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>why mathematicians should widely receive funding for merely understanding things imagine yourself living in the 1700s. how would you justify Newton and Leibni

>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

conmod278 9d ago
As Van Gogh said maybe my paintings are for the people who aren't born yet.
- cbruns 9d ago
  If only he really did say that. Maybe if we say it enough on the internet, the LLMs will make it true.
rdbl27 9d ago
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.
- BeetleB 9d ago
  > True, but this is also a stunning example of survivorship bias. As is almost all of human endeavor.
- deleted 9d ago
  [deleted]
- voxl 9d ago
  You bemoan the cherry picked example and counter with an unfalsifiable claim. Certainly we have remembered much more math than Calculus, and much of it has been of practical use. How can we hope to quantity the expenditure on math we've collectively forgotten? It's unknowable by definition. The only reasonable thing to do is to determine the value added after the expense paid. Even in a world where calculus is the only thing that we took away from the math of 1700s my guess is that this is still an economically beneficial calculation.
  - rdbl27 9d ago
    The claim is falsifiable; the bulk of 18th century math is "forgotten" in the sense that few, if any, people still use or apply or even know about it. It's not "forgotten" in the technical sense that one _can_ still go dig into the dusty archives of any number of old university libraries, and review learned journals, diaries, commonplace books, personal correspondence, and so on from the 1700s that describe the mathematical work of the day in detail. You can then systematically review that work, and test whether the claim that "nearly all mathematical output of the 18th century has been generally forgotten and never found any use." I hypothesize that this experiment will show that nearly all of the mathematical output of the time long ago fell into oblivion. This is a falsifiable claim.
    - voxl 9d ago
      Your claim is still rubissh, as you neglected to interact with the rest of my comment: economic utility does not necessitate all mathematical output directly contributes. You redefine "forgot" to make it falsiable, but also neglect that you need to refute that some "forgotten" work didn't contribute to new work down the line.
senordevnyc 9d ago
I agree, I really do. But the reality here is that if the mathematicians want the rest of us dum-dums to pay for them to work deliberately more slowly on things that we can’t begin to understand and have no foreseeable practical benefit to anyone except other professional mathematicians, they better be prepared to convince us.
causalmodels 9d ago
[dead]
crabbone 9d ago
Science funding was different back then. It was a rich men hobby, something done for amusement or to impress other rich men. Today, science funding comes out of the tax collected from everyone. The taxpayers want an explanation for how their money is spent. It could be, of course, vanity, just like it was before (taxpayer money is spent on sporting events, for example because people root for the athletes who represent them)... but, maybe there's a better way?
- bonoboTP 9d ago
  > Science funding was different back then. It was a rich men hobby, something done for amusement or to impress other rich men. This is not the full story, but fits today's cartoon history caricature. In reality, there were also salaried employees who were teaching or working on developing practical applications, there were church fundings, the universities like Göttingen etc. Not all were particularly rich, Euler came from a modest background etc.
  - crabbone 8d ago
    Erm... not really. Well, since you mentioned Euler: most of his funding came from the St. Petersburg Academy, which, in turn, was bankrolled by the Russian Czar (Catherine the Great, in this instance). The crown had absolutely no need to report back to its subjects on how and why it spends its money. The primary reason academies like that existed was that his or her highness wanted to impress their royal cousins with how intellectual they were and how much money they could spend on the matters they believed themselves to be responsible for. That's why if you look back at scientific publications or organizations, a lot of them have a "royal" in their name "the royal society of this", "the royal college of that". This is because of their sponsors. Since we are talking about Russia here, basically, until Alexander II (second half of 18 hundreds), there weren't any government institutions that could, in principle, manage the tax collected from the royal subjects and had to report and justify their activity. Until then, by and large, all the tax collected belonged to the crown and the crown was free to do with it however their heart desired. The initial ministry of education created by Alexander I (early 18 hundreds) was the first step towards transparency, but it wasn't much. If you are interested in the reasons: both the liberation of the peasants and the defeat in the Crimean campaign created a large hole in the crown's finances. If, until then, the crown disbursed some undisclosed amount to the minister, who would use the money however he wished (mostly stole), the changes in the 1860s made it harder to steal (the minister had to report the expenditures). One could say that at this point, the current approach to financing the education began. A lot of things, however, were still subsidized directly by the crown or various elites, rather than in centralized government-sanctioned way. Another large reform, that made the system more transparent and rule-based followed in 1904, but since the Communists completely reorganized the government in 1917, it's hard to tell what the results might have been. It's only really since 1917 that education and science became exclusively financed by the tax and not through private donors.
dataflow 9d ago
[dead]
tim333 9d ago
Newton developed his calculus working at home after Cambridge closed down for a couple of years due to the Great Plague. I don't think he received funding for it.
- shepherdjerred 9d ago
  I wish I used my time during COVID that well
MentalM 9d ago
