> we urgently need to come up with good ways of explaining the value of having a large pool of human mathematical experts, even if it is no longer part of their role to find new proofs of theorems.
This is the main issue, and while I fully agree with that value sentiment, the Fields medallists’ letter failed to provide convincing arguments for why mathematicians should widely receive funding for merely understanding things, and how competition for postdoc and tenure positions would work under these circumstances.
>why mathematicians should widely receive funding for merely understanding things
imagine yourself living in the 1700s. how would you justify Newton and Leibniz's work on calculus?
all maritime engineering and trade was done with geometry and arithmetic at the time. there were no practical applications, not for likely at least a century until hydrodynamics were incorporated into shipbuilding
now look at today. how many of our modern technologies rely on the field having been birthed? that could only exist because of even further decades-worth of antecedent refinements, extrapolations, applications that had, at their time, no direct utilitarian cause?
there's no KPI to be derived from any academic field of study at the bleeding edge of theory. theoretical underpinnings lead to practical applications much further down the line after many paradigm shifts
semiotics and cultural capital as theoretical concepts is another example - at the time they were purely seen as navel-gazey literary theory work. these days, half a century later, they're in wide use (for better or worse) in marketing and advertising - they birthed the whole concept of 'branding'
not everything needs immediate, quantifiable justification. to believe it does indicates a need for a period of self-reflection, to figure out how and when you became so heavily influenced by the MBA-brained propaganda that the world should revolve around the quarter-by-quarter creation of capital
True, but this is also a stunning example of survivorship bias.
Countless other mathematical curiosities were developed in the 1700s -- and forgotten. Calculus just happens to be the one that found practical applications later, so that's the one that's well known today.
It's difficult to draw the conclusion that "every possible branch of learning ought to be funded" by appealing to "later practical value" based on this cherrypicked example.
On the other hand, clearly _some_ novel theoretical work with no apparent immediate value _does_ yield real world benefit later.
Since we lack the resources to fund every PhD with a crazy theory on what the next new subfield ought to be, how do we decide?
Seems like AI could help massively there, by removing a huge bottleneck around technical elaboration and application seeking.
> Countless other mathematical curiosities were developed in the 1700s -- and forgotten. Calculus just happens to be the one that found practical applications later, so that's the one that's well known today.
1. You may not agree, but some people will argue that knowledge is worth accumulating in itself. We fund astronomy well beyond the solar system despite there being no real prospect of practical applications.
2. The value of calculus justifies the cost of all the curiosities. The economic benefits of funding lots of "curiosities" was well worth the few that were useful.
1. is debatable, but in any case that is not the argument that the GP post made -- the post specifically argued that it's worth developing knowledge with no immediate known application, because some application may be developed later.
That's a different argument than "knowledge ought to be accumulated for its own sake."
2. is unclear; the economic funding model of the 18th century was very different. At that time, there were very few academics, and nearly all were independently wealthy and self-funding. That is, they chose to spend their own money on mathematical curiosities to amuse themselves.
Now, in modern academia, we are discussing the case that public tax money ought to be appropriated and allocated to pure knowledge / curiosity discovery _at scale_, for work which -- by definition -- has no known application or use. This is a very different economic and ethical proposal. This is no longer the question of how one rich man chooses to spend his own money; we are discussing the social application of common resources -- compulsory tax payments for all.
It's easy to imagine other ways to spend that tax money that have much less debatable social value -- how about free healthcare for all? Better roads, or high speed trains? No famines? Flood control? There are a million other ideas with immediate benefit.
I appreciate the value of pure knowledge as much as anyone, but it's also hard to make the case that it should be pursued indefinitely, whereever possible, and without limit or boundary when so many competing priorities exist. It's a question of competition for very scarce resources, versus unlimited wants. How do we decide appropriate allocations?
layer8 · · focus · HN ↗
This is the main issue, and while I fully agree with that value sentiment, the Fields medallists’ letter failed to provide convincing arguments for why mathematicians should widely receive funding for merely understanding things, and how competition for postdoc and tenure positions would work under these circumstances.
paimapi · · focus · HN ↗
imagine yourself living in the 1700s. how would you justify Newton and Leibniz's work on calculus?
all maritime engineering and trade was done with geometry and arithmetic at the time. there were no practical applications, not for likely at least a century until hydrodynamics were incorporated into shipbuilding
now look at today. how many of our modern technologies rely on the field having been birthed? that could only exist because of even further decades-worth of antecedent refinements, extrapolations, applications that had, at their time, no direct utilitarian cause?
there's no KPI to be derived from any academic field of study at the bleeding edge of theory. theoretical underpinnings lead to practical applications much further down the line after many paradigm shifts
semiotics and cultural capital as theoretical concepts is another example - at the time they were purely seen as navel-gazey literary theory work. these days, half a century later, they're in wide use (for better or worse) in marketing and advertising - they birthed the whole concept of 'branding'
not everything needs immediate, quantifiable justification. to believe it does indicates a need for a period of self-reflection, to figure out how and when you became so heavily influenced by the MBA-brained propaganda that the world should revolve around the quarter-by-quarter creation of capital
rdbl27 · · focus · HN ↗
Countless other mathematical curiosities were developed in the 1700s -- and forgotten. Calculus just happens to be the one that found practical applications later, so that's the one that's well known today.
It's difficult to draw the conclusion that "every possible branch of learning ought to be funded" by appealing to "later practical value" based on this cherrypicked example.
On the other hand, clearly _some_ novel theoretical work with no apparent immediate value _does_ yield real world benefit later.
Since we lack the resources to fund every PhD with a crazy theory on what the next new subfield ought to be, how do we decide?
Seems like AI could help massively there, by removing a huge bottleneck around technical elaboration and application seeking.
graemep · · focus · HN ↗
1. You may not agree, but some people will argue that knowledge is worth accumulating in itself. We fund astronomy well beyond the solar system despite there being no real prospect of practical applications.
2. The value of calculus justifies the cost of all the curiosities. The economic benefits of funding lots of "curiosities" was well worth the few that were useful.
rdbl27 · · focus · HN ↗
That's a different argument than "knowledge ought to be accumulated for its own sake."
2. is unclear; the economic funding model of the 18th century was very different. At that time, there were very few academics, and nearly all were independently wealthy and self-funding. That is, they chose to spend their own money on mathematical curiosities to amuse themselves.
Now, in modern academia, we are discussing the case that public tax money ought to be appropriated and allocated to pure knowledge / curiosity discovery _at scale_, for work which -- by definition -- has no known application or use. This is a very different economic and ethical proposal. This is no longer the question of how one rich man chooses to spend his own money; we are discussing the social application of common resources -- compulsory tax payments for all.
It's easy to imagine other ways to spend that tax money that have much less debatable social value -- how about free healthcare for all? Better roads, or high speed trains? No famines? Flood control? There are a million other ideas with immediate benefit.
I appreciate the value of pure knowledge as much as anyone, but it's also hard to make the case that it should be pursued indefinitely, whereever possible, and without limit or boundary when so many competing priorities exist. It's a question of competition for very scarce resources, versus unlimited wants. How do we decide appropriate allocations?