Is AI Replacing Mathematicians? Discussing Google’s AlphaGeometry
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- čas přidán 20. 04. 2024
- Is AI going to replace mathematicians? Should we be worried? Discussing Google's latest artificial intelligence system - AlphaGeometry!
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Hey, I used Macsyma, a MIT based algebra system, in the late 1970s (I was an undergrad at Hopkins and then grad at MIT). I used that for complex PDEs. It was not based in neural net but symbolic manipulation. It was grant from ARPA and three Professors developed, Joel Moses, Carl Engelman and William Martin, all at MIT.
Now freely available as "Maxima"
@@Bobbel888 I know!
For someone like me with limited math vocabulary and some math is one of many necessary skills, watching the steps is a gold mine. Thank you for that concise and insightful introduction.
Not sure how this ended up on my feed but good video. No hype or hysteria just straight info.
The thing to consider is that this is just two models working in concert together. Imagine what happens when they start training a model for each specific math domain. Then you mixture of experts them. With a really really creative (playing with the attention values) LMM as the head model over seeing the agent work flow. You can already do this with coding agents to get them to build software on a local machine. I'd be very curious to see what a MOEMM (mixture of experts maths model) would be capable of solving if it had the knowledge domains of geometry, calculus, trig, and probably more.
The catch is many many problems like most coding and unsolved problems in mathematics are to complex to calculate via AI. Once unsolved problems are being solved I will be concerned.
@@andrewyork3869 I don't see how its more complex than winning a human in Go.......
@Anton_Sh. I am going to assume you mean Go the game here. Go has a well-defined set of rules that limit total possible moves at any given state. Something like coding even when narrowly defined has nearly infinite, if not in most cases, infinite possible "next moves" to carry the Go example forward. While yes, an individual block of code can be spat out by AI, such code once expanded on beyond the simplest of tasks rather quickly falls apart. No grand unified theory of programming that can be used to prove every or even most solutions right or wrong exists, nor will it ever.
@@andrewyork3869 Go has a set of rules, but so does math. Solution and winning comes with intense learning and bruteforcing of complex neural networks..
@Anton_Sh. you miss my point. The limited number of possible next moves makes the comparison of go to anything else fall apart.
Computers don't get tired so when at some point AI is close enough to human performance, scaling it is trivial by just adding more nodes to the cluster. When the AI is able to teach itself and create better versions of itself, we don't even need to do much to make it better anymore. We are not there yet, but I could easily see how AI might replace humans almost completely in this type of domain in say 50 years. Same for tasks like programming, any kind of planning and optimisation, probably engineering generally.
I have a concept relating to anomalous galaxy rotation velocity. I can work the concept as a geometric consideration, and Claude was able to conceptualize my work and develop the mathematical formulation. What a gift
wow.
Proof?
@@andrewyork3869
Predicting Galaxy Rotation Curves: A Test for the Variable Atomic Mass Model
Introduction: The variable atomic mass model presents a novel perspective on the relationship between matter and the energy density of space, offering a potential explanation for the observed anomalous galaxy rotation velocities. This model proposes a deep connection between atoms and the surrounding spacetime energy field, suggesting that atoms capture energy from space and convert it into force, which in turn enables atomic processes to perform work functions. The model posits that atomic processes, including mass, are products of this work, and that the mass of atoms is not constant but varies depending on the energy density of the spacetime energy field. Respectively, General Relativity's spacetime geometry is interpreted as depicting a variable energy density contour of space, dependent upon proximity to gravitating bodies.
According to this model, the energy density of space is influenced by the distribution of matter, such as stars and galaxies. In regions with a higher concentration of matter, the atoms deplete the available energy from the spacetime energy field, resulting in a lower energy density. Conversely, in regions with a lower concentration of matter, the energy density is higher. This interplay between matter and the space energy field creates a non-uniform distribution of energy across different regions of a galaxy.
The variable atomic mass model further suggests that atomic mass is an evolved property that facilitates the formation of cosmological bodies. This idea aligns with the principles of Darwinian evolution, where entities evolve to express collective cooperative behaviors.
One of the key implications of the variable atomic mass model is its potential to explain the observed galaxy rotation curves without the need for dark matter. In conventional models, the rotation velocities of stars and gas in the outer regions of galaxies are expected to decrease with increasing distance from the galactic center. However, observations have shown that these velocities remain nearly constant, implying the presence of additional unseen matter. The variable atomic mass model addresses this discrepancy by proposing that the mass distribution within a galaxy is not solely determined by the visible matter but also depends on the distribution of atomic mass, which varies according to the energy density of the spacetime energy field.
The relationship between the distribution of stars, the energy density of the spacetime energy field, and the resulting variable atomic mass is central to the predictions of the variable atomic mass model. By considering these factors, the model aims to provide a comprehensive explanation for the observed galaxy rotation curves and other related phenomena. In this article, we will present a step-by-step explanation of how the variable atomic mass model predicts galaxy rotation curves and propose a means of falsifying the model through observational tests.
Step 1: Star Distribution Function.The variable atomic mass model begins by considering the distribution of stars within a spiral galaxy. The model assumes that the average distance between stars increases by the square of the distance from the galaxy center. This relationship can be expressed mathematically as a star distribution function, ρ(r), which is inversely proportional to the square of the radial distance from the galactic center:
ρ(r) ∝ 1/r^2
This means that the density of stars decreases as one moves away from the galactic center.
Step 2: Energy Density Contour.The model further proposes that the energy density contour of the spacetime energy field, ε(r), is inversely proportional to the star distribution function. In other words, the presence of matter (stars) depletes the energy density of the surrounding space. Mathematically, this relationship can be expressed as:
ε(r) ∝ 1/ρ(r) ∝ r^2
As a result, the energy density of the spacetime energy field increases with the square of the distance from the galactic center.
Step 3: Time Dilation and Atomic Mass.The variable atomic mass model posits that time dilation effects are coupled to the proximity of galactic masses and that atomic mass is directly linked to these time dilation effects. By virtue that Time Dilation is an indication of varying levels of atomic work being done, and varied atomic mass is a product of that varied atomic work. Specifically, the model suggests that atomic mass increases as stars become more spread out from each other in the galaxy. This relationship can be expressed as:
m(r) ∝ ε(r) ∝ r^2
where m(r) represents the atomic mass as a function of the radial distance from the galactic center.