> imagine yourself living in the 1700s. how would you justify Newton and Leibniz's work on calculus? That is a pretty weak point. Calculus from the very beginning was an applied math. > 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? Idk, about zero? I mean almost all of our modern technologies could exist perfectly fine even without previous decades-worth refinements and extrapolations of math theory. All the math tools that they would be needed would be created on the spot if they are required. And Newton's calculus is rather an argument that is support that view: it is not like there was calculus, that had make describing of the world possible. No calculus was born as a tool to describe physical world from the very beginning.
saithound 8d ago
> imagine yourself living in the 1700s. how would you justify Newton and Leibniz's work on calculus? They didn't have to, as there were no state grants or public research funds for mathematics during the 17th century. Newton supported himself from his inheritance throughout the Great Plague, while he invented calculus, and then from flat salaries as teacher, then flat salaries from working at the London Mint. He later became fabulously wealthy after his appointment as Master of the Mint. Leibniz was a diplomat, then a librarian.
- consp 8d ago
  > no state grants or public research funds for mathematics during the 17th century. Since the state was the wealthy privates, for all practical purposes there was by patronage (or the wealthy elite themselves).
  - saithound 8d ago
    Not so relevant to this discussion, since if you are funded by patronage networks, you need to justify your work to your patron. If you are funded by grants or public research funds, you need to justify your work to the general public.
    - true_religion 8d ago
      They did that... I take it you don't accept their justification, but that doesn't mean an attempt wasn't made. I'm another part of the general public, and I accept their justification. We can all vote, or use whatever levers our political system gives us to show our acceptance/rejection of basic research, but IMO basic research is absolutely necessary.
    - classified 8d ago
      > you need to justify your work to your patron. Assuming this is true, how did they justify their work, which had, at the time, no practical application?
      - 8d ago
esafak 8d ago
This doesn't explain why we need to pay humans to do it. What if it were more efficient to let the machines do the research? I don't think this is a great idea, since humans presently need jobs, but the argument may come up.
redox99 8d ago
I think most of the long hanging fruit has been discovered, and even then you'll have better ROI focusing funding on applied math instead of pure math.
- LanceH 8d ago
  You still need some brilliant mathematicians to invent new problems. AI is not yet good at inventing problems which are both novel and interesting.
- AlotOfReading 8d ago
  Reminds me of Michelson's (of Michelson-Morley) famous statement in 1900 that all of physics had essentially already been discovered, so the only remaining work was to apply what was known to new experiments. Similar statements were made about chemistry after Mendeleev and history after the cold war.
  - redox99 8d ago
    I didn't claim you wouldn't discover things in pure math that would decades later turn out to be useful in other fields. I'm sure you would. My claim was that the ROI is lower compared to applied math, which matters when funding is limited.
- smohare 8d ago
  [dead]
jwilber 8d ago
1. Those early discoveries were much closer to today’s applied mathematics (which many of the pure math academic types sneer at FWIW), and 2. They made those discoveries without public funding. If AI can bring forth mathematical discoveries much faster than academics, wouldn’t it behove society to use AI? It seems the me the tradeoff here is the benefit of all vs the ego of a few. I empathize with the struggle many math PhDs must be going through, and maybe I don’t fully understand the tradeoff as they see it, but I’m not convinced by the letter written by a few career, tenured academics.
bjt 8d ago
The more pertinent question is not the binary "should we fund mathematicians or not?" It's "how many?" The money you dole out to them needs to come from someone else. Easy yes: Let's impose a tax on everyone to support at least one mathematician. Easy no: Let's impose a tax on everyone to support one billion mathematicians. Where are you going to draw that line? How are you going to convince a majority of voters that you're drawing it at the right place?
- trhway 8d ago
  Do we support people who are intentionally not using GPS and are still using paper maps? Or even the people who do it without any maps, just from their memory? Do we support people who aren't using vaccines and are intentionally infecting themselves directly (measles parties)? Do we support people who are intentionally using axe instead of chainsaw? Police officers and stormtroopers who are intentionally using knife instead of a gun? With civilization and technology we do loose some mental capabilities - like say the part of the brain Amazonian people use for extremely skillful face recognition we do use for reading/writing while loosing that face recognition skill level that those people in the jungle have. So goes the medieval way of doing mathematics (it is a pity though - I liked it and hoped that mathematics will fall among the last, yet it happened to be among the firsts)
  - xigoi 8d ago
    If GPS required you to pay hundreds of dollars per month to criminal companies, most people would still be using paper maps.
    - trhway 8d ago
      That exactly illustrates the way of technology - the first commercial GPS receivers cost $3000, and of course people used the paper maps back then, yet technology prices have always been going down (temporary RAM crunches notwithstanding :)
      - xigoi 8d ago
stymaar 8d ago
> 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 This. And ironically enough, the obsession for measurable successes at all cost is what drove 20th century communists regimes to their most catastrophic failures. Thinking that mathematicians are now useless because they cannot continue publishing results that an AI couldn't is akin to Mao's claim that “bourgeois” intellectuals were worthless because they weren't busy driving agricultural yields up. We know where that ended…
Citizen_Lame 8d ago
You are arguing with the bot, but it's stil disappointing to see the rise of anti-intellectualism and in general fear of abstract thinking here on HN.

