Shadowing Practice: The End of Human Mathematics? AI's Recent Breakthrough -- And What's Next - Learn English Speaking with Video
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Maths is cooked!
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I heard this recently on a podcast, and I agree.
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I also agree that heard it on a podcast is not the greatest argument, but there's more to it,
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including the question of why everyone's suddenly so interested in solving obscure maths problems that no one had heard of before,
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or may I try to convince you it's the biggest thing ever.
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Today I have a brief update on what AI has been doing to maths recently,
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but mostly I want to look at how people have reacted to it and what's likely to come next.
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Even just at the present pace, we're talking about essentially all Frontier Math Tier 4,
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all professional research -grade math problems being solved in the next four or five years.
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So math is cooked.
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I'll say it, you know, second time, math is cooked.
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That was physicist and computer scientist Alexander Wisner -Gross commenting on the AI takeover of maths.
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He's not the only one who sees it coming, and things are moving quickly now.
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In the past four years, large language models have progressed in maths extremely fast.
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They've basically gone from not being able to add 2
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and 2 to solving maths Olympia problems to solving problems that no one cares about.
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Then, two weeks ago, for the first time, a large language model solved a reasonably well -known maths problem.
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The model in question is not a publicly available one.
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It's an internal OpenAI model, which is somewhat disappointing because we can't try it, and it also makes you wonder where OpenAI is going with this.
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The problem the model solved was posed by Paul Erdős 80 years ago.
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The solution made big headlines primarily, I think, because it's a case where the problem is actually understandable.
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If you put points in a plane, how do you have to place them so that you have a maximal number of pairs with the same distance between them?
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Erdős conjecture, that'd be a square lattice, but he didn't prove it.
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The OpenAI model disproved Edo's conjecture with a counterexample.
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Not just that, it allegedly one -shotted it on the first attempt.
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OpenAI also checked how often the model arrived at the correct answer in multiple test runs.
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With enough computing time, they found that the model got it right about 50 % of the time.
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So it's clear that the model is still not any good at checking its own logic, but it's also clearly not just randomly outputting strings that look mathy,
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which is more than can be said for some conference abstracts I've read.
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Here are some recent reactions from mathematicians.
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I find this existentially upsetting.
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I see myself shriveling to nothing.
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I'm saddened.
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It may be the case that within the decade reasoning models will outperform the greatest living mathematicians.
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We're cooked.
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This is the best proof to come out in a year.
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We're completely fucked.
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And the computer scientist Scott Aronson relates,
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I heard the news maybe an hour after it broke when some UT grad students came to my office to tell me.
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For what it's worth, these students were morose, musing about how everything might soon be over for young scientists and mathematicians like themselves.
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This is what makes academia special.
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In industry, people worry that AI will take their jobs.
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In academia, they worry that AI will take their jobs before they even get jobs.
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But what I find most interesting about this recent proof is that, for all I can tell,
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most mathematicians thought that a Deutsch conjecture was correct.
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And the counterexample which the AI came up with is the kind of unintuitive, slightly ugly construction that humans are unlikely to think of.
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It's not that the machine is smarter, but that it has worse taste.
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That said, rumors of the demise of mathematics have been somewhat exaggerated because it took only a few hours until someone, and I mean a human being,
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improved the Oak May Eye result.
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There's also been a lot of pushback of the idea that maths is over.
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A group of 150 mathematicians just signed a declaration warning
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that these developments put the autonomy of mathematics under threat
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and there's currently a strong commercial incentive on the part of the technology industry to overstate the capabilities of their products.
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The latter quite plausibly answers the question of why the US media makes such a big deal of this
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when usually they can't be bothered writing about maths at all.
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It's a kind of sabre -retting for the Chinese, basically.
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Personally, I think what's.. going to happen is not that mathematics will end.
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What we'll see instead is that a lot of mathematicians will shift to AI -supported techniques.
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This is because the existing mathematical literature contains sufficient information for a lot of conclusions,
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proofs even, that are within reach for someone or something
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that can rapidly digest and analyze a lot of data and go through many attempts at proofs quickly.
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There must be many low -hanging fruits to pick, like this recent counterexample, and we're going to see more of this.
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The open question is whether AI can go beyond extracting patterns in human methods
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and filling in the holes in the literature to develop its own methods.
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I continue to insist that large language models are not going to get us there.
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So yes, maths may be cooked, but only partially, more like ardente.
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One -shotting an Erdős problem is of course impressive, but wait until they can explain to normal people why they show care.
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A few years ago, I received some ugly letters from a debt collection company.
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They threatened to sue me for ordering something online and then not paying it.
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Turned out that someone had stolen my private data.
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I managed to get out of this, but since then I've become very protective of my personal information, which is why I've signed up to Incogni,
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who've been sponsoring this video.
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Each time you open a website, it'll try to collect data about who you are and where you are and what other websites you've visited.
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Many firms then make money by selling your private information to data brokers.
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Most countries have laws against that and you can ask for your data to be removed, but doing this takes up a lot of time.
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Incogni automates the process of getting you out of those databases.
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You sign up and they'll contact the big sinners, request that your personal details be removed.
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They'll keep on doing that and, if you want, send you updates about the progress they're making.
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They now also have a custom removal feature where you can submit specific websites.
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I'll be using this a lot.
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Incogni has really made my life better.
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If that sounds like something you could need to, use my link Sabine or the custom link in the info
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because the first 100 people to use it will get 60 % off.