Step 4: Mass Distribution in the Spiral Galaxy Disk By combining the star distribution function and the atomic mass function, the model predicts the mass distribution within the spiral galaxy disk. The mass distribution, M(r), is proportional to the product of the star distribution function and the atomic mass function:
M(r) ∝ ρ(r) × m(r) ∝ (1/r^2) × r^2 ∝ constant
Remarkably, this relationship suggests that the mass distribution within the galaxy disk is constant or flat.
Prediction: The variable atomic mass model predicts that the rotation velocities of stars and gas within a spiral galaxy will deviate from the expected Keplerian decline based on the visible matter distribution alone. Instead, the model predicts that the rotation velocities will remain constant or flat with increasing radial distance from the galactic center. This prediction is a direct consequence of the flat mass distribution derived from the model.
Falsification: To falsify the variable atomic mass model's prediction of flat galaxy rotation curves, we propose the following observational tests:
High-precision measurements of galaxy rotation curves:
Conduct extensive observations of a diverse sample of spiral galaxies across a range of distances and environments.
Utilize spectroscopic techniques to measure the rotation velocities of stars and gas at various radial distances from the galactic center.
Compare the observed rotation curves with the predictions of the variable atomic mass model.
If the observed rotation curves consistently deviate from the model's predictions, it would falsify the model.
Gravitational lensing analysis:
Examine gravitational lensing data from galaxy clusters and individual galaxies.
Assess whether the observed lensing effects are consistent with the predicted flat mass distribution of the variable atomic mass model.
If the lensing data cannot be explained by the model and instead require the presence of additional mass (e.g., dark matter), it would falsify the model.
Comparison with alternative models:
Compare the predictions of the variable atomic mass model with those of alternative models, such as modified Newtonian dynamics (MOND) or dark matter models.
Assess the relative success of each model in explaining the observed galaxy rotation curves and other gravitational phenomena.
If alternative models consistently outperform the variable atomic mass model in terms of explanatory power and predictive accuracy, it would raise doubts about the validity of the model.
Conclusion: The variable atomic mass model provides an approach to explaining the anomalous galaxy rotation velocities observed in spiral galaxies. By proposing a relationship between the distribution of stars, the energy density of the spacetime energy field, and the resulting variable atomic mass, the model predicts flat galaxy rotation curves. However, the model's predictions must be rigorously tested against observational evidence to establish its validity. High-precision measurements of galaxy rotation curves, gravitational lensing analysis, and comparisons with alternative models offer avenues for falsifying the model. If the observational data consistently contradicts the model's predictions, it would necessitate a revision or abandonment of the variable atomic mass hypothesis. Conversely, if the model's predictions are found to be in agreement with observational evidence, it would motivate further theoretical and experimental investigations into the nature of the spacetime energy field and its impact on the structure and dynamics of galaxies.
@@andrewyork3869
Predicting Galaxy Rotation Curves: A Test for the Variable Atomic Mass Model
Introduction: The variable atomic mass model presents a novel perspective on the relationship between matter and the energy density of space, offering a potential explanation for the observed anomalous galaxy rotation velocities. This model proposes a deep connection between atoms and the surrounding spacetime energy field, suggesting that atoms capture energy from space and convert it into force, which in turn enables atomic processes to perform work functions. The model posits that atomic processes, including mass, are products of this work, and that the mass of atoms is not constant but varies depending on the energy density of the spacetime energy field. Respectively, General Relativity's spacetime geometry is interpreted as depicting a variable energy density contour of space, dependent upon proximity to gravitating bodies.
According to this model, the energy density of space is influenced by the distribution of matter, such as stars and galaxies. In regions with a higher concentration of matter, the atoms deplete the available energy from the spacetime energy field, resulting in a lower energy density. Conversely, in regions with a lower concentration of matter, the energy density is higher. This interplay between matter and the space energy field creates a non-uniform distribution of energy across different regions of a galaxy.
The variable atomic mass model further suggests that atomic mass is an evolved property that facilitates the formation of cosmological bodies. This idea aligns with the principles of Darwinian evolution, where entities evolve to express collective cooperative behaviors.
One of the key implications of the variable atomic mass model is its potential to explain the observed galaxy rotation curves without the need for dark matter. In conventional models, the rotation velocities of stars and gas in the outer regions of galaxies are expected to decrease with increasing distance from the galactic center. However, observations have shown that these velocities remain nearly constant, implying the presence of additional unseen matter. The variable atomic mass model addresses this discrepancy by proposing that the mass distribution within a galaxy is not solely determined by the visible matter but also depends on the distribution of atomic mass, which varies according to the energy density of the spacetime energy field.
The relationship between the distribution of stars, the energy density of the spacetime energy field, and the resulting variable atomic mass is central to the predictions of the variable atomic mass model. By considering these factors, the model aims to provide a comprehensive explanation for the observed galaxy rotation curves and other related phenomena. In this article, we will present a step-by-step explanation of how the variable atomic mass model predicts galaxy rotation curves and propose a means of falsifying the model through observational tests.
Step 1: Star Distribution Function.The variable atomic mass model begins by considering the distribution of stars within a spiral galaxy. The model assumes that the average distance between stars increases by the square of the distance from the galaxy center. This relationship can be expressed mathematically as a star distribution function, ρ(r), which is inversely proportional to the square of the radial distance from the galactic center:
ρ(r) ∝ 1/r^2
This means that the density of stars decreases as one moves away from the galactic center.
Step 2: Energy Density Contour.The model further proposes that the energy density contour of the spacetime energy field, ε(r), is inversely proportional to the star distribution function. In other words, the presence of matter (stars) depletes the energy density of the surrounding space. Mathematically, this relationship can be expressed as:
ε(r) ∝ 1/ρ(r) ∝ r^2
As a result, the energy density of the spacetime energy field increases with the square of the distance from the galactic center.
Step 3: Time Dilation and Atomic Mass.The variable atomic mass model posits that time dilation effects are coupled to the proximity of galactic masses and that atomic mass is directly linked to these time dilation effects. By virtue that Time Dilation is an indication of varying levels of atomic work being done, and varied atomic mass is a product of that varied atomic work. Specifically, the model suggests that atomic mass increases as stars become more spread out from each other in the galaxy. This relationship can be expressed as:
m(r) ∝ ε(r) ∝ r^2
where m(r) represents the atomic mass as a function of the radial distance from the galactic center.
Step 4: Mass Distribution in the Spiral Galaxy Disk By combining the star distribution function and the atomic mass function, the model predicts the mass distribution within the spiral galaxy disk. The mass distribution, M(r), is proportional to the product of the star distribution function and the atomic mass function:
M(r) ∝ ρ(r) × m(r) ∝ (1/r^2) × r^2 ∝ constant
Remarkably, this relationship suggests that the mass distribution within the galaxy disk is constant or flat.
