[
  {
    "start": 0.06,
    "end": 2.38,
    "text": "I say it's the Harry Potter approach, you know."
  },
  {
    "start": 2.46,
    "end": 13.84,
    "text": "In the beginning we have to learn the basic magic spells like Wingardium Leviosa or something and then later than also use some more advanced spells."
  },
  {
    "start": 14.5,
    "end": 17.34,
    "text": "The forbidden spells are equivalent of choice."
  },
  {
    "start": 17.86,
    "end": 18.8,
    "text": "Tetsuya Mondator."
  },
  {
    "start": 20.18,
    "end": 21.56,
    "text": "They're three forbidden ones right?"
  },
  {
    "start": 27.68,
    "end": 27.84,
    "text": "Hi."
  },
  {
    "start": 28.42,
    "end": 33.68,
    "text": "Yeah, welcome to one of our in-between premises right?"
  },
  {
    "start": 33.9,
    "end": 38.86,
    "text": "Welcome and what do you are better at this Dennis?"
  },
  {
    "start": 39.72,
    "end": 46.54,
    "text": "I remind people to subscribe To buy us a coffee And to hype or whatever."
  },
  {
    "start": 46.8,
    "end": 47.38,
    "text": "Like or"
  },
  {
    "start": 47.5,
    "end": 52.42,
    "text": "comment and Do all sort of nice things and tell your friends about it if you like It."
  },
  {
    "start": 52.48,
    "end": 55.48,
    "text": "If You don't like it keep quiet That's okay."
  },
  {
    "start": 57.52,
    "end": 58.88,
    "text": "Okay, Dennis."
  },
  {
    "start": 59.46,
    "end": 61.48,
    "text": "What shall we talk about today?"
  },
  {
    "start": 62.92,
    "end": 69.24,
    "text": "There is one thing and I mean... We were thinking of having more computer AI-focused series."
  },
  {
    "start": 69.38,
    "end": 74.52,
    "text": "even within that And something quite related to it was Interactive Theory Improving."
  },
  {
    "start": 75.26,
    "end": 80.04,
    "text": "So maybe i wanted a basic episode but it's interactive theory improving."
  },
  {
    "start": 80.14,
    "end": 81.5,
    "text": "Do you know how to prove us?"
  },
  {
    "start": 82.14,
    "end": 87.28,
    "text": "You use this in your education or teaching something I would like to talk about."
  },
  {
    "start": 87.32,
    "end": 87.44,
    "text": "Yes,"
  },
  {
    "start": 87.92,
    "end": 88.02,
    "text": "so."
  },
  {
    "start": 89.42,
    "end": 100.22,
    "text": "and then i'm now using Lean in a second year logic course which is called Introduction To Formal Reasoning Which Is Actually Compulsory In The Second Year."
  },
  {
    "start": 100.98,
    "end": 114.7,
    "text": "So My Goal Here Is To Teach People Basically A Predicate Logic How To Express Yourself In Predicate Logics."
  },
  {
    "start": 115.4,
    "end": 119.08,
    "text": "Yeah, to have a language where you can make precise statements."
  },
  {
    "start": 119.2,
    "end": 147.28,
    "text": "I mean this is something even computer scientists are interested in because... You find often when you make statements in English or German that they're a bit vague and open to different interpretations And what we want do sometimes talk about programs or even systems you implement, whatever."
  },
  {
    "start": 147.82,
    "end": 173.28,
    "text": "You want to make precise statements so I think it's good for computer science to understand what this means and... To do this we use lean as a logical language where you can also express proofs And i think that is quite important because I mean, the approach is a bit different than in mathematics."
  },
  {
    "start": 173.34,
    "end": 183.58,
    "text": "In mathematics people learn proofs by doing lots of them and they learn them in some semantic way or actually semantically."
  },
  {
    "start": 183.66,
    "end": 190.28,
    "text": "but then there are also these proof techniques like induction-proof by contradiction"
  },
  {
    "start": 190.36,
    "end": 190.5,
    "text": "etc.,"
  },
  {
    "start": 192.22,
    "end": 194.3,
    "text": "But it's still vague."
