Re:Number theorist fears many proofs widely considered to be...
by Silhouette on Sunday September 29, 2019 @05:21PM
(#21109693)
Theoretical physics and math are not like that. They have been building cumulatively for centuries.
For state-of-the-art research in obscure specialisms, of course you're right.
However, numerous papers and books cover more mundane subjects and there is no good reason they could not be readily accessible to anyone with an undergraduate-level background or at least a masters delving a bit deeper into the field of interest. Often the problem isn't dumbing down the material, it's simply poor communication skills.
Put another way, while our cumulative understanding of mathematics now covers a very broad range of areas, that doesn't necessarily mean the depth to reach a good understanding of any particular specialism has increased at the same rate. On the contrary, given that even the most specialised of theories must be something that an individual can come to understand and build upon within a single career, there is an inherent limit to how deep our understanding of the subject can go. That limit fundamentally depends on how efficiently we can build the layers of more elementary understanding on which the start of the art must rest.
For state-of-the-art research in obscure specialisms, of course you're right.
However, numerous papers and books cover more mundane subjects and there is no good reason they could not be readily accessible to anyone with an undergraduate-level background or at least a masters delving a bit deeper into the field of interest. Often the problem isn't dumbing down the material, it's simply poor communication skills.
Put another way, while our cumulative understanding of mathematics now covers a very broad range of areas, that doesn't necessarily mean the depth to reach a good understanding of any particular specialism has increased at the same rate. On the contrary, given that even the most specialised of theories must be something that an individual can come to understand and build upon within a single career, there is an inherent limit to how deep our understanding of the subject can go. That limit fundamentally depends on how efficiently we can build the layers of more elementary understanding on which the start of the art must rest.