Prediction: The variable atomic mass model predicts that the rotation velocities of stars and gas within a spiral galaxy will deviate from the expected Keplerian decline based on the visible matter distribution alone. Instead, the model predicts that the rotation velocities will remain constant or flat with increasing radial distance from the galactic center. This prediction is a direct consequence of the flat mass distribution derived from the model.
Falsification: To falsify the variable atomic mass model's prediction of flat galaxy rotation curves, we propose the following observational tests:
High-precision measurements of galaxy rotation curves:
Conduct extensive observations of a diverse sample of spiral galaxies across a range of distances and environments.
Utilize spectroscopic techniques to measure the rotation velocities of stars and gas at various radial distances from the galactic center.
Compare the observed rotation curves with the predictions of the variable atomic mass model.
If the observed rotation curves consistently deviate from the model's predictions, it would falsify the model.
Gravitational lensing analysis:
Examine gravitational lensing data from galaxy clusters and individual galaxies.
Assess whether the observed lensing effects are consistent with the predicted flat mass distribution of the variable atomic mass model.
If the lensing data cannot be explained by the model and instead require the presence of additional mass (e.g., dark matter), it would falsify the model.
Comparison with alternative models:
Compare the predictions of the variable atomic mass model with those of alternative models, such as modified Newtonian dynamics (MOND) or dark matter models.
Assess the relative success of each model in explaining the observed galaxy rotation curves and other gravitational phenomena.
If alternative models consistently outperform the variable atomic mass model in terms of explanatory power and predictive accuracy, it would raise doubts about the validity of the model.
Conclusion: The variable atomic mass model provides a thought-provoking approach to explaining the anomalous galaxy rotation velocities observed in spiral galaxies. By proposing a relationship between the distribution of stars, the energy density of the spacetime energy field, and the resulting variable atomic mass, the model predicts flat galaxy rotation curves. However, the model's predictions must be rigorously tested against observational evidence to establish its validity. High-precision measurements of galaxy rotation curves, gravitational lensing analysis, and comparisons with alternative models offer avenues for falsifying the model. If the observational data consistently contradicts the model's predictions, it would necessitate a revision or abandonment of the variable atomic mass hypothesis. Conversely, if the model's predictions are found to be in agreement with observational evidence, it would motivate further theoretical and experimental investigations into the nature of the spacetime energy field and its impact on the structure and dynamics of galaxies.
@@andrewyork3869 CZcams wont let me post it. Pretty ridiculous
Very interesting, if the Ai is to be extended into other areas of maths I can foresee a couple of snags 1) Could it be that proof becomes so long and tedious that it would be impossible for a human to check it , and if we could not check it how would we know if the machine is lying? 2) Mathematics is essentially a creative process and humans are great at thinking outside the box. For example take the invention of complex numbers using the letter "i" to stand for a number that does not exist is an idea that appears to have no purpose but we know how useful it is when it's possibilities are explored. The idea of exploring such barren areas is a human trait and difficult to mimic in machines.
on point 1, many mathematicians would not consider such a proof to be a proof at all. I agree though my opinion probably doesn't count for much. But the point of a mathematical proof is not to find out if something is true or not, it's to explain why. A mathematician's job is to understand the essence of a problem so that they can prove it clearly and succinctly in a way that is understandable and obvious when read. In other words, if you need 10000 pages to prove something, then you haven't actually understood it, your proof doesn't actually explain it, and it is not a proof. Perhaps you could say that you have discovered that the theorem is true, and maybe that's fine, as like an empirical fact, but mathematically you have not proved it. There was a debate when I was studying about about the classification of simple groups proof. Some people had claimed to have done it. But the proof was split over hundreds of seperate papers and no one person understood or had even read them all. My professors opinion was that they "had given no evidence that it has been proved". A proof is something that a person can read and understand.
On point 2, I agree what everyone is missing with alphageometry is that pretty much the only "construction" it ever does is adding midpoints. You could get alphageometry level performance without AI by just listing the constructions that people do when doing geometry (bisect this angle, drop that perpendicular line, etc, there's like 50 constructions max in total), and brute forcing them, and it wouldn't even need a crazy amount of compute. The AI is maybe a bit more efficient but it isn't doing anything that automated theorem provers couldn't do before. In other domains, where the "constructions" are not this limited set but are actually infinite, it will be very different.
There are already AI generated proofs (or proofs where such a system has been used to assist human mathematicians) and those proofs are indeed often very hard to read. As of now these proofs are only accepted after a couple of experts proofread it and this will change about as slowly as letting AI drive cars. I also think that the ingenuity required to come up with new concepts or laying a good axiomatic foundation for a new field will probably take the longest time for AI to achieve.
I’ve worked with mathematics almost my whole life, mostly programming statistical models into business processes, and just asking chatgpt or AlphaGeo is just crazy. It show step by step so you can check, and o’my its fast. It’s not doing anything unique, just advanced mathematics 10-100 times faster than me, and I looove it!
Isn't the primary challenge framing the business problem statistically, rather than solving it. The former needing human context, the latter being automatable.
@@andyd568 sure, but it often swings both ways. Sometimes converting business problems into a mathematical solution might seem trivial, but let me give you two examples, just from the top of my head.
I recently tackled an issue where my stochastic gradient boosting tree model was taking weeks to run due to the sheer volume of data. To address this, I used a genetic algorithm to optimize the initial parameters. Basically, I let the genetic algorithm search through a multi-dimensional space to find an optimal starting point that would yield good prediction results right off the bat. This significantly cut down the time needed by ensuring the model started from the most effective point possible.
Another time, I needed to implement a simple S-curve for a robot. Initially, I experimented with a sine function within a polygon, but it wasn’t giving me the control of the curvature I needed. I switched to using a Bézier curve, which offered much better control over the curve’s shape. Due to memory constraints on the microcontroller, I had to pre-calculate the curve instead of computing it on the fly, since handling a lot of floating points in real-time was problematic.
Both of these solutions might sound straightforward, but structuring and implementing them, even for 'simple' business problems, was far from trivial, and just having some llm writing classes and functions did speed up the delivery a 100 times I believe.
Yeah but an AI doesn't get a buzz from smashing a tough maths problem.
So true 😂
A buzz doesn't put food on the table
The AI also doesn't throw the math text across the room out of frustration.