  },
  {
    "start": 196.26,
    "end": 210.26,
    "text": "I think it's sometimes difficult to know whether a student actually understands what is meant by your proof, or its not because you can ask them to prove something which was false and they will come up with the proof in many cases."
  },
  {
    "start": 212.36,
    "end": 226.7,
    "text": "So really have this idea of a proof as sort of very convincing statement that at least convinces yourself – hopefully It's actually not so easy."
  },
  {
    "start": 226.9,
    "end": 243.14,
    "text": "And I think to use an interactive proof system is quite helpful because, for example... ...I give a number of things to prove and some of them are actually not true!"
  },
  {
    "start": 246.18,
    "end": 247.92,
    "text": "Then they sit there and try to prove it?"
  },
  {
    "start": 248.26,
    "end": 249.88,
    "text": "That's interesting sometimes."
  },
  {
    "start": 254.6,
    "end": 258.839,
    "text": "The x is the y, implies that some relation rx and y helps."
  },
  {
    "start": 259.44,
    "end": 264.14,
    "text": "Then it implies there exists an X for all y so you can commute quantifiers."
  },
  {
    "start": 264.9,
    "end": 267.52,
    "text": "And they were then trying to prove this."
  },
  {
    "start": 269.3,
    "end": 270.08,
    "text": "We have this lab."
  },
  {
    "start": 270.24,
    "end": 274.16,
    "text": "They said I'm stuck here Can't prove this."
  },
  {
    "start": 275.04,
    "end": 277.5,
    "text": "What about if everybody loves somebody?"
  },
  {
    "start": 277.72,
    "end": 280.18,
    "text": "Is someone loved by everyone?"
  },
  {
    "start": 280.86,
    "end": 282.66,
    "text": "No, oh yeah if you can't prove this."
  },
  {
    "start": 283.28,
    "end": 299.8,
    "text": "So to navigate the question of what's actually provable and not valid I find it extremely helpful to use an interactive proof assistant."
  },
  {
    "start": 300.92,
    "end": 304.76,
    "text": "now obviously has got some other ideas behind that."
  },
  {
    "start": 304.82,
    "end": 319.68,
    "text": "there are interesting applications in providing formal evidence for important properties of programs, which is quite laborious to do by hand."
  },
  {
    "start": 320.26,
    "end": 345.72,
    "text": "But now we have the help off AI so it actually becomes more feasible what the output of the AI is then, it's a formal proof which can be independently verified."
  },
  {
    "start": 346.4,
    "end": 355.24,
    "text": "So understanding interactive proof system now becomes even more important in the age of AI right?"
  },
  {
    "start": 356.42,
    "end": 363.48,
    "text": "And while you... In the end if want to delegate boring proof tasks to the AI."
  },
  {
    "start": 364.26,
    "end": 371.02,
    "text": "You need an understanding or the proof actually is."
  },
  {
    "start": 371.24,
    "end": 376.38,
    "text": "And then once you understand this, Then You can ask an AI to help you."
  },
  {
    "start": 377.92,
    "end": 394.18,
    "text": "one tiny question there and as far I'm aware lean Is not so heavily used in these program verification In comparison To something like maybe iris rock or others But it's more use than the math community."
  },
  {
    "start": 396.12,
    "end": 404.18,
    "text": "Yes So Lean is very close too rock or what was called cock earlier but for some reasons they changed the name."
  },
  {
    "start": 405.3,
    "end": 405.36,
    "text": "No"
  },
  {
    "start": 405.58,
    "end": 411.12,
    "text": "idea, don't say their old names too often otherwise we'll reach."
  },
  {
    "start": 412.82,
    "end": 419.54,
    "text": "Okay after the male chicken...the French word for male chicken anyway."
  },
  {
    "start": 419.58,
    "end": 423.98,
    "text": "yeah I'm not sure what's happening."
  },
  {
    "start": 424.34,
    "end": 446.92,
    "text": "what was called, initial I must implement by Leonardo de Moura who already had these proof systems and he wanted to have a language in which you can also express more generally the proofs."
  },
  {
    "start": 447.68,
    "end": 465.2,
    "text": "He initially used Rock at that time but then decided to implement his own system basically in spirit, very similar to what's called lean because it is smaller and faster."