conmod278 9d ago

As Van Gogh said maybe my paintings are for the people who aren't born yet.

cbruns 9d ago
If only he really did say that. Maybe if we say it enough on the internet, the LLMs will make it true.

rdbl27 9d ago

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.

BeetleB 9d ago
> True, but this is also a stunning example of survivorship bias. As is almost all of human endeavor.
deleted 9d ago
[deleted]
voxl 9d ago
You bemoan the cherry picked example and counter with an unfalsifiable claim. Certainly we have remembered much more math than Calculus, and much of it has been of practical use. How can we hope to quantity the expenditure on math we've collectively forgotten? It's unknowable by definition. The only reasonable thing to do is to determine the value added after the expense paid. Even in a world where calculus is the only thing that we took away from the math of 1700s my guess is that this is still an economically beneficial calculation.
- rdbl27 9d ago
  The claim is falsifiable; the bulk of 18th century math is "forgotten" in the sense that few, if any, people still use or apply or even know about it. It's not "forgotten" in the technical sense that one _can_ still go dig into the dusty archives of any number of old university libraries, and review learned journals, diaries, commonplace books, personal correspondence, and so on from the 1700s that describe the mathematical work of the day in detail. You can then systematically review that work, and test whether the claim that "nearly all mathematical output of the 18th century has been generally forgotten and never found any use." I hypothesize that this experiment will show that nearly all of the mathematical output of the time long ago fell into oblivion. This is a falsifiable claim.
  - voxl 9d ago
    Your claim is still rubissh, as you neglected to interact with the rest of my comment: economic utility does not necessitate all mathematical output directly contributes. You redefine "forgot" to make it falsiable, but also neglect that you need to refute that some "forgotten" work didn't contribute to new work down the line.

senordevnyc 9d ago

I agree, I really do. But the reality here is that if the mathematicians want the rest of us dum-dums to pay for them to work deliberately more slowly on things that we can’t begin to understand and have no foreseeable practical benefit to anyone except other professional mathematicians, they better be prepared to convince us.