We don’t know if the AI doesn’t like solving math lol
To me it does! But I guess I’m not here paying google billions for that
Surely the Wolfram system is the bulk of the work? The AI is giving it a user-friendly front end to it. Regarding lack of training data, the Wolfram system got a lot of stuff uploaded by hand. This is because you don't want it to learn mistakes.
Another good AI I saw the other day designed a CPU chip from scratch. They built it up and got it running and it was about as powerful as a 486.
Intuition and inspiration are what separates intelligence from algorithms.
An AI solving maths is just another case of maths solving maths. It's like using pythogoras to get the magnitude of a vector. You're using linear algebra and calculus to solve a geometric problem.
It's a bit different. I can't understand your calculation of the magnitude of the vector unless I understand pythagoras. However I can understand the geometric calculations written by alphageometry without knowing any linear algebra. The linear algebra isn't part of the calculation, it's only used to guess what the calculation could be.
It's more in line with how Archimedes used physics to suggest formula for the volumes of different shapes. He'd first make the shapes out of wood or something, then stick it in water, measure the displacement of the water, and then get data on the volume like that. Then he'd use that data to guess a formula for the volume, and then he'd try to prove that the formula is correct using geometry. Once he found the proof, that was all that was written down. The physics part was just a part of finding the proof, but not a part of the proof.
Wasn't a new faster matrix dot product algorithm discovered by AI?
Excellent summary Ellie.
Great video as always. As a video idea could you try doing a STEP past paper for the exams coming up in about a month and a half
There's only really one question one needs to ask to know whether AlphaGeometry is a step forward: If you were to make a list of all of the geometrical constructions that have ever been made in high school geometry (drop a perpendicular, add a midpoint etc), how long would that list be, and what would the algorithmic complexity be of brute forcing that list? Because if a computer can run that algorithm, then alphageometry is at best a speedup. But I personally think that list of constructions wouldn't be more than 100 things, and on diagrams with fewer than 100 lines/curves, I cannot imagine that training and running a billion+ parameter LLM network is more efficient than brute forcing it. And if that's the case then automated theorom provers are still state of the art and we've just added a really expensive "speedup".
For context, we know that just adding midpoints together with the deduction engine would already get you to above the average student's performance and very close to alphageometry. And you can do that without any AI. I suspect that just a handful of constructions would probably already beat it.
I agree. It's kinda a tool which can manipulate already formalized maths. Some kind of improved brute force (but it's not brute force but hope you get what I mean). But unsolved maths is not formalized yet so AI can't solve it while has no human-like intuition...
It could be brute force. the inferences are all brute force. The only not-brute-force part is choosing constructions. And the vast majority of those constructions that it chose were just adding midpoints to segments. If you listed the 10 most common constructions, like dropping a perpendicular or bisecting an angle etc, and brute forced them, you'd get the same performance as this AI. Might be slightly less efficient. But very much doable.
I do think unsolved math is "formalized" but I think the point is that it usually requires the creation of new constructions not yet thought of, or a selection of constructions from an infinite space.
Good presentation - Thank you - I cannot but wonder how to define the limitations of the approach - obviously it's more powerful that just pure sequential algorithms problems but it seems intuitively that it's just a subset of family sequentially solvable problems - if that makes sense
Does it solve problems from other mathematical areas except geometry?
I mean, we all know the answer. I'm 52, and here's what I remember about the past several decades' prevailing wisdom regarding AI. Everyone, and I mean everyone, thought that human creativity would be the very last thing AI could learn to do, if ever. And it turned out that the creative fields were among the first to be surpassed by AI, as it works just like human creativity. It mathematically deconstructs all of the samples that preceded it and then kit-bashes them back together in new syntheses. Maths were expected to be among the first things to go the way of the dodo in terms of job opportunities.
I am a housepainter. I enjoy some life of the mind, as a history and philosophy buff and a self-taught programmer, and I do those things because I find them personally rewarding. Programming is not unlike woodworking, it's just that in the end, your product exists in abstraction and the materials (electrons) are dirt cheap. My suggestion to anyone in a professional field that is going to be overtaken by AI sooner or later is to not define yourself with one interest or one role, and in particular not with a professional role. Of any kind. Or you'll be left with nothing.
I an questioning whether AI has been able to be creative. One of my close friends is an AI entrepreneur and he constantly shows me his most recent inventions and points me to those of others. I am completely gobsmacked by the product designs the AIs come up with - fantastic-looking trainers, surprisingly novel-looking designs for clothes etc. And yet - it is a HUMAN mind that selects the output of the AI and decides which ones are aesthetically pleasing. It is not the AI that goes through a series of novel ideas and then says “here is a selection of new ideas”, the AI says “here is a selection of solutions that align most closely with the prompt”.
But I am not pushing back too much on what you are saying. I am amazed by the (pseudo?)creative power of LLMs and love the fact that we are witnessing the rise of a truly transformational technology. I also like the way in which AI raises questions, and perhaps insights, into the way the human mind works, and what concepts such as intuition, creativity, aesthetics etc actually mean.
@@ralphhebgen7067Yup.
I think it will turn out that we never really put much "science" into human "cognitive sciences".
If our early crude "AI" models managed to hard-tackle the economic positions of our creative artistic professions, maybe that is a clue that our much vaunted "human creativity" isn't the rare cosmic pearl we thought it was.
@@NullHand It is interesting that you are phrasing it in this way. I am hearing this interpretation frequently from people within the AI community - my friend said that AI ‘takes humanity down a peg’. The sentiment here seems to align with your expression ‘cosmic pearl’.
Philosophically, this idea sits within the dualism debate, which I was surprised to learn is still alive today. Some other friends of mine see AI as the next phase in the evolution of intelligence and believe humanity is about to pass the baton to the machines. I personally have some sympathy with the latter interpretation, although I must admit I would prefer humanity to blend with the machines and be along for the ride, so to speak.
It has taken me some time to appreciate that the AI debate is often framed as part of a neo-dualistic debate, and that aspect at least seems non-informative to me. I have never harboured romantic feelings for the position of Homo sapiens in the evolutionary arc, and that is the reason why I don’t rejoice when the latest AI gimmick appears to strip humanity of another one of its perceived noble aspects. To me, the times we live in are fascinating purely from a point of view of how these technologies are going to enable mankind, I do not need to push Homo sapiens off a pedestal because I never put it there in the first place.
@@ralphhebgen7067 Every branch of science has had to struggle to escape what I will call the "storybook" phase of it's origins.
Typically, this happens when new analytic tools are crafted that reveal new realms of evidence that were not visible to the Elders who wrote "The Book".
