Yes, the AI-human teamwork opportunity in math is taking off. I wrote about this teamwork in my book, Understanding Machine Understanding, and now have put that into practice by using AI assistants to help me make new discoveries in number theory. With help from GPT-o1, Claude 3.0 Opus and 3.5 Sonnet, and Grok-2 I have submitted a new formal proof of a well known conjecture about factorial numbers. I have also written about this project on my Substack.
A joy to read—kudos and thanks! Just a minor note.
We mostly have humans to compare AI against. While humans currently outperform AI on certain axes, this isn’t conclusive evidence that humans represent the optimal way of doing things—in a mathematical or objective sense (as used in AI)—on those axes.
Regarding data efficiency: it's possible that humans are over-generalizers by design. Evolution may have favored our ability to learn quickly from limited data, even if that means occasionally drawing exaggerated or "overconfident" conclusions. For instance, when forming a significant "bump" in the probability distribution of "(rustling leaves, tiger)" based on very little evidence. The shape of this distribution might not mathematically reflect the data in a rigorous way, but it might offer a survival advantage to get to some "bump" quickly rather than slowly. Better to over-generalize than under-generalize—the utility of being "wrong and skittish" versus "wrong and eaten" is highly asymmetrical.
In "ML speak," this feels analogous to stochastic gradient descent (SGD) with an overly high learning rate, or using an overly large novelty constant (e.g., 1e-1 instead of 1e-2 or 1e-3) in online adaptation. The system adapts quickly, yes, but often to the wrong features or patterns, risking instability.
Humans naturally integrate multiple types of sensory information and experiences:
Multi-modal learning: As you noted, a child experiences dogs through sight, sound, touch, smell, and even interactions - they get a rich, multi-sensory understanding of what "dog" means
Context: Children see dogs in different situations - at home, in parks, on walks - learning about their behaviours and roles in human life
Temporal understanding: They observe how dogs move, play, and interact over time, not just static snapshots
Social learning: They also learn about dogs through language, stories, and how other people interact with dogs
Current AI systems are often trained on just one type of data (like images) in isolation. While there is progress in multi-modal AI that can process both images and text, or video and audio together, these systems still don't integrate information in the rich, embodied way that humans do naturally from birth.
This "embodied cognition" - learning through multiple senses and physical interaction with the world - might be one of those key algorithmic differences the tweet is talking about. It could help explain how humans can build such robust understanding from relatively few examples, compared to AI systems trained on millions of isolated data points.
Yes, the AI-human teamwork opportunity in math is taking off. I wrote about this teamwork in my book, Understanding Machine Understanding, and now have put that into practice by using AI assistants to help me make new discoveries in number theory. With help from GPT-o1, Claude 3.0 Opus and 3.5 Sonnet, and Grok-2 I have submitted a new formal proof of a well known conjecture about factorial numbers. I have also written about this project on my Substack.
A joy to read—kudos and thanks! Just a minor note.
We mostly have humans to compare AI against. While humans currently outperform AI on certain axes, this isn’t conclusive evidence that humans represent the optimal way of doing things—in a mathematical or objective sense (as used in AI)—on those axes.
Regarding data efficiency: it's possible that humans are over-generalizers by design. Evolution may have favored our ability to learn quickly from limited data, even if that means occasionally drawing exaggerated or "overconfident" conclusions. For instance, when forming a significant "bump" in the probability distribution of "(rustling leaves, tiger)" based on very little evidence. The shape of this distribution might not mathematically reflect the data in a rigorous way, but it might offer a survival advantage to get to some "bump" quickly rather than slowly. Better to over-generalize than under-generalize—the utility of being "wrong and skittish" versus "wrong and eaten" is highly asymmetrical.
In "ML speak," this feels analogous to stochastic gradient descent (SGD) with an overly high learning rate, or using an overly large novelty constant (e.g., 1e-1 instead of 1e-2 or 1e-3) in online adaptation. The system adapts quickly, yes, but often to the wrong features or patterns, risking instability.
Humans naturally integrate multiple types of sensory information and experiences:
Multi-modal learning: As you noted, a child experiences dogs through sight, sound, touch, smell, and even interactions - they get a rich, multi-sensory understanding of what "dog" means
Context: Children see dogs in different situations - at home, in parks, on walks - learning about their behaviours and roles in human life
Temporal understanding: They observe how dogs move, play, and interact over time, not just static snapshots
Social learning: They also learn about dogs through language, stories, and how other people interact with dogs
Current AI systems are often trained on just one type of data (like images) in isolation. While there is progress in multi-modal AI that can process both images and text, or video and audio together, these systems still don't integrate information in the rich, embodied way that humans do naturally from birth.
This "embodied cognition" - learning through multiple senses and physical interaction with the world - might be one of those key algorithmic differences the tweet is talking about. It could help explain how humans can build such robust understanding from relatively few examples, compared to AI systems trained on millions of isolated data points.
*(children cannot be copy/pasted)* peak daveshap experience
thanks for insights as always!
A more empirical person would have at least tried before making such an assertion.
Interpol wants your home address
This is an important consideration when deciding where to allocate 4 megawatts of power!