  },
  {
    "start": 465.6,
    "end": 485.02,
    "text": "And so lots of things which he didn't like about this French system that he tried to fix but there isn't a fundamental difference became, was then very much used by mathematicians."
  },
  {
    "start": 485.2,
    "end": 502.08,
    "text": "Like we had already Kevin Buzzard who's one of the main proper protagonists there others and they started now building this moth lip which but I think Linus is also increasingly."
  },
  {
    "start": 505.98,
    "end": 507.4,
    "text": "And then"
  },
  {
    "start": 509.42,
    "end": 516.9,
    "text": "the other question, Lien is often thought to be rather classical in comparison with some other Provers."
  },
  {
    "start": 517.74,
    "end": 519.659,
    "text": "Is your course simply classical?"
  },
  {
    "start": 521.64,
    "end": 528.48,
    "text": "No my course is intuitionistic aware as you may imagine."
  },
  {
    "start": 530.52,
    "end": 548.32,
    "text": "so I start by explaining this idea of having evidence for proposition, and then I introduced this... compared with truth tables."
  },
  {
    "start": 548.42,
    "end": 554.34,
    "text": "And we notice that there are things which are provable in truth tables but not provable by evidence."
  },
  {
    "start": 555.18,
    "end": 571.44,
    "text": "so for my main example is if you know that i don't have dogs or cats do Yeah, so I would say if you think of evidence."
  },
  {
    "start": 572.18,
    "end": 575.22,
    "text": "You have evidences that don't have dogs and cats forever."
  },
  {
    "start": 575.28,
    "end": 576.7,
    "text": "they're not fighting or whatever."
  },
  {
    "start": 577.44,
    "end": 596.04,
    "text": "but do you know whether it's because there are no dogs?"
  },
  {
    "start": 597.36,
    "end": 602.0,
    "text": "to use classical logic and for other things not."
  },
  {
    "start": 602.86,
    "end": 618.06,
    "text": "And so I have introduced the idea of a logic poker, you get ten propositions... ...and now you either have to prove them or say that they're not provable…."
  },
  {
    "start": 618.7,
    "end": 620.44,
    "text": "…or approve them using classical logic!"
  },
  {
    "start": 622.2,
    "end": 623.62,
    "text": "So we have to classify them."
  },
  {
    "start": 625.24,
    "end": 626.0,
    "text": "You lose points."
  },
  {
    "start": 626.64,
    "end": 633.42,
    "text": "So, if you prove something which is provable internationally using classical logic."
  },
  {
    "start": 634.1,
    "end": 641.04,
    "text": "Famous counter example it's not that P if and only if NOTP."
  },
  {
    "start": 642.24,
    "end": 644.66,
    "text": "It's not the case that P is equivalent to NOTP."
  },
  {
    "start": 647.3,
    "end": 648.06,
    "text": "How would your proof this?"
  },
  {
    "start": 655.66,
    "end": 657.38,
    "text": "Poverty works right?"
  },
  {
    "start": 658.56,
    "end": 659.4,
    "text": "I mean"
  },
  {
    "start": 660.26,
    "end": 661.52,
    "text": "if and only of one not p."
  },
  {
    "start": 662.74,
    "end": 666.0,
    "text": "Yeah, north break it's key."
  },
  {
    "start": 666.22,
    "end": 669.56,
    "text": "if you don't have a lot p Not open or break its."
  },
  {
    "start": 670.28,
    "end": 671.0,
    "text": "It's not the case."
  },
  {
    "start": 671.04,
    "end": 671.04,
    "text": "I"
  },
  {
    "start": 671.1,
    "end": 672.84,
    "text": "mean I grew up classically."
  },
  {
    "start": 673.08,
    "end": 677.4,
    "text": "i would use stuff with heads from right away But yeah"
  },
  {
    "start": 678.44,
    "end": 679.28,
    "text": "What do think you need is"
  },
  {
    "start": 679.34,
    "end": 680.08,
    "text": "what's the constant?"
  },
  {
    "start": 681.46,
    "end": 684.16,
    "text": "now that you asked no but Normally"
  },
  {
    "start": 686.5,
    "end": 688.12,
    "text": "I can tell you how it works."