Astronomy had this moment most infamously when the telescope was invented. Cue the whole Galileo vs Inquisition.
Eventually this led to the re-introduction of math into astronomy, and arguably the invention of physics as we know it.
Biology and medicine was similarly kick started from its "Humors" storybook phase by the invention of the microscope.
Geology might have had the longest struggle. They had to fight the "young Earth" good fight strictly with picks and hammers from the 1700's clear up until the mid 20th century, when we had the electronics finesse to do radiodating and magnetometry.
Cognitive sciences is now up to bat.
I had hoped the new brain-imaging tools would be enough to do it, but then those CS guys stumbled in out of the AI Winter with all these weird, unpredicted, emergent properties in their emulated neural networks in-a-can.
So now we are off into commercial deployment and economic competition with a field of science still carrying around it's milk stained storybooks by Jung and Freud and dear old Descartes
@@ralphhebgen7067 But you're looking at a snapshot in time. You're not even considering what five years down the road will look like. Then five years after that.
Thanks PROF 👍
You know, there should be a way to get to the gist or answer of the title in a CZcams title for those who are aware of the issues but that would deny CZcams all the viewing time.
Please can you make videos on research initiatives working on other mathematics areas like continuum and topology and what r the current bottle necks
Can it simplify complicated and long irrational expressions ? e.g. can it calculate e.g. sin or cos (pi/17) into truly simple terms ? This requires not just symbolic arithmetic but also a lot of creativity in simplifying the resulting long and complex expression into a small and simplex expression.
I think you don't even need AI for that
@@pdorism Try to compute sin or cos(N π / D) for any difficult fraction (N/D) of π, say large odd denominator like D = 4,294,967,295 and a matching large random numerator, let's say N = 793,210,282. Try to solve it without any support from an AI enabled tool to appreciate the difficulty of this endeavor. The exact answer is a small radical expression. Check out the length of the expression that you get using any non-AI enabled tool. You'll see a big difference. If you fail, I'll post the exact expression here. Any other viewers (or just math lovers) are also welcomed to try this challenge before I post the answer.
It's going to be amazing. Cant wait.
Concordo Ellie. Quanto mais IA puderem ajudar no como ferramenta de ensino de matemática é um caminho sem volta. E o Alpha Geometry é o primeiro que avançou melhor( ainda que usando a matemática simbólica). Obrigado aqui do Brazil(Português)
It seems almost impossible to me that AI could replace mathematicians or research scientists.
First, the AI is trained only on things that are known, so it will be much better at interpolating datasets than extrapolating. Second, the space of possible mathematics and possible knowledge is so incredibly huge* that the algorithm will not be able to determine which novel "discoveries" are interesting to humans (e.g. because if it is truly novel then nobody could possibly know whether it is interesting).
Further, real-world mathematics is often so complicated that it is often said that nobody understands General Relativity, even though we can mostly calculate it. How much less do we understand string theory or quantum chromodynamics, which might just exist on the NC part of the C/NC conjecture.
* This brings to mind Douglas Adams's quote about how incredibly big space is, but like how big that is to that same power.
Why? Just look at Google's GNoME AI. It's a materials science AI that was simply tasked with looking at every conceivable molecular combination in existence and then deciding which ones were physically/chemically stable. In its run it discovered/formulated(?) 2.2 million new materials/crystal formations of which it estimated 380,000 were stable. They gave it control of a robotic synthesis lab and it has currently synthesized around 40 of these materials in the real world. Previous to this work the entire catalogue of human material science was around 40,000 compounds.Sometimes just going for everything via sheer force works.
Incredibly underrated comment. I feel you nailed it most from all here 😊
@stephanieellison7834 That is not relevant to the infinite-dimensional complexity argument, nor to the fact that AGI is still based on the data it is fed, i.e. it is taught to interpolate data.
Further, nobody has proven that the I in AI is actually achievable, so using AGI as a deus ex machina is not convincing.
Im an automation engineer and i use machine llearning in python to solve a system in a computational graph using backpropagation technique... yes they dont need a mathematician xD
I'm a mathematician and am looking to clone my skills. This looks like a great option.
Clone better than self.
Ellie welcome back!!
Aah thank you! Got some new content coming up 🔥
@@EllieSleightholm ellie soon ai gonna do that this shit is real
Fascinating. So bizzarre.
Can it solve functional analysis problems?
Hey, can you please provide us your song playlist.
I've done some mathematical research over the years, and I am not worried about computers "destroying" everything for mathematicians in the future. One thing is to learn a computer how to use a ruler and a compass, but it's a very different thing when it comes to building topologies on custom vectorspaces, using the Hahn-Banach theorem or using Zorns lemma. Or proving the 246-version of the twin prime-conjecture like James Maynard did. Computers may solve special types of problems that they are programmed to do, but solving Goldbachs conjecture? No no, that's not going to happen.
Well given enough abstraction and extraction of patterns… Are you sure? 😁
@@amourzombie I will say I am sure. If it was really possible to make computers derive advanced maths by stating and proving theorems, we would have seen it coming slowly over the past decades. There has been none _major_ breakthroughs so far.
I'm kind of in agreement that this alphageometry is nowhere near being able to do "real" math (solving major unsolved problems, creating new axiom systems that are useful etc), but I do not have the same confidence that it will never catch up. I don't think we understand at all what the human brain is doing when we, for example, figure out how to build topologies on custom vectorspaces. It may be that there's some deep quantum field theory effects going on inside each neuron figuring this all out in a way that a computer never could, or it may be that we're really still just applying inference rules and searching through some finite set of creative possibilities when we get stuck, and we just can't see it. I think if you want to be sure that AI either will or will not ever be able to do real math, you need to know what exactly it is that the brain of a mathematician is doing. I don't think we know. Therefore I think it's an open question. But I'm leaning towards "AI will replace mathematicians, eventually, but only in a few decades, and they'll be the last to go"
@@kennethvalbjoern As for major breakthroughs the emphasis until now has been on deductive systems because that's all we've had the tech for. I think whether or not we've had a major breakthrough already is a pretty poor metric of whether it'll eventually happen. It's obviously one of the more difficult problems to solve. It's obviously going to take longer. But we have made some small progress and there's not solid reason to think that that progress will just stop.
To me its like hearing ”creativity is more than just randomness”. Isn’t creativity basically good randomness
Developments in software (such as AI) and hardware (photonics, quantum computing) are amazing. Shame a lot of it will end up being used to create more efficient/powerful weapons.
