> 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.
You can call it survivorship bias, but another way to phrase it is that it's very difficult to forecast the practical benefit of any one piece of mathematics even while the long-term impact of mathematics as a whole is undeniable. And any schemes to further ration resources among mathematicians ignores the reality that for such foundational subject, math research already one of the least funded compared to other disciplines or domestic priorities.
"Falsifiability" is generally understood in terms of physical observations. Mathematics is ultimately tautological: they are true or false by their own definition, without reference to the physical world.
It just so happens that certain kinds of mathematics are unreasonably effective in drawing parallels to the physical world, but as far as mathematicians are concerned those mathematics are neither better nor worse than those that do not correspond to anything tangible.
> those mathematics are neither better nor worse than those that do not correspond to anything tangible.
A sweeping generalization. I certainly know professional mathematicians who disagree.
Also: many consider “inter-connectedness”, not “tangible” to be a sign that a topic is interesting. That is, it touches branches of mathematics aside from its own.
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.
curt15 · · focus · HN ↗
moritzwarhier · · focus · HN ↗
Calculus (e.g. differentiation), for example, is mind-blowing when taking it seriously, and not only useful.
The idea of "speed at an infinitely short moment", for example, is philosophy!
jfengel · · focus · HN ↗
It just so happens that certain kinds of mathematics are unreasonably effective in drawing parallels to the physical world, but as far as mathematicians are concerned those mathematics are neither better nor worse than those that do not correspond to anything tangible.
[deleted] · · focus · HN ↗
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brobdingnagians · · focus · HN ↗
fn-mote · · focus · HN ↗
A sweeping generalization. I certainly know professional mathematicians who disagree.
Also: many consider “inter-connectedness”, not “tangible” to be a sign that a topic is interesting. That is, it touches branches of mathematics aside from its own.