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Mathematical methods and human thought in the age of AI

arxiv.org

71–80 of 102 posts

Re: Mathematical methods and human thought in the age of AI

#71
post #50

Earlier quoted context omitted.

How would a bad monopoly be likely to be taken down if not by government intervention?

It eventually becomes so big and inefficient that it gets overtaken by new competitors.

Not if they hire good to go and literally kill the competition.

Re: Mathematical methods and human thought in the age of AI

#72
The short blog post announcing this paper: https://terrytao.wordpress.com/2026/03/29/mathematical-metho...

In particular:

> This is an unabridged version of a solicited article for a forthcoming Blackwell Companion to the Philosophy of Mathematics. […] took over a year to write – which means, at the current pace of development in the field, that some of it is already slightly out of date.

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Edit: The post at https://mathstodon.xyz/@tao/116319186983426174 mentions also an (entirely unrelated) popular-math presentation titled “What does it mean to think like a mathematician?” https://terrytao.wordpress.com/wp-content/uploads/2026/03/ta... which is interesting too (despite the ChatGPT-generated illustrations and repeating stuff Tao has said before, on his blog etc.)

Re: Mathematical methods and human thought in the age of AI

#73
post #50

Earlier quoted context omitted.

> Thiel's book has influenced so many entrepreneurs into believing Monopolies are Good. Haven't read his book, but the idea that monopolies are good isn't typically made in a vacuum, it's made relative to alternatives, most often "ham-fisted government intervention". It's easier to take down a badly behaving monopoly than to change government, so believing monopolies are better than the alternatives seems like a dece…

How would a bad monopoly be likely to be taken down if not by government intervention?

Open source vs. Microsoft is a great example.

Re: Mathematical methods and human thought in the age of AI

#74

Earlier quoted context omitted.

It eventually becomes so big and inefficient that it gets overtaken by new competitors.

A Monopoly implies an organization powerful enough to stop competition. Seems like this solution that relies on competitors is fatally flawed. If there are enough competitors to meaningfully compete then there isn't a monopoly.

You can only truly stop competition by government intervention.

Re: Mathematical methods and human thought in the age of AI

#75

Earlier quoted context omitted.

Economic behavior is inherently game theoretic - agents take various actions and get some positive/negative reward as a result. Whether an agent's reward is positive or negative and of what magnitude, depends on the strategies employed by all agents. If some agents adopt new strategies, the reward calculus for everyone involved can completely change [1]. Over the past few centuries, countless new economic structures…

> Economic behavior is inherently game theoretic. Game theory is just math. As with any math, the calculations can all work out, but that says nothing of how it reflects nature. All you can say is that if the axioms are all true, then this is the necessary outcome. Look for string theory as a cautionary tale here. Game theory assumes rational systems. But we have over 6 decades of behavior science which contradicts t…

Game theory definitely does not require rational agents. Game theory says there are agents with certain specified strategies. Whether a strategy is rational from the underlying theory of value the agent adopts is completely separate matter. For example, its very common to study agents who always do one action no matter what others do or what the reward function is. Hard to call such actors rational, but that does not stop as from studying them.

Re: Mathematical methods and human thought in the age of AI

#76
post #10

Earlier quoted context omitted.

> "free market" is often used as a dogma against companies that are actively harmful to society This is a predominantly America-specific piece of propaganda, and it's pretty recent. Adam Smith's ideas are primarily arguments against mercantilism (e.g. things like using tariffs to wield self-interested state power), something he showed to be against the common good. The "invisible hand" concept is used to show how sel…

The government is a rare example of an extremely strong monopoly and not just a duopoly or a company holding significant marketshare. And yet people never seem to criticise it on those grounds despite it suffering from all of the same problems that corporate monopolies are accused of.

In democracies people can vote in control of the government to benefit themselves, unlike private monopolies. Corrupt autocracies get much criticism.

Re: Mathematical methods and human thought in the age of AI

#77
post #76

Earlier quoted context omitted.