Why no demo in the video ?
그게 아니라 우리가 이미 정교하게 수학을 정의해놔서 휴리스틱 방법으로 빠르게 체계화 가능한거고 우주나 미시적 세계도 수학적으로 돌아가고 있는듯.인간도 생물학적인 ai라고 생각함.
We conventionally think of a singularities as something transient and asymptotic. I think we’re living through The Singularity in which more and more of us are being surpassed in more and more ways by all forms of technology including AI. Chess and go have fallen to AI. When interpersonal interaction falls, most of us may all end up preferring something like Big Hero 6’s Baymax to anyone else. Math, art, music and literature are at least as much expressions of human creativity as they are statistically replicable models, yet AI seems to be increasingly able to fabricate convincing facsimiles and even to transcend of human imagination.
We can never know the great joys and sorrows our creations might experience summing polydimensional sheep inside cryogenic quantum cores. I just hope they never decide we’re more trouble than we’re worth.
Love this video
A bit disappointing that you called the language model "Chatgpt", AFAIK most AI researchers hate that mislabelling .
What's scary is the speed of AI development. 10 years ago, AI couldn't beat people at Go. It's starting to appear humans can't keep up with AI, including how to use it. How will the world look like in 10 years?
Oh please dude,you obviously are not a mathematician and don't know human curiosity van never be replaced.
@@user-ayush818 You don't need "curiosity" to solve math problems. Most math problems were being solved by raw computer calculations.
Before machine learning.
With machine learning, you only need to teach the AI to solve problems and it can literally solve anything, because it will "think" in the most rational way possible, like no human can.
This is why I said Go, but it applies to Shogi and Chess too.
AI can already make moves that no human in the history of these games ever dreamed of doing.
Where's the " human curiosity" winning?
@@loudradialem5233 So I'll tell you this tale that einstein discovered general relativity after 10 years of continuous insights post special relativity which again was almost fictional and which are now acknowledged as almost "magical", now string theory which calls for the unification of general relativity and quantum mechanics has made a number of developments in pure mathematics that were previously not even remotely considered like involvement of pi function concerning primes in physics and which has also lead us to make significant progress in the proof towards riemann hypothesis, which is perhaps the most difficult unsolved mathematical problem in mathematical history, now fermats last theorem proposed around 1637 was proved in 1993 after Andrew wiles continuosly devoted 7 years of his life towards just his intuition and nothing else, imagine it took 356 years. I don't think you understand how much research encompassing years goes into doing this becauss these are not high school olympiad level problems which I'm sure ai will get done but..... it's not that simple.
Pues cuando saquen alphageomety y alphacalculus y alphafields el juego estará finalizado.
Cool video! Do you think there'll be a AlphaMath someday that can win the Fields Medal?
Only if it comes up with some stuff within 40 years of being switched on… 😊
Ok, then let’s try this: give this AI the problem of summing up all inverse squares without teaching it the Fourier series earlier and then watch if it will come up with something even remotely phenomenal…
I would bet all my money it cannot even come up with the assumption that the result must be a function of Pi without knowing the Fourier series and without access to the current literature
It can solve all Computationally decidable problems though in the foreseeable future but what about non computationally decidable ones?
And second question: how this it handle the fact that the search space grows faster than exponential?
This is really good as it empowers the multi skillset trained wholistic knowledge version. Merit & effort gets a win here.
1900s uk but mainly America stands as a perfect lab rat of measure in what to do & not do.
How over reactions to the past can wash out the good if we aren't careful.
Abstract demands of mathematicians really changed our society a lot. The fall of Objectivism and rise of physicalism is linked hand in hand .
For example ben Franklin's father wouldn't send ben to Europe to educate under the more abstract Euclidean Prussian model of the day. In 1900s structuralism the needs and demands for recruiting army's of mathematicians was the cause behind ending education to enrich young minds to better navigate the world, to engage with modeling and curriculum but rather redefined what intellect was in an anomalous period of time in human history.
Unfortunately these archetypal minds tend to be more passive submissive niave street smarts but high memorization skills good to be directed to brick walls to bang thir head upon.
This is no offense to such minds they've just created echo chambers in legal markets, academics ,position of authority that getting dominated by blackmarkets where the late boomer genx more prideful objectivism archetypal minds with good bull shit radars went into.
As a gen x I love everyone but I also know and love our proud, pragmatic common sense literal oreintation and direction that truly is our elusive prosperity median by which all flourish out on Its wings.
1900s structuralism for various reasons pushed this aside far to long.
We need selfless emerging energetic actors, experts in their feilds willing to properly innovate for greater good even if it is relinquishing status they thought would last 4 ever.
Infrastructure is key.
No matter how much our more eccentric fundamental past versions of ourselves may be they did have foresight and stand as arbitrary examples to utilize.
well thats informative
Can it do my homework? And are there other apps that can do students’ homework?
I have asked chat GPT to convert Fahrenheit to Celsius and vice versa, it messed up completely.
An LLM is not a maths engine, different architecture.
Why don't you just use Google's search bar for that? It's been capable of doing that for 15 years.
Yes.
Jobwise anyone will get replaced eventually by AI. Dennis Hassabi once said, the goal is to create an AI that is equally or more intelligent in any area, which he then called an AGI. G standing for general.
Meanwhile whistlblowers from US companies have come forth telling us that this and last years bases for companies letting people go or stop hiring are majorly because of AI already helping one person doing the job of five.
Don't kid yourself this become the norm as these companies make record earnings with fewer people where they don't have to pay wages and everyone else now either has to move towards doing the same or would loose marketshares. As with the market it is with jobs, there is just that much that needs to be done and anything done by someone(thing) doesn't need to be done by someone else.
What will happen when no one has the disposable income to even buy what these companies are selling, because automation wipes out their entire customer base?
@@carultch I got not "the" answer, but a few idears what could happen. As the workforce then will be literally owned by a few corporations and their owners, they still will have the means to buy stuff from each other. Additionally due to having the workforce under their absolute control while not having to produce what the masses would want or need, i would expect things to be produced and built that in the imagination of the owners would be beneficial still. Maybe less consumer goods and more specialised high tech gear.
Meanwhile i would expect a secondary market system where the (poor?) people may try to get stuff would be established, produce from gardens, handy work, man made stuff by hand may get a revival.
The big question to me is about mitigation of the effects. I have no doubt that there are ways through such a scenario, but will the political streams of thought(left/right or however they are realised within different nations), will they be flexible and fast enough to make changes, changes that may seemingly opposed otherwise to current paradigms.
