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"Also unrealistic is that one mathematician would be familiar with so wide a range of mathematical and scientific techniques as Charlie." This is the only bit

"Also unrealistic is that one mathematician would be familiar with so wide a range of mathematical and scientific techniques as Charlie." This is the only bit I disagree with. Math is his life. Baseball fans know an amazing array of statistics about ALL major baseball teams. They can quote all kinds of crazy things. Epps does the same thing, but with mathematical theories. It doesn't surprise me a bit for a single person to know about all those techniques. Successfully implementing a given one within 24 consecutive hours is another story altogether. But that's already addressed.

mikebenfield 15y ago
There is a lot less to learn (and, probably more relevant, it's much easier to learn) in the world of baseball statistics than there is in mathematics. Nobody knows more than a small fraction of the math that's out there, including people whose lives revolve around mathematics. It's just too much.
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.
masterzora 15y ago
This is the only bit I disagree with. Math is his life. In some respects, that's like expecting someone whose "life is languages" to be able to speak every language on the planet fluently. Math is definitely a coherent whole with the different subfields like algebra and analysis being a part of it but, at the same time, there are enough differences between them and enough depth in each that we're not going to see anyone remotely close to the level at which Eppes is portrayed.
- wccrawford 15y ago
  No, not really. I don't expect him to know EVERY math technique. He knows many. Too many, possibly... But he could easily know all the ones used in the show, if that were his focus in life. Likewise, a linguist would know the differences between languages without actually being able to speak all the languages in the world. If a relatively-unknown language had a special property that no other language did, I'd expect serious linguists to know that. Eventually, anyhow.

mikebenfield 15y ago

There is a lot less to learn (and, probably more relevant, it's much easier to learn) in the world of baseball statistics than there is in mathematics. Nobody knows more than a small fraction of the math that's out there, including people whose lives revolve around mathematics. It's just too much.

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.

masterzora 15y ago

This is the only bit I disagree with. Math is his life. In some respects, that's like expecting someone whose "life is languages" to be able to speak every language on the planet fluently. Math is definitely a coherent whole with the different subfields like algebra and analysis being a part of it but, at the same time, there are enough differences between them and enough depth in each that we're not going to see anyone remotely close to the level at which Eppes is portrayed.

wccrawford 15y ago
No, not really. I don't expect him to know EVERY math technique. He knows many. Too many, possibly... But he could easily know all the ones used in the show, if that were his focus in life. Likewise, a linguist would know the differences between languages without actually being able to speak all the languages in the world. If a relatively-unknown language had a special property that no other language did, I'd expect serious linguists to know that. Eventually, anyhow.