  },
  {
    "start": 689.98,
    "end": 694.3,
    "text": "You want to prove that P if only not P implies false, right?"
  },
  {
    "start": 696.76,
    "end": 699.04,
    "text": "So P implies NOTP means"
  },
  {
    "start": 700.64,
    "end": 700.64,
    "text": "P"
  },
  {
    "start": 701.16,
    "end": 702.92,
    "text": "implies P implies FALSE."
  },
  {
    "start": 703.44,
    "end": 704.22,
    "text": "then you have NOTP."
  },
  {
    "start": 705.06,
    "end": 709.9,
    "text": "If we have NOTp ,you also have p and you have P and NOTp are false."
  },
  {
    "start": 710.0,
    "end": 710.56,
    "text": "Interesting!"
  },
  {
    "start": 711.24,
    "end": 721.36,
    "text": "This is something that looks more classic than it But it's just the law of non-contradiction somehow, right?"
  },
  {
    "start": 721.7,
    "end": 721.88,
    "text": "Yes."
  },
  {
    "start": 722.24,
    "end": 722.3,
    "text": "So"
  },
  {
    "start": 722.98,
    "end": 723.72,
    "text": "after a while we"
  },
  {
    "start": 723.88,
    "end": 725.3,
    "text": "could have guessed this one."
  },
  {
    "start": 726.24,
    "end": 726.94,
    "text": "It is dual."
  },
  {
    "start": 727.42,
    "end": 730.02,
    "text": "so Law of Extraordinary Middle is not provable institutionistically."
  },
  {
    "start": 731.16,
    "end": 731.4,
    "text": "Cool!"
  },
  {
    "start": 734.96,
    "end": 762.9,
    "text": "One aspect I recently was in talk from where system called waterproof was presented and that was like for math educators Eidhofen, I think who built up on verbose lean and they had like a system that really helped students to for instance introduce variables And do this busy work so-to speak."
  },
  {
    "start": 763.12,
    "end": 765.78,
    "text": "So it's something That you use don't seem"
  },
  {
    "start": 766.3,
    "end": 768.44,
    "text": "too few proponents of good idea?"
  },
  {
    "start": 777.8,
    "end": 779.84,
    "text": "fancy system on top."
  },
  {
    "start": 780.02,
    "end": 787.14,
    "text": "So I mean, i haven't looked at this waterproof but it sounds to me a bit too close to the water"
  },
  {
    "start": 789.12,
    "end": 789.52,
    "text": "than..."
  },
  {
    "start": 790.38,
    "end": 790.52,
    "text": "Sorry!"
  },
  {
    "start": 790.8,
    "end": 792.96,
    "text": "I forgot to mention something you said."
  },
  {
    "start": 793.08,
    "end": 795.96,
    "text": "lean is very classical and yeah?"
  },
  {
    "start": 796.66,
    "end": 820.6,
    "text": "The use of lean in the mudflip Is very classical And It's sometimes very difficult to separate constructive and classical arguments in Lien because somehow the classical arguments are built into some books, which actually don't need it."
  },
  {
    "start": 821.46,
    "end": 825.38,
    "text": "That's a bit a nuisance for the constructivists."
  },
  {
    "start": 825.94,
    "end": 830.82,
    "text": "but there certainly systems I... In many ways Lien is rather ad hoc."
  },
  {
    "start": 831.72,
    "end": 839.86,
    "text": "It's another example of a system which is actually not so well designed being the most popular."
  },
  {
    "start": 840.22,
    "end": 848.06,
    "text": "You find there's lots of programming languages, often good programming languages are not too popular but this really ad hoc ones."
  },
  {
    "start": 849.4,
    "end": 853.82,
    "text": "where computer scientists shakes their head they become very popular."
  },
  {
    "start": 853.92,
    "end": 856.26,
    "text": "I mean JavaScript or name it."
  },
  {
    "start": 856.32,
    "end": 856.42,
    "text": "yeah."
  },
  {
    "start": 857.44,
    "end": 860.24,
    "text": "It's common experience and also happens in proof systems."
  },
  {
    "start": 860.28,
    "end": 863.86,
    "text": "So i think that much better interactive proof systems."