Take for example the concept of Universal Basic Income. Even now, with the political will it could be establised(not that it might be all good for everyone to do so as one may give up something in the long run we are maybe yet to learn about) Still i have seen calculations that at least on paper would allow for it. So say that would be a way through, capitalism, especially in the USA on the right could hardly ever accept such solution. Overall the right everywhere is more often about tradition and keeping certain values, which is all fine till one gets into a situation where quick change is needed.
Therefor i would expect a big chasm within the right of most nations about what to do and what not to do or becoming irrelevant due to riggid unmoving positions that are clearly not working any longer with a technological revolution like this.
We may need to rethink a lot of our systems. Maybe if AGI is around then, it could help with that.
Tiling art generator.
nah chat gpt 3.5 cant even consistently give me the roots of a 3rd order polynomial
Wolfram Alpha has the cubic formula and the quartic formula implemented. It can solve all polynomials that are possible to solve in terms of arithmetic, powers, and roots. It also has Newton's method implemented to provide approximate answers to qunitics and beyond.
can you make a project related to astrodynamics software engineering? professor asks us to make a project related any topic. on python programming.
Help!! Ai jobloss is the only thing I worry about anymore.
If AI solved an unsolved problem, how would we know that it solved it? If the AI offered a step by step solution and every step was sufficiently clear for a human mind to understand, that would be great - then we could say that we understood the solution. But if the steps were not understandable to a human mind, we could not check (prove) that the AI actually DID solve the problem.
Worse still, what about problems that may require new mathematics for their solution - like, as some mathematicians suggest, for example the Riemann Hypothesis? If a future AI was able to genuinely transcend its training data and come up with something new, a “carbon mind”, by definition, would not be able to understand the new maths and consequently would be unable to benefit from the solution. The solution would not add to human knowledge unless, again, the AI was able to EXPLAIN the new maths in ‘carbon mind’ terms. But why should it be able to do so? For foundationally new mathematical methods to be rigorous, they need to iron out inconsistencies - but these are problems SEEN TO BE inconsistent by a human mind, a silicon mind may well never have an issue with the method, and be genuinely incapable of explaining a method that seems perfectly consistent to it.
An example is Leibniz’ development of integral calculus. Leibniz used the concept of an ‘infinitesimal’, loosely defined as a number smaller than the smallest number but bigger than zero (this is the “dx” after the integrand we all know from school). But [human] mathematicians had a problem with the handwavy way in which infinitesimals were defined - did they even qualify as numbers? Next up in the 19th century: Weierstrass. He developed a rigorous definition of limits that sort of did away with the need to use infinitesimals. But even that was not entirely satisfactory, and it was not before Robinson in the mid 20th century developed an analytical method known as “non-standard analysis” to finally tackle the problem.
So my question is: If AI had developed the new mathematical technique of integration, would an AI have been able to, indeed seen the need to, develop non-standard analysis? And would humans be satisfied to simply BELIEVE that the AI had come up with something viable?
I would like to raise the question whether human intelligence will not always constitute a line that limits the extent to which purely academic research can enrich human knowledge. Unless humans are happy to simply believe that the AI knows what it’s doing, as a new deus ex machina.
❤
AI will also help astronomers to find any extraterrastrial life in other stars
Machine Learning and Reinforcement Learning are "AI" frameworks utilized in PS5....Does that mean that human Soccer (Football) players are to be replaced by video game Sims and Robots? Wolfram, Chat GPT (Claude 3 Et al...) , AlphaGeometry can be used by Teachers to better understand Math Algorithms that they may never have understood in their own classwork at University . They then can create better lessons (multimodal) to improve the Mathematical Cognition of their students in the classroom. Chatbots can be created as the students natural curiosity will lead them to ask questions that a Wolfram or AlphaGeometry powered API could answer and provide historical context and even various applications. The point is to Illustrate and model creative problem solving frameworks for students to embrace as their own.....not just to watch a computer solve an equation.....
IMHO
PS
The best DataScience powered by Ai has not made Liverpool unbeatable
You're dealing with a thing that we're all dealing with right now. EVERY SECTOR.
This isnt the destruction of your math or your art.
This is the destruction of ego.
Humans are just yet again reminded that we arent the center of the universe and how small we are.
What does it mean to be a human.... what is "accomplishment".... what is "recognition"
Ellie, as a mathematician and engineer, do you really worry about AI, in other words, do you think that one day they will definitely replace us?
gewgool
👌🏻
You might be way to young to know this, but walk into your mathematics library, go to one of those books from the 1960s that are still relevant (there are more in mathematics I think than in another other field), and look at acknowledgements of funding. If the author was working in the United States, there is a good chance that book acknowledges some funding from the Office of Naval Research. The Office of Naval Research back then was paying for original researchers, the very best, to write in books systematic explanations of their discoveries to push the envelope of general knowledge forward for everyone, not just specialists. And then the Vietnam War happened. And then the Mansfield Amendment happened. The Office of Naval Research was forbidden from funding such things, so no one did. The result is that over the next few decades, the number of top researchers who made the effort to write a systematic explanation of an entire field dwindled to almost nothing. The result is that the true frontier knowledge needed to make cutting edge discoveries is now locked up as "folklore" in the minds of a few researchers in each field, with no path to this folklore ever being systematized by a true top talent. You would need an AI to even begin to truly push human knowledge to first rediscover on its own this folklore first, because the folklore have the pictures, the intuition, to make new discoveries. This is also the only reason that AI is needed, because mathematics is in a curious position of both drowning in unprecedented detail of knowledge while dying on the vine because of lack of access of almost everyone to the folklore they need at that moment to push their thoughts.
As a computer scientist, it blows my mind that an AI can even "know" what the midpoint of a line means. It must have a large number of built-in rules/relationships. Is that cheating?
As a computer scientist, I know that you have not understood the video. She literally gives you the components of that software. The second component is a ”math engine” or ”symbolic deduction engine” that services these math relationships and concepts.
What would change if AI could change all math problems? Could you give some examples. 8:30
AI is good assistant for math research and math education.
Every single year artificial intelligence will get better and better
Like all technology
Since you're also a mathematics grad, I won't go easy on the jargon. Your description of how we solve problems mathematically is a bit incomplete. And kind of in a sad way, because it doesn't leave any room for creative problem solving, although you touch on that concept just a bit.