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Stay safe.
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Thanks for watching.
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See you tomorrow.
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Vocabulary and speaking notes for this lesson
This video has 86 sentences and 1168 words to shadow. The speech runs for 7:35. The speaker talks at a natural 154 words per minute, close to everyday conversation. Only 80% of the words are among the 3,000 most common in English, so the vocabulary is demanding.
Key vocabulary in this video
15 words from the video worth learning, with pronunciation and meaning:
| Word | Pronunciation | Meaning |
|---|---|---|
| mathematics noun | /mæθ(.ə)ˈmæt.ɪks/ | An abstract representational system studying numbers, shapes, structures, quantitative change and relationships between them. |
| solve verb | /sɒlv/ | To find an answer or solution to a problem or question; to work out. |
| scientist noun | /ˈsaɪəntəst/ | One whose activities make use of the scientific method to answer questions regarding the measurable universe. A scientist may be involved in original research… |
| custom noun | /ˈkʌstəm/ | Frequent repetition of the same behavior; way of behavior common to many; ordinary manner; habitual practice; method of doing, living or behaving. |
| ugly adjective | /ˈʌɡli/ | Displeasing to the eye; aesthetically unpleasing. |
| podcast noun | /ˈpɑdˌkæst/ | A program, especially an audio program, produced on a regular basis, delivered over the Internet in a compressed digital format and designed for playback on… |
| academia noun | /ˌæk.əˈdi.mi.ə/ | The scientific and cultural community engaged in higher education and research, taken as a whole. |
| primarily adverb | /ˈpɹaɪ.mə.ɹə.li/ | Of a primary or central nature, first and foremost. |
| impressive adjective | /ɪmˈpɹɛsɪv/ | Making, or tending to make, a positive impression; having power to impress. |
| technique noun | /tɛkˈniːk/ | The practical aspects of a given art, occupation etc.; formal requirements. |
| output noun | /ˈaʊtpʊt/ | Production; quantity produced, created, or completed. |
| essentially adverb | /ɪˈsɛnʃəli/ | In essence: by nature. |
| steal verb | /stiːl/ | To take illegally, or without the owner's permission, something owned by someone else without intending to return it. |
| conclusion noun | /kənˈkluːʒən/ | The end, finish, close or last part of something. |
| string noun | /stɹɪŋ/ | A long, thin and flexible structure made from threads twisted together. |
Phrasal verbs you will hear
| Word | Meaning |
|---|---|
| come out in verb | to be afflicted by (a visible disruption of the body) |
| come up with verb | To manage to produce, deliver, or present (something) by inventing, creating, thinking of, or obtaining it. |
| get off verb | To move from being on top of (something) to not being on top of it. |
| get out of verb | To leave, exit or escape from; to become free of. |
| go through verb | To travel from one end of something to the other. |
| sign up verb | To add a name to the list of people who are participating in something. |
| take up verb | To pick up. |
| turn out verb | To end up; to result. |
Pronunciation to watch
The speaker uses 22 contractions and reduced forms, such as we're, I've, can't. Say them the short way, as you hear them.
- The “th” sounds: mathematics /mæθ(.ə)ˈmæt.ɪks/, bother /ˈbɑðɚ/, mathematical /ˌmæθ(.ə)ˈmæt.ɪ.kəl/, threaten /ˈθɹɛt.n̩/, mathematician /ˌmæθ.(ə.)məˈtɪʃ.ən/
- The “sh” and “zh” sounds: essentially /ɪˈsɛnʃəli/, conclusion /kənˈkluːʒən/, sufficient /səˈfɪʃənt/, partially /ˈpɑɹʃəli/, declaration /ˌdɛk.ləˈɹeɪ.ʃən/
- Long words — get the stress right: mathematics /mæθ(.ə)ˈmæt.ɪks/, academia /ˌæk.əˈdi.mi.ə/, primarily /ˈpɹaɪ.mə.ɹə.li/, essentially /ɪˈsɛnʃəli/, declaration /ˌdɛk.ləˈɹeɪ.ʃən/
How to practise with this video
- Listen to the whole video once without speaking and note the words you do not know.
- Start at 0.75× speed, shadow it sentence by sentence, then go back to normal speed once it feels easy.
- Record yourself and compare with the original, paying attention to words like mathematics, solve, scientist.
Grammar in this video
The structures the speaker uses most, with the exact words from the video:
| Structure | In the video |
|---|---|
| Present perfect continuous have/has been + -ing — an action that started earlier and is still going on | has been doing · who've been sponsoring |
| Passive voice be + past participle — the focus is on what happens, not who does it | is cooked · being solved · was posed |
| Present perfect have/has + past participle — a past action that still matters now | have reacted · have progressed · They've basically gone |
| Relative clauses who / which + clause — extra information about a person or thing | one who sees · model, which is · information, which is |
What is the Shadowing Technique?
Shadowing is a science-backed language learning technique originally developed for professional interpreter training and popularized by polyglot Dr. Alexander Arguelles. The method is simple but powerful: you listen to native English audio and immediately repeat it out loud — like a shadow following the speaker with just a 1–2 second delay. Unlike passive listening or grammar drills, shadowing forces your brain and mouth muscles to simultaneously process and reproduce real speech patterns. Research shows it significantly improves pronunciation accuracy, intonation, rhythm, connected speech, listening comprehension, and speaking fluency — making it one of the most effective methods for IELTS Speaking preparation and real-world English communication.