  },
  {
    "start": 863.98,
    "end": 882.7,
    "text": "And my favorite one is this one here, ACTA which really very close to types theory and also implements hot in cubicle ACTA."
  },
  {
    "start": 883.32,
    "end": 899.66,
    "text": "so from a point of the type theoretician I mean both ACTA are based on types theory but ACTA much more type theoretic and in many ways, a much more beautiful language than Lien."
  },
  {
    "start": 900.36,
    "end": 912.58,
    "text": "But as far as popular culture is concerned, Lien was successful And for my module I use Lien actually For various reasons."
  },
  {
    "start": 912.62,
    "end": 920.74,
    "text": "so one reason that i don't really want to introduce types theory but mainly interested in predicate logic And for lean, you can really separate this."
  },
  {
    "start": 920.78,
    "end": 922.5,
    "text": "So that's certainly advantage in Akta."
  },
  {
    "start": 923.5,
    "end": 942.34,
    "text": "there isn't a good way to just do sort of... ...to separate types daily from logic and on the other hand since Lean is also more used in practice it's obviously more interesting and relevant for students here."
  },
  {
    "start": 943.06,
    "end": 949.64,
    "text": "but my own preference for ACTA."
  },
  {
    "start": 953.92,
    "end": 971.9,
    "text": "I have an advanced module where i teach ACTA, which is called Proofs, Programs and Types And this level four module which is elective whereas the lean module as Level two and it's a compulsory reason."
  },
  {
    "start": 975.62,
    "end": 984.12,
    "text": "Me coming from the whole other side And it's hard to convince a mathematician sometimes, too use restricted language."
  },
  {
    "start": 984.26,
    "end": 984.44,
    "text": "Right?"
  },
  {
    "start": 984.5,
    "end": 984.84,
    "text": "Because"
  },
  {
    "start": 987.56,
    "end": 988.78,
    "text": "what would be restricted languages?"
  },
  {
    "start": 988.82,
    "end": 989.26,
    "text": "in this case"
  },
  {
    "start": 990.14,
    "end": 993.06,
    "text": "I mean particular programming language whichever."
  },
  {
    "start": 994.48,
    "end": 1013.04,
    "text": "so you can if i understand the proof of my got default semantics If I know why it holds and I cannot press this down into The excite syntax that feels like a tedious task to learn the syntax at some point."
  },
  {
    "start": 1013.22,
    "end": 1016.72,
    "text": "So coming from the other side, you might want... Yeah?"
  },
  {
    "start": 1016.78,
    "end": 1016.86,
    "text": "At"
  },
  {
    "start": 1018.42,
    "end": 1019.84,
    "text": "first there are two arguments here."
  },
  {
    "start": 1020.04,
    "end": 1036.7,
    "text": "I mean one is which Vladimir Bovatsky himself observed That most mathematical proofs are incorrect and The question is either fixable or not Which isn't an issue And he suffered from this himself."
  },
  {
    "start": 1037.859,
    "end": 1044.18,
    "text": "So yes, you would like to know that your proofs are actually correct and most mathematicians don't."
  },
  {
    "start": 1044.4,
    "end": 1052.96,
    "text": "And if I put more complex proof whether this is correct even though it's been reviewed in a journal or whatever right?"
  },
  {
    "start": 1055.22,
    "end": 1055.86,
    "text": "Fine with that."
  },
  {
    "start": 1055.96,
    "end": 1060.4,
    "text": "but there was the opposite counterargument for making your language verbose."
  },
  {
    "start": 1061.3,
    "end": 1068.22,
    "text": "one also want Whether a formal proof is hundred percent true whether it's really the right definitions, where"
  },
  {
    "start": 1068.56,
    "end": 1069.4,
    "text": "there are things"
  },
  {
    "start": 1069.52,
    "end": 1070.74,
    "text": "or were something went wrong."
  },
  {
    "start": 1070.96,
    "end": 1075.34,
    "text": "So to make that human readable at the same time as also"
  },
  {
    "start": 1075.64,
    "end": 1090.98,
    "text": "yes I mean human readability is obviously important but That actually i think achieved too large degree in modern proof systems and this is not very different from syntax of Mathematics."