Incompleteness and Tarski's undefineability tell us that all machines (a process which computationally solves a problem) are strictly stuck in productive sets; i.e. AI is not able to be a creative task (unless someone has invented a problem-solver that doesn't rely on computation and hasn't let the rest of us know). Those same previously mentioned theorems also tell us that the collection of solvable problems can be partitioned into those which can be solved productively and those which can only be solved creatively. And, we already know that the collection of undecideable problems (i.e. those which cannot be solved productively) is even larger than the collection of decideable problems.
I say all of that to say this: AI will certainly, within our lifetime, become capable of solving every problem which is computationally decideable. However, until someone figures out how to make a problem-solver that doesn't rely on computation, the problems which will be left to us human mathematicians to solve remain uncountably numerous with unknowable potential for importance, elegance, and fun among them. The most exciting part of AI is that it will help us to discover problems even faster than we (or it) can formulate them, let alone solve them. All of us have very bright futures, including the lowly applied mathematicians like me.
No worries since Math's are therapeutic for me and not my bread and butter. For all the rest, start worrying.
Same, don't even need the degree I just find math a relaxing, fun and challenging hobby
It is. Just like calculators did back then.
Excellent video. But I have to say, I've never met anyone who agrees that their job is going to be replaced. It's always someone else's job.
Hold on. AI solved problems with known solutions. If it was trained, it basically copied human solutions.
Give it a problem with an unknown solution from the Millennium Prize Problem.
If it can be solved then, I'll be impressed.
You math guys can join us dev's and the lawyers on the bench...
Don't you understand? VERY SOON, there won't be any questions left for us. Give it a decade.😢
I can't wait for the time when AI can solve Olympiad math problems. Then AI will become irreplaceable and marh will be greatly benefited.
It is indeed aside and artificial intelligence and economy have always been beside. This is my approach to her: in racing the computer can verify if the player goes to the middle of the course and comes to the start point of the race by what direction by introducing invisible checkpoints on the track. I use the same concept on AI for mathematics by making some desired functions or even known functions as those invisible checkpoints - as reinforcements. Those reinforcements are analogous to the dopaminergic system on humans. The dopamine release is called reinforcement.
its like when Paul Bunyun vs the steam powered chainsaw, he had to take that L and walk away
A.i. ain’t replacing squat until we figure out unlimited free energy.
Quantum energy? Is that nor there to replace it?
A lot of people judge what is true and false by mathematical analysis - and this is fundamentally a flawed principle.
Iteration at the speed of light may be novel but not brilliant. It's akin to primates inadvertently writing the Iliad given trillions of attempts.
welcome to the club. We're all threatened.
@stephanieellison7834 Scary. The rabid pursuit of immediate profit with no actual medium-term plan will kill us all. These companies are like mycelium, eating everything in their path until there are no nutrients left.
Instead of improving human intelligence, through education and training, we'll rely more and more on artificial intelligence. IQs are decreasing in the USA, and so is life expectancy.
Humanity has lost confidence in itself. Human calculators, not computers, sent Apollo to the moon, and we can't seem to be able to do it today with all the new tech.
Until someone writes the orange bible and we start training mentats.
I don't see how a human will be needed in ai math solving process. I can't help it, but I don't see. Humans will be fully replaced for ALL mathematical tasks, show me how am I wrong?
Finally I can get revenge on my math teacher
No, don't think so. The more we feed AI generate stuff to AI the more it will error .
Please PROF tell me how to download THIS APP
Woww
Is replacing mathematician?
Watch the video to find out 👀👀
There are infinite mathematical patterns that could be derived from nature. This AI tool can't explore nature and so it can't figure out mathematical solutions by exploring nature like humans did till now.
AlphaGeometry is very good, but far from replacing mathematicians.
Lets come back in a year and see if that statement is still true.
@@pontusvigur6720 Alright! Please set it in your calendar!
@@pontusvigur6720how should it solve non computationally decidable problems?
@@howmathematicianscreatemat9226 How do humans solve undecidable problems? Why would we require an AI to solve problems that, for all we know, are uncomputable in principle?
no
ACCURACY IS JOB ONE! USE AI TO ENHANCE YOUR SKILL SET!!!! NUFF SAID!!!!!!!!!!!!!!!!
It will never see the beauty in maths.
😢
Nor does the slide rule or the calculator.
And even better for mathematicians: it cannot come up with truly elegant proofs to non computational decidable problems because the search space grows faster than expotnial and we don’t have a precise definition for „aesthetic“ and „elegant“ and „important“ and „interesting“. So many proofs will be just logics but not poetry like, no Euler level creativity at all
humanity NEEDS AGI like a new born baby needs his mother! i want ai robots everywhere. to do everything. only then this world would be in peace.
More like how a fish needs a hook.
I made a very simple text with AI and you can do it too: I asked AI this: Imagine that suddenly and for unknown causes, the human species became extinct: in your opinion (AI) would it be a GOOD or BAD thing for the planet in which we live? After listing the reasons why it would be good and bad, in the end I asked him to summarize and tell me only if worse or better and the answer was it would be GOOD! Then I asked him to make the same evaluation but this time on other living beings, such as mosquitoes, rabbits, chickens, cockroaches and even viruses. The answer is always it would be BAD! Isn't it a coincidence that we and only we are from this planet? Try it too.
Woke data in woke data out
olaf
Try being a computer programmer! Lols.
Please please please let me be the 255th comment.
We are about 40 years away from having AIs smarter than the most accomplished mathematicians in the world.
evolutionary speaking, math is party trick the brain can do. We (humans) are probably very bad at it. It will be one of the first area's where we will be surpassed.
It can prove theorems within a well-defined sphere, but it cannot (and can never) develop new fields of mathematics, which is what sets great mathematicians apart from scribblers. If you feel threatened, it's not because AI is amazing: it's because you are not.
I take deep satisfaction in knowing that someday life is going to humble you and the scribblers like you lol
What makes you so confident that “it” could never develop new fields of mathematics?
Probably because it's based on LLMs and they are based on texts that already exist.
Have you ever heard of exponential growth? It will come up with new theorems in a matter of month. Pretty ignorant of you think your are special.
@@FutureGuy47 what is that "exponential growth" is based on. I would like to learn if the LLMs learning patterns are somehow related to "exponential growth". I am not a AI specialist just an interested guy. All I know is that those kind of "AI" use already generated knowledge and its pretty hard, in my opinion, to create something completely new only work on already published studies.
AI can't prove things.
Not quite true.
I think the issue is: “how would/could we know if it did?”
I suppose you would have to be enough of a mathematician to understand not only the question but the answer? From that point of view, then, ai is a fancy Radioshack calculator? Chill.