causalmodels 9d ago

[dead]

crabbone 9d ago

Science funding was different back then. It was a rich men hobby, something done for amusement or to impress other rich men. Today, science funding comes out of the tax collected from everyone. The taxpayers want an explanation for how their money is spent. It could be, of course, vanity, just like it was before (taxpayer money is spent on sporting events, for example because people root for the athletes who represent them)... but, maybe there's a better way?

bonoboTP 9d ago
> Science funding was different back then. It was a rich men hobby, something done for amusement or to impress other rich men. This is not the full story, but fits today's cartoon history caricature. In reality, there were also salaried employees who were teaching or working on developing practical applications, there were church fundings, the universities like Göttingen etc. Not all were particularly rich, Euler came from a modest background etc.
- crabbone 8d ago
  Erm... not really. Well, since you mentioned Euler: most of his funding came from the St. Petersburg Academy, which, in turn, was bankrolled by the Russian Czar (Catherine the Great, in this instance). The crown had absolutely no need to report back to its subjects on how and why it spends its money. The primary reason academies like that existed was that his or her highness wanted to impress their royal cousins with how intellectual they were and how much money they could spend on the matters they believed themselves to be responsible for. That's why if you look back at scientific publications or organizations, a lot of them have a "royal" in their name "the royal society of this", "the royal college of that". This is because of their sponsors. Since we are talking about Russia here, basically, until Alexander II (second half of 18 hundreds), there weren't any government institutions that could, in principle, manage the tax collected from the royal subjects and had to report and justify their activity. Until then, by and large, all the tax collected belonged to the crown and the crown was free to do with it however their heart desired. The initial ministry of education created by Alexander I (early 18 hundreds) was the first step towards transparency, but it wasn't much. If you are interested in the reasons: both the liberation of the peasants and the defeat in the Crimean campaign created a large hole in the crown's finances. If, until then, the crown disbursed some undisclosed amount to the minister, who would use the money however he wished (mostly stole), the changes in the 1860s made it harder to steal (the minister had to report the expenditures). One could say that at this point, the current approach to financing the education began. A lot of things, however, were still subsidized directly by the crown or various elites, rather than in centralized government-sanctioned way. Another large reform, that made the system more transparent and rule-based followed in 1904, but since the Communists completely reorganized the government in 1917, it's hard to tell what the results might have been. It's only really since 1917 that education and science became exclusively financed by the tax and not through private donors.

dataflow 9d ago

[dead]

tim333 9d ago

Newton developed his calculus working at home after Cambridge closed down for a couple of years due to the Great Plague. I don't think he received funding for it.

shepherdjerred 9d ago
I wish I used my time during COVID that well

MentalM 9d ago

> imagine yourself living in the 1700s. how would you justify Newton and Leibniz's work on calculus? That is a pretty weak point. Calculus from the very beginning was an applied math. > 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? Idk, about zero? I mean almost all of our modern technologies could exist perfectly fine even without previous decades-worth refinements and extrapolations of math theory. All the math tools that they would be needed would be created on the spot if they are required. And Newton's calculus is rather an argument that is support that view: it is not like there was calculus, that had make describing of the world possible. No calculus was born as a tool to describe physical world from the very beginning.

saithound 8d ago

> imagine yourself living in the 1700s. how would you justify Newton and Leibniz's work on calculus? They didn't have to, as there were no state grants or public research funds for mathematics during the 17th century. Newton supported himself from his inheritance throughout the Great Plague, while he invented calculus, and then from flat salaries as teacher, then flat salaries from working at the London Mint. He later became fabulously wealthy after his appointment as Master of the Mint. Leibniz was a diplomat, then a librarian.