  },
  {
    "start": 1091.16,
    "end": 1091.22,
    "text": "It"
  },
  {
    "start": 1092.66,
    "end": 1098.1,
    "text": "might get a problem once AI is involved and produce these very long proofs."
  },
  {
    "start": 1098.38,
    "end": 1103.02,
    "text": "No, but I can help you... I mean the AI helps to bridge exactly this gap."
  },
  {
    "start": 1103.16,
    "end": 1116.8,
    "text": "as you said The mathematician doesn't really want to do all of those details of syntactic fiddling But that's where they use AI to help them."
  },
  {
    "start": 1117.62,
    "end": 1117.66,
    "text": "So"
  },
  {
    "start": 1118.48,
    "end": 1120.18,
    "text": "i was talking now about Auto Mart."
  },
  {
    "start": 1122.62,
    "end": 1127.32,
    "text": "If you just give the problem and you have your AI, I'll say oh find a lean proof."
  },
  {
    "start": 1128.0,
    "end": 1131.44,
    "text": "This lean prove can be very long and has weird detours..."
  },
  {
    "start": 1132.54,
    "end": 1144.98,
    "text": "Right but usually would put turn your big theory into lemmas."
  },
  {
    "start": 1147.08,
    "end": 1157.3,
    "text": "the AI to help you with dilemmas, I think it's a mathematician."
  },
  {
    "start": 1157.36,
    "end": 1172.82,
    "text": "You want use your high-level argument which maybe in some cases... Some arguments can be found by approval or an AI and in some case the AI may not able do that."
  },
  {
    "start": 1173.44,
    "end": 1174.48,
    "text": "but what?"
  },
  {
    "start": 1174.54,
    "end": 1186.36,
    "text": "we can then bridge the gap from this high level understanding to the low level proof, which is actually where I see as a most important application of AI."
  },
  {
    "start": 1187.72,
    "end": 1192.32,
    "text": "To use AIs and find arguments themselves."
  },
  {
    "start": 1192.84,
    "end": 1211.56,
    "text": "not sure that there's some excitement about it but I think mathematicians still want come up with our argument that they are correct and then as you said, there's this gap."
  },
  {
    "start": 1212.92,
    "end": 1223.1,
    "text": "I mean in the moment using these proof systems requires quite a high level of specialized expertise yeah?"
  },
  {
    "start": 1223.64,
    "end": 1240.84,
    "text": "And if correctly stated mathematicians mostly wouldn't want to gather some exceptions but many don't want to do this, they wanted to continue doing research in their particular subject and don't wanna spend lots of time."
  },
  {
    "start": 1241.38,
    "end": 1245.2,
    "text": "To learn the intricacies of formal proof systems."
  },
  {
    "start": 1245.86,
    "end": 1253.72,
    "text": "but what I'm saying is that using a combination of AI and proofs system can help bridge the gap?"
  },
  {
    "start": 1254.14,
    "end": 1265.08,
    "text": "Still you have to understand how this proof system works But then with concrete application all the detailed analysis."
  },
  {
    "start": 1265.24,
    "end": 1286.36,
    "text": "And I'm doing this, using AI is quite helpful to do laborious proofs which are can-do but it takes a long time whereas you ask Claude or Chachi PT and they just do it."
  },
  {
    "start": 1287.7,
    "end": 1288.38,
    "text": "that's what we want."
  },
  {
    "start": 1291.6,
    "end": 1293.0,
    "text": "There one aspect there."
  },
  {
    "start": 1294.04,
    "end": 1299.5,
    "text": "In math education in Germany we have this, or maybe English as well."
  },
  {
    "start": 1299.88,
    "end": 1301.08,
    "text": "Mathematical maturity."
  },
  {
    "start": 1301.52,
    "end": 1307.66,
    "text": "so you aren't allowed to use the real machinery first?"
  },
  {
    "start": 1307.78,
    "end": 1310.98,
    "text": "You are first needed to do everything by hand and tediously... Exactly!"
  },
  {
    "start": 1311.32,
    "end": 1316.32,
    "text": "And after doing it once you can abstract away from it just use tactics and"
  },
  {
    "start": 1317.68,
    "end": 1318.04,
    "text": "AI."
  },
  {
    "start": 1318.4,
    "end": 1321.2,
    "text": "whatever I see is a Harry Potter approach."