The government is a rare example of an extremely strong monopoly and not just a duopoly or a company holding significant marketshare. And yet people never seem to criticise it on those grounds despite it suffering from all of the same problems that corporate monopolies are accused of.

In democracies people can vote in control of the government to benefit themselves, unlike private monopolies. Corrupt autocracies get much criticism.

The amount of political control individuals have in a democracy is much less than people think. I get to vote every few years for a small preselected handful of representatives, none of whom represent me or my views, and that vote is usually meaningless anyways. In my political life none of the parties I have voted for have won an election. So tell me how much control of the government do I have? How much do any of us have? Especially when the government itself often goes against the wishes of their voters anyways. The reason democracy is preferable to a dictatorship is because it prevents the government from doing things which are widely unpopular, like committing acts of genocide and political violence. But that's it really.

Remember, governments have a monopoly in areas of life that impact everybody constantly. Private monopolies do not, in every case you can simply ignore them and not purchase their products, and by doing so you exert more control over them than you do casting a meaningless vote every few years.

The idea of democracy being will of the people is pure fantasy. It's useful to prevent governments from doing really bad things, that's it. It doesn't even matter who you vote for, broadly speaking. Just that you are able to exert that pressure.

Re: Mathematical methods and human thought in the age of AI

#78

Earlier quoted context omitted.

A Monopoly implies an organization powerful enough to stop competition. Seems like this solution that relies on competitors is fatally flawed. If there are enough competitors to meaningfully compete then there isn't a monopoly.

You can only truly stop competition by government intervention.

When an organization gets big enough it is indistinguishable from government.

Re: Mathematical methods and human thought in the age of AI

#79

Earlier quoted context omitted.

> Economic behavior is inherently game theoretic. Game theory is just math. As with any math, the calculations can all work out, but that says nothing of how it reflects nature. All you can say is that if the axioms are all true, then this is the necessary outcome. Look for string theory as a cautionary tale here. Game theory assumes rational systems. But we have over 6 decades of behavior science which contradicts t…

Game theory definitely does not require rational agents. Game theory says there are agents with certain specified strategies. Whether a strategy is rational from the underlying theory of value the agent adopts is completely separate matter. For example, its very common to study agents who always do one action no matter what others do or what the reward function is. Hard to call such actors rational, but that does not…

When I said rational I meant it in this way. That rational agents will perform in a way in which maximizes their utility (or reward function). In psychology we call this theory homo economicus[1]. Regardless of theories of value, perceived rewards, and utilities, human beings have biases, prejudice, superstition, dogma, etc. etc. In real economies these non-strategic behaviors are consistently observed. This is why I say that economics are not just game theories, they are psychology, sociology, religion, as much as they are zero-sum games between actors.

> Hard to call such actors rational, but that does not stop as from studying them.

This is precisely why I object to your first post. “Shut up and do the math” has not done the wonders which string theorists had hoped. Game theory is a perfectly fine way to mathematics, and to study certain strategies, but it tells us nothing about the nature of economies in the real world.

https://en.wikipedia.org/wiki/Homo_economicus

Re: Mathematical methods and human thought in the age of AI

#80
post #59

Earlier quoted context omitted.

> Society is better if we sacrifice one horse and buggy driver job for two engineering jobs. That's a "statistic" you're pulling out of your butt, and it's doing a lot of work. No one ever knows if something like that will actually happen. It could actually turn out that AI sacrifices 100 engineering jobs for 10 low-level service or prostitution jobs and a crap-ton of wealth to those already rich. > The drivers suffe…

> It could actually turn out that AI sacrifices 100 engineering jobs for 10 low-level service or prostitution jobs and a crap-ton of wealth to those already rich. That's where wealth redistribution (Taxation) comes in. The USA is not good at progressive taxation, but everyone could be better off if it were implemented properly.

> The USA is not good at progressive taxation

The top 10 percent of incomes pay 76% of all income taxes, the top 5% pays around 55% of all income tax.

I would say it’s pretty progressive.

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