consp 8d ago
> no state grants or public research funds for mathematics during the 17th century. Since the state was the wealthy privates, for all practical purposes there was by patronage (or the wealthy elite themselves).
- saithound 8d ago
  Not so relevant to this discussion, since if you are funded by patronage networks, you need to justify your work to your patron. If you are funded by grants or public research funds, you need to justify your work to the general public.
  - true_religion 8d ago
    They did that... I take it you don't accept their justification, but that doesn't mean an attempt wasn't made. I'm another part of the general public, and I accept their justification. We can all vote, or use whatever levers our political system gives us to show our acceptance/rejection of basic research, but IMO basic research is absolutely necessary.
  - classified 8d ago
    > you need to justify your work to your patron. Assuming this is true, how did they justify their work, which had, at the time, no practical application?
    - 8d ago

esafak 8d ago

This doesn't explain why we need to pay humans to do it. What if it were more efficient to let the machines do the research? I don't think this is a great idea, since humans presently need jobs, but the argument may come up.

redox99 8d ago

I think most of the long hanging fruit has been discovered, and even then you'll have better ROI focusing funding on applied math instead of pure math.

LanceH 8d ago
You still need some brilliant mathematicians to invent new problems. AI is not yet good at inventing problems which are both novel and interesting.
AlotOfReading 8d ago
Reminds me of Michelson's (of Michelson-Morley) famous statement in 1900 that all of physics had essentially already been discovered, so the only remaining work was to apply what was known to new experiments. Similar statements were made about chemistry after Mendeleev and history after the cold war.
- redox99 8d ago
  I didn't claim you wouldn't discover things in pure math that would decades later turn out to be useful in other fields. I'm sure you would. My claim was that the ROI is lower compared to applied math, which matters when funding is limited.
smohare 8d ago
[dead]

jwilber 8d ago

1. Those early discoveries were much closer to today’s applied mathematics (which many of the pure math academic types sneer at FWIW), and 2. They made those discoveries without public funding. If AI can bring forth mathematical discoveries much faster than academics, wouldn’t it behove society to use AI? It seems the me the tradeoff here is the benefit of all vs the ego of a few. I empathize with the struggle many math PhDs must be going through, and maybe I don’t fully understand the tradeoff as they see it, but I’m not convinced by the letter written by a few career, tenured academics.

bjt 8d ago

The more pertinent question is not the binary "should we fund mathematicians or not?" It's "how many?" The money you dole out to them needs to come from someone else. Easy yes: Let's impose a tax on everyone to support at least one mathematician. Easy no: Let's impose a tax on everyone to support one billion mathematicians. Where are you going to draw that line? How are you going to convince a majority of voters that you're drawing it at the right place?

trhway 8d ago
Do we support people who are intentionally not using GPS and are still using paper maps? Or even the people who do it without any maps, just from their memory? Do we support people who aren't using vaccines and are intentionally infecting themselves directly (measles parties)? Do we support people who are intentionally using axe instead of chainsaw? Police officers and stormtroopers who are intentionally using knife instead of a gun? With civilization and technology we do loose some mental capabilities - like say the part of the brain Amazonian people use for extremely skillful face recognition we do use for reading/writing while loosing that face recognition skill level that those people in the jungle have. So goes the medieval way of doing mathematics (it is a pity though - I liked it and hoped that mathematics will fall among the last, yet it happened to be among the firsts)
- xigoi 8d ago
  If GPS required you to pay hundreds of dollars per month to criminal companies, most people would still be using paper maps.
  - trhway 8d ago
    That exactly illustrates the way of technology - the first commercial GPS receivers cost $3000, and of course people used the paper maps back then, yet technology prices have always been going down (temporary RAM crunches notwithstanding :)
    - xigoi 8d ago

stymaar 8d ago

> 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 This. And ironically enough, the obsession for measurable successes at all cost is what drove 20th century communists regimes to their most catastrophic failures. Thinking that mathematicians are now useless because they cannot continue publishing results that an AI couldn't is akin to Mao's claim that “bourgeois” intellectuals were worthless because they weren't busy driving agricultural yields up. We know where that ended…

Citizen_Lame 8d ago

You are arguing with the bot, but it's stil disappointing to see the rise of anti-intellectualism and in general fear of abstract thinking here on HN.