  },
  {
    "start": 1322.96,
    "end": 1329.32,
    "text": "In the beginning you have to learn those basic magic spells, like Wingardium Leviosa or something."
  },
  {
    "start": 1330.32,
    "end": 1335.04,
    "text": "And then later than you can also use more advanced spells."
  },
  {
    "start": 1335.24,
    "end": 1337.36,
    "text": "and what do we have to master?"
  },
  {
    "start": 1337.84,
    "end": 1342.56,
    "text": "is a basic spell before you continue with the Polyjuice potion?"
  },
  {
    "start": 1342.84,
    "end": 1342.92,
    "text": "The"
  },
  {
    "start": 1344.54,
    "end": 1347.2,
    "text": "forbidden spells are equivalent of choice."
  },
  {
    "start": 1350.44,
    "end": 1351.8,
    "text": "They are three forbidden ones, right?"
  },
  {
    "start": 1351.86,
    "end": 1353.4,
    "text": "And they're fathering not to tell you sure."
  },
  {
    "start": 1354.48,
    "end": 1358.76,
    "text": "Yeah yeah that's a good analogy I thought about this year."
  },
  {
    "start": 1358.8,
    "end": 1368.04,
    "text": "You can see it is an interesting approach but i mean there too pass into the future."
  },
  {
    "start": 1368.24,
    "end": 1379.68,
    "text": "Right There one of convincing people and One different schools living next To each other at once gets bigger or not takes over And I think... No,"
  },
  {
    "start": 1380.38,
    "end": 1384.24,
    "text": "as you say there are different ways to look at mathematics."
  },
  {
    "start": 1384.78,
    "end": 1398.12,
    "text": "It's not my goal to turn everybody into a constructivist but what would be nice is have some constructivity awareness in mathematics and that's what it's like."
  },
  {
    "start": 1401.22,
    "end": 1408.8,
    "text": "That how i grew up so I can send regards to my teachers."
  },
  {
    "start": 1411.12,
    "end": 1411.42,
    "text": "great!"
  },
  {
    "start": 1412.4,
    "end": 1414.0,
    "text": "Is there any other point?"
  },
  {
    "start": 1414.32,
    "end": 1415.12,
    "text": "I think about this."
  },
  {
    "start": 1415.5,
    "end": 1421.4,
    "text": "AI, automates what would mean for the mathematical community."
  },
  {
    "start": 1421.54,
    "end": 1424.3,
    "text": "This is another episode which we definitely have."
  },
  {
    "start": 1425.44,
    "end": 1428.0,
    "text": "We should talk about AI and it's old."
  },
  {
    "start": 1429.92,
    "end": 1433.38,
    "text": "Anything else about your teaching approach that you'd love to share?"
  },
  {
    "start": 1436.76,
    "end": 1437.3,
    "text": "It quite fun!"
  },
  {
    "start": 1441.22,
    "end": 1450.92,
    "text": "sessions is very good to false interaction with the students so they are stuck on a problem and then you can help them."
  },
  {
    "start": 1453.06,
    "end": 1471.88,
    "text": "Yeah, I wonder if AI could have negative impact because instead of really getting their head bloody by banging it against something which was quite important They have also this easy way out to ask an AI."
  },
  {
    "start": 1472.64,
    "end": 1475.02,
    "text": "And I don't know how to convince them..."
  },
  {
    "start": 1475.42,
    "end": 1475.9,
    "text": "Yeah,"
  },
  {
    "start": 1477.08,
    "end": 1490.02,
    "text": "not to do that because they should learn how to use the AI but if and how to support learning is actually quite effective."
  },
  {
    "start": 1490.08,
    "end": 1499.78,
    "text": "you can use it as a tutor or understand something You can have a dialogue, you can repeat still."
  },
  {
    "start": 1499.84,
    "end": 1500.6,
    "text": "I don't understand this."
  },
  {
    "start": 1500.66,
    "end": 1504.1,
    "text": "blah-blah-blAH and...and ...you find the dialogue which helps you."
  },
  {
    "start": 1504.62,
    "end": 1522.38,
    "text": "but if you have an exercise like solving a particular problem uh..which is supposed to really get you working and should not be easy And then to choose the easier way out and say okay let's ask the AI here's proof we are done."
