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Terence Tao says

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The old rules of mathematics no longer work

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For a mathematical proof

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from being written to being truly absorbed by humans

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how long does it take

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The old answer was months to years

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The answer now is

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nobody knows

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Because proofs are being produced

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faster than anyone can read them

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Hello

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everyone

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I am Leo Wang

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In early May 2026

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one of the smartest mathematicians in the world

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Fields Medal winner Terence Tao

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at the Future of Mathematics workshop at Stanford

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gave a talk

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called New Mathematical Workflows

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That title sounds quite mild

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But what he said

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was a wake up call for all of mathematics

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He made one crucial point

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AI is generating proofs

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faster than humans can absorb them

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Notice

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he was not saying AI will soon be able to do math

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He was saying

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AI is already producing mathematics

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faster than humans can keep up

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This is a fundamental turning point

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We used to worry whether AI was smart enough

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Now the problem has flipped

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AI is too fast

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and humans are too slow

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What does that mean

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Let us first look at some numbers

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Mathematics has a famous collection of Erdos problems

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It contains over a thousand unsolved problems

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posed over decades by the legendary mathematician Erdos

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Their difficulty varies

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Some offer rewards of a few hundred dollars

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Others offer over ten thousand dollars

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Many have puzzled mathematicians for decades

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In just a few months

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a large number of Erdos problems have been solved

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And on the list Tao himself maintains

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a substantial share explicitly credit AI involvement

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Let me give you a concrete example

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There is a problem numbered 728 in the Erdos collection

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In January 2026

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AI produced a complete proof

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It was also translated into a formal language

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and passed automated machine verification

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Tao said

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the process was largely autonomous

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It became one of the landmark cases

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of AI independently solving an Erdos problem

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But the story did not end there

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More crucially

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another batch of AI assisted solutions

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is waiting in line for peer review

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He also warned

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even when AI has solved a problem

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and a machine has verified it

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human experts may still be unable to explain it

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let alone answer questions about it

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Waiting in line for review

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Think about what those words mean

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The bottleneck in mathematics used to be

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who could produce a proof

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Now the bottleneck has changed

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to who will read all these proofs

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Production is exploding

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while understanding waits in line

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It is like a factory assembly line

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where upstream machines suddenly run ten times faster

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but there are still just a few inspectors downstream

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checking things one by one at the old pace

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What happens

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Unfinished goods fill the warehouse

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Tao divided mathematical work into three stages

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First comes generating proofs

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Second comes verifying proofs

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Third comes absorbing proofs

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Generation

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AI can now do this independently

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or at least speed it up dramatically

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Verification

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we have formal verification tools

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Mathematicians have a system called the Lean proof assistant

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It checks every logical step of a proof line by line

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This stage is also being automated

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But the third stage

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absorption

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remains wide open

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Absorption is subjective

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It can only move at a human pace

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Few tools can do it for you

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Let me explain something here

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Verification and understanding are completely different

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Verification checks whether each logical step is correct

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A machine can do that

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But what is understanding

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Understanding means that after reading a proof

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you know why it is right

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Not just that every step is correct

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but why the whole argument takes this direction

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and why another direction would not work

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What structures in known mathematics does it connect with

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You have to connect a new conclusion

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to the knowledge you already carry in your mind

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At some moment you have to feel

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Ah

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so that is the key

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This is not logical deduction

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It is cognitive restructuring

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A machine can tell you a proof is correct

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but it cannot tell you what that proof means

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This creates a strange situation

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Mathematics no longer lacks answers

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but it lacks understanding

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Look at a similar phenomenon

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AI generated junk code

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Programmers use AI to write code

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and production speed skyrockets

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but maintainability falls off a cliff

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The code AI writes

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humans cannot understand

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cannot modify

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and cannot debug

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Production has outrun understanding

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You see

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mathematics and programming

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two seemingly different fields

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have hit exactly the same structural problem

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I call it the absorption bottleneck

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The problem is not on the production side

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The absorption side cannot keep up

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And absorption is precisely the hardest part to automate

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But Tao saw something deeper

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He said

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the incentive system mathematics has used for centuries

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rests on an implicit assumption

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That assumption is

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proofs are scarce

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Under that assumption

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whoever proves something first

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gets the honors the job and the academic prestige

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The whole evaluation system revolves around proving things first

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But what if proofs are no longer scarce

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This is a classic case of Goodharts law

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Goodharts law says

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when a measure becomes a target

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it ceases to be a good measure

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Think about it

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In the past

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being first to prove something was a good measure

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because it closely tracked deep mathematical understanding

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You had to really understand

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to produce the proof

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But now

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AI can generate proofs in bulk

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The link between being first and truly understanding

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is breaking down

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Someone can use AI to prove a theorem first

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without truly absorbing the result

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People still chase the metric

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but it no longer measures what it was meant to measure

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At this point

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does this feel familiar

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How many metrics like this have you seen at work

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The KPI was met

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but things did not actually improve

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The paper was published

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but knowledge did not actually grow

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The code was committed

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but the system did not actually improve

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Goodharts law is at work everywhere

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His closing advice was straightforward too

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Those who submit results

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must take responsibility for verification and absorption

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Formalization should be required

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You cannot just hand raw AI output to reviewers

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The reason is simple

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Proofs can be mass produced

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but responsibility cannot be passed off in bulk

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Some actual person has to

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truly understand it

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and be willing to sign their name to it

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Tao suggested a new direction

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He argued that academic prestige should shift from proof producers

