercolor paintings placed all around
| the room. They were all very traditional in technique, well-
| painted but lacking any real inspiration. The paintings reflected
| the electric light from outside the window, like a group of
| flickering screens, "I became passionate about painting, even
| though I know I can't become Van Gogh."
| skhunted wrote:
| If your father is who I think he is then his fame is large in
| the mathematics community. His Ph.D. advisor was a terrible
| teacher as far as my experience with taking classes from him
| goes.
| gautamcgoel wrote:
| Are you thinking of Yitang Zhang?
| gradschoolfail wrote:
| Don't we just love all these unidentified Examples in the
| room.
| skhunted wrote:
| Yes.
| alberto_ol wrote:
| The video is by the mathematician Michel Talagrand.
|
| https://en.wikipedia.org/wiki/Michel_Talagrand
|
| A surprising tip from his personal page.
|
| "If you are desperate to get my books and your library can't
| afford them, try to type the words "library genesis" in a search
| engine. I disagree with piracy, but this site saved me many trips
| to the library, which unfortunately does not carry electronic
| versions of older books."
|
| http://michel.talagrand.net/
| xanderlewis wrote:
| It's not that surprising to me. For academic publications, it's
| generally only the publisher who makes a significant profit --
| and even then it's probably negligible in most cases.
|
| I've even been personally sent PDFs of books by the author
| under the condition that I don't tell anyone.
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