  },
  {
    "start": 1523.52,
    "end": 1530.36,
    "text": "That is not helpful and it's difficult in teaching to separate these aspects."
  },
  {
    "start": 1530.4,
    "end": 1533.88,
    "text": "So one is good, the other one is also not"
  },
  {
    "start": 1534.0,
    "end": 1534.38,
    "text": "helpful.\"."
  },
  {
    "start": 1536.08,
    "end": 1540.32,
    "text": "It really a hard task... I mean find a word on that too."
  },
  {
    "start": 1541.04,
    "end": 1543.76,
    "text": "say something about waterproof system as well?"
  },
  {
    "start": 1544.52,
    "end": 1553.32,
    "text": "And it has this tutoring functionalities even there like restricted coding Agents that say you could try this here."
  },
  {
    "start": 1553.42,
    "end": 1557.8,
    "text": "You might get stuck so to have immediate feedback at home all the time."
  },
  {
    "start": 1558.56,
    "end": 1561.52,
    "text": "This may be one major benefit in comparison, too."
  },
  {
    "start": 1561.6,
    "end": 1568.38,
    "text": "The math model where you submit your homework and you forget about them And somebody grades them then forgets about them."
  },
  {
    "start": 1569.04,
    "end": 1569.34,
    "text": "Handsome."
  },
  {
    "start": 1569.38,
    "end": 1590.38,
    "text": "I'm back to you just see oh there's a mistake but Everything is not their anymore while like if you really see your variable was never introduced, then you can might see oh okay I should introduce that variable right away and understand let epsilon be bigger than zero."
  },
  {
    "start": 1590.52,
    "end": 1591.72,
    "text": "does some heavy lifting?"
  },
  {
    "start": 1591.8,
    "end": 1593.06,
    "text": "it's not just there for fun."
  },
  {
    "start": 1594.12,
    "end": 1597.06,
    "text": "Sure but i think we do need the waterproof system here."
  },
  {
    "start": 1597.4,
    "end": 1614.52,
    "text": "use a proof assistant in conjunction with an AI going to a lab or demonstrators as a code."
  },
  {
    "start": 1614.9,
    "end": 1615.3,
    "text": "We"
  },
  {
    "start": 1615.78,
    "end": 1617.16,
    "text": "should don't have them at some point"
  },
  {
    "start": 1618.36,
    "end": 1619.18,
    "text": "because of AI."
  },
  {
    "start": 1620.52,
    "end": 1622.54,
    "text": "No, I think no there is different quality."
  },
  {
    "start": 1622.66,
    "end": 1623.54,
    "text": "you can use both."
  },
  {
    "start": 1623.76,
    "end": 1633.94,
    "text": "i mean sometimes explanation by human and we have some good PhD students who are really good in explaining things."
  },
  {
    "start": 1634.52,
    "end": 1644.32,
    "text": "it can be helpful but on your own, then using an AI is a reasonable replacement for this."
  },
  {
    "start": 1644.38,
    "end": 1649.96,
    "text": "But you shouldn't do one or the other as actually it's a combination which works quite well I think."
  },
  {
    "start": 1652.54,
    "end": 1652.78,
    "text": "Great!"
  },
  {
    "start": 1653.2,
    "end": 1665.54,
    "text": "So that was our third episode of About Logic Premises and next week we will have probably something in the direction of linguistics but i'm not entirely sure yet."
  },
  {
    "start": 1667.9,
    "end": 1673.2,
    "text": "so Record it right after the second episode of premises."
  },
  {
    "start": 1673.34,
    "end": 1680.3,
    "text": "So there is no reason why I don't know yet what happens next week and that's not three weeks in future or whatever."
  },
  {
    "start": 1682.06,
    "end": 1686.9,
    "text": "Okay, okay great then as always you know What do have to do?"
  },
  {
    "start": 1687.54,
    "end": 1690.04,
    "text": "And we will see us next week with our guests."
  },
  {
    "start": 1691.04,
    "end": 1691.22,
    "text": "Bye"
  },
  {
    "start": 1692.42,
    "end": 1693.06,
    "text": "bye."
  }
]