MediMath Science

One of the most difficult skills in research is not learning how to develop an idea, but knowing when to abandon one. Scientific training naturally emphasizes persistence. Researchers are taught not to give up when experiments fail, reviewers disagree, or evidence appears inconsistent with an initial hypothesis. This persistence is essential. Most important discoveries would never have been made without it. Yet persistence has a less discussed counterpart. What happens when the idea itself is wrong? The problem becomes particularly difficult when a research program has developed over many years. A theory or methodology gradually accumulates papers, data, techniques, grants, students, collaborations, and professional recognition. What began as a hypothesis becomes an intellectual ecosystem. At that point, abandoning the idea is no longer a simple scientific decision. There are also powerful intellectual mechanisms that favor continuation. When observations conflict with a theory, it is ...

Recent discussions about slowing the development of artificial intelligence are often framed in dramatic terms: artificial general intelligence may become smarter than humans