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Mathematics for humans

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The 20th-century computer scientist Edsger W. Dijkstra famously compared the question of "whether computers can think" to that of "whether submarines can swim." I find this analogy excellent: it does not deny that the machine can accomplish certain tasks more effectively than an unassisted human, nor that humans must learn to use the machine to remain relevant; but it also makes clear that the machine does not replace human ability. If your submarine breaks down in the middle of the water, you better hope you still know how to swim. Today's computers are much more capable than those of Dijkstra's era, but his point remains equally valid. If this distinction between human thinking and "AI" eludes many people, perhaps it is because most people do very little thinking anyway. The distinction between human and computer is especially stark in mathematics, because mathematics is the science of logical thinking. For two decades I have taught mathematics students who struggled to fake their wa

Mathematics for humans Mathematics for humans The threat from AI is not that it will gain self-consciousness or a soul. The threat is that we will destroy ours-that, bewitched by the appearance of AI-consciousness and AI-souls, we will lose interest in cultivating and honoring our own. In doing so, we will cease to produce students capable even of cheating intelligently, let alone of writing coherent papers themselves. At the same time, we will cease to produce teachers capable of telling the difference.... To maximize the chance of not having their jobs replaced by machines, students need to

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