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Mathematics is the tool with which we pierce the veil that our minds place over reality. To compare it with memorizing baseball statistics is, is unjustifiable.

by Dn_Ab 15y ago

Mathematics is the tool with which we pierce the veil that our minds place over reality. To compare it with memorizing baseball statistics is, is unjustifiable. I understand your sentiment but I must say I strongly disagree with you. The blog post was actually very accurate, not the fluff piece I was expecting. Knowing of something is very different from properly understanding it to the extent of being able to contribute meaningfully with it. The difference between data and knowledge. The amount of information out there is growing exponentially. The amount that needs to be known before you can contribute keeps exploding with each generation. Such that the practitioner might know just as much if not more than their predecessors but the scope of their knowledge as a fraction of the full body is many orders of magnitude smaller. It is not just a matter of will but of physics of time and the chemistry of the brain. Underutilized connections fade such that unless you spent time actively practising the wide skill sets to sufficient depth they will fade. But there is not enough time to be able to do that. I do think that more must be done in enabling bridges as a counter to this. It is a shame category theorist must wrap their material in such obtuse language as it seems that it would be just the tool for the job.

Xurinos 15y ago
Mathematics is the tool with which we pierce the veil that our minds place over reality. It's not just another illusion we have conjured to make sense of our perceptions, to organize them?
pmiller2 15y ago
I've studied mathematics at the graduate level, and I agree 100% with your assessment. I found all the criticisms in the article to be fair and accurate. I'd like to provide a little more perspective here. I think people don't understand how broad a field mathematics itself is. In graduate school, one will gain a broad knowledge of one particular subfield (e.g. algebra, analysis, topology/geometry, or discrete math, for instance), a very deep knowledge of a particular subject within that subfield (e.g. sheaves of smooth functions on manifolds), and become the world's leading expert on a particular subject (the dissertation). Along the way, one will certainly pick up at least a couple of courses in perhaps 2 or 3 other major subfields sufficient to pass the comprehensive exams set by the department, but that's it. So, a mathematician graduates knowing a lot about very little compared to the whole of mathematics. Over the course of an entire career, one will usually pick up bits and pieces that were neglected in grad school, and perhaps enough knowledge to contribute in maybe one or two additional subfields. This, of course, is how it works for an average mathematician -- the average Joe or Jane who makes it through grad school. Superior mathematicians might contribute more broadly (Erdos comes to mind), but they're sufficiently rare that we can practically discount them. Charlie Epps goes beyond this because dramatic license allows (indeed, practically requires) him to.

by Dn_Ab 15y ago

Xurinos 15y ago

Mathematics is the tool with which we pierce the veil that our minds place over reality. It's not just another illusion we have conjured to make sense of our perceptions, to organize them?

pmiller2 15y ago

I've studied mathematics at the graduate level, and I agree 100% with your assessment. I found all the criticisms in the article to be fair and accurate. I'd like to provide a little more perspective here. I think people don't understand how broad a field mathematics itself is. In graduate school, one will gain a broad knowledge of one particular subfield (e.g. algebra, analysis, topology/geometry, or discrete math, for instance), a very deep knowledge of a particular subject within that subfield (e.g. sheaves of smooth functions on manifolds), and become the world's leading expert on a particular subject (the dissertation). Along the way, one will certainly pick up at least a couple of courses in perhaps 2 or 3 other major subfields sufficient to pass the comprehensive exams set by the department, but that's it. So, a mathematician graduates knowing a lot about very little compared to the whole of mathematics. Over the course of an entire career, one will usually pick up bits and pieces that were neglected in grad school, and perhaps enough knowledge to contribute in maybe one or two additional subfields. This, of course, is how it works for an average mathematician -- the average Joe or Jane who makes it through grad school. Superior mathematicians might contribute more broadly (Erdos comes to mind), but they're sufficiently rare that we can practically discount them. Charlie Epps goes beyond this because dramatic license allows (indeed, practically requires) him to.