[HN Gopher] Is Mathematics Invented or Discovered? (2020) [video]
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       Is Mathematics Invented or Discovered? (2020) [video]
        
       Author : janandonly
       Score  : 17 points
       Date   : 2023-11-14 20:44 UTC (2 days ago)
        
 (HTM) web link (www.youtube.com)
 (TXT) w3m dump (www.youtube.com)
        
       | Mimmy wrote:
       | I went to an in-person Q&A featuring a Fields medalist. The
       | audience was a collection of undergraduate and high school math
       | students, with a few professors in attendance.
       | 
       | One of the young students asked exactly this question to which
       | everyone in the audience collectively groaned. The Fields
       | medalist gave a short answer, something along the lines of "I
       | don't know a single mathematician that thinks it's invented."
       | 
       | He was being polite, but you could tell he didn't think there was
       | anything else interesting to say.
        
         | pa7x1 wrote:
         | It's both. The axioms are invented, the corpus of theorems is
         | discovered. As once the axioms are chosen the provable theorems
         | are already fixed.
         | 
         | But the axioms are a choice, and we can pick different ones.
         | The common choice of axioms is utilitarian, they lead to
         | interesting math that helps us describe the universe.
        
           | random3 wrote:
           | Are the theories beyond axiom fundamentally different if
           | axioms are changed, though? And if not, aren't then axioms
           | merely props or placeholders for invariants?
        
           | sweezyjeezy wrote:
           | I'm not sure I see why the axioms were not also discovered
           | though? Choice between irreducible assumptions does not seem
           | to make them any more 'invented'.
        
           | Mimmy wrote:
           | I would agree the axioms are chosen, but what's the
           | connection between choosing something and inventing it?
           | 
           | Choosing to study molecular biology doesn't mean cells are a
           | human invention.
        
       | photochemsyn wrote:
       | Different sets of axioms open the doors to different mathematical
       | universes? I'm given to understand that's the general concensus
       | on what Godel's incompleteness theorems mean, practically
       | speaking.
        
       | lupire wrote:
       | Is a new pharmaceutical invented or discovered? How about a new
       | iPhone?
       | 
       | This is linguistics, not science.
        
       | svara wrote:
       | Are space ships in game of life invented or discovered? I've come
       | to believe that's ultimately exactly the same question.
       | 
       | We're talking about rich structures that emerge from simple rule
       | sets. That's really all there is to mathematics.
       | 
       | We started from structures that provide helpful abstractions for
       | things in real life, which might lead some to believe that
       | mathematics points to some hidden reality behind things, but
       | that's ultimately just spiritual thinking in rational sounding
       | clothing.
        
       | dang wrote:
       | Url changed from https://abakcus.com/video/roger-penrose-is-
       | mathematics-inven..., which points to this.
        
       | dang wrote:
       | Discussed at the time:
       | 
       |  _Roger Penrose - Is Mathematics Invented or Discovered? [video]_
       | - https://news.ycombinator.com/item?id=22896671 - April 2020 (311
       | comments)
        
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