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toward those who absorb proofs

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In other words

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the most respected mathematicians of the future

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may not be those who prove the most theorems

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but those who can translate AI proofs

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into knowledge humans can understand

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That amounts to acknowledging

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that mathematics is entering an age of proof abundance

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In the past

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the arrival of a proof was news in itself

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In the future

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proofs will be like tap water

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available at the turn of a handle

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What becomes valuable is someone telling you

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which glass is worth drinking

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and why it is worth drinking

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That is a bold judgment

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because it touches the foundations of mathematics

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What kind of work deserves respect

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You might be thinking

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what does this have to do with me

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I do not work in mathematics

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But look around you

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The pattern Tao describes

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is repeating in every industry

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In media

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AI can mass produce articles

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but who decides which ones are worth reading

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In law

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AI can draft contracts and search case law

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but who understands the real dispute in a case

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In medicine

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AI can analyze scans and suggest diagnoses

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but who talks with the patient

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and turns cold data into a treatment plan they can accept

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In education

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AI can set questions grade homework and even teach

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but who can tell whether a student has memorized something

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or actually understood it

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All these industries

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face the same absorption bottleneck

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AI has accelerated production

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but understanding still moves at a human pace

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Tao used a historical analogy

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roughly speaking

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nineteenth century infrastructure meeting the invention of cars

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Imagine this

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when cars were first invented

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city roads were designed for horse drawn carriages

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Cars could move faster than horses

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but roads traffic rules and parking had not caught up

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The result was not more efficient transport

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but worse congestion and chaos

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Our academic management and education systems today

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are that city designed for carriage speeds

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AI is already moving at automobile speeds

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but our roads still belong to the carriage era

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This is more than a problem of efficiency

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It is a problem with our cognitive ecosystem

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When production far exceeds absorption

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what happens

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The signal gets buried in noise

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A truly valuable mathematical discovery

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may disappear among a hundred AI generated proofs

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that are correct but uninteresting

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It is like using a short video platform

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and scrolling through five hundred videos a day

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Every one is beautifully made

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but how many do you remember

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And there is another more hidden consequence

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When nobody absorbs a proof

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the proof exists

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but it has not truly entered human knowledge

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It is merely a machine verified sequence of symbols

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sitting in some database

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Many great breakthroughs in mathematical history

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did not happen when a proof was written

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but when someone understood that proof

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saw its connections with other fields

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and explained those connections to others

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If nobody does that work

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those proofs are like treasure on the ocean floor

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They are there

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yet they are absent

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This is a new predicament human civilization has never faced

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The old scarcity was too little knowledge and answers too slow

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Now it is too little attention and understanding too shallow

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Let us return to Tao himself

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Among his recommendations in the talk

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he urged less emphasis on being first

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and more on absorption

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A Fields Medal winner

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actively urging people to compete less over the first proof

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and spend more effort on absorption

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is a signal in itself

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Think about what this means for education

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Our education system today

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from primary school to doctoral programs

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essentially trains people to produce

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Faster problem solving more papers more code

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Exams test

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whether you can within a time limit

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produce the standard answer

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Academia counts how many papers you publish

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Employers ask how many lines of code you can write

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The whole system selects for faster producers

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But if Tao is right

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if absorption and understanding become the scarcest skills

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then our entire education system

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is developing a skill that is about to lose value

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We train humans to compete with AI at what it does best

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while neglecting what AI does worst

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This is not just a problem for mathematics

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Every parent every teacher

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and every young person planning a career

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should think seriously about it

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When the finest minds of our time

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start redefining what valuable work means

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perhaps we should pause and think too

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In an age when AI can produce almost everything for you

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what makes you truly irreplaceable

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It is not producing faster

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AI will always be faster than you

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It is not remembering more

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The parameter space of AI

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compared with the number of synapses in your brain

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is several orders of magnitude larger

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It is understanding

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It is absorption

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It is assembling fragments into a picture you can understand

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and then telling others

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what that picture means

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Taos argument

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is broadly that mathematics needs to shift some prestige from proof generators

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to proof verifiers and those who absorb proofs

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The work of helping others understand

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should not be valued less than proving something first

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What does this tell us

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Under new conditions of production the old rules

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have begun rewarding the wrong behavior

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Finally

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I want to talk about something more fundamental

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The progress of human civilization

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has never come simply from knowing more

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Accumulating information is not the same as gaining wisdom

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The ancient Greeks knew far fewer facts than we do

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but their questions about the nature of the world

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are still starting points for our thinking today

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The physics formulas Newton knew

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were less than one percent of those in modern textbooks

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but the moment he connected a falling apple with the orbit of the Moon

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he redefined how humanity understood the world

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That moment was not production

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It was absorption

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A mind made a cognitive connection across fields

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AI is helping us know more at an unprecedented pace

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But understanding more deeply

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at least so far

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can still happen only in the neural network of a biological brain

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It happens between you and a concept

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in that silent slow

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encounter that cannot be accelerated

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When Tao says the old rules of mathematics no longer work

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he is really pointing to something larger

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When production is no longer the bottleneck

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understanding becomes the scarcest resource

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Yet the incentive systems of our entire civilization

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are still desperately rewarding production

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That mismatch

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is the real crisis of our time

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It is not that AI is too powerful

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but that we have not learned how to live with it

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In an age when AI accelerates all production

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what do you think we most need to redistribute

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above all else

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Share your thoughts in the comments

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I am Leo Wang

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See you next time