[HN Gopher] Advice to Young Mathematicians [video]
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       Advice to Young Mathematicians [video]
        
       Author : Anon84
       Score  : 51 points
       Date   : 2024-06-30 23:47 UTC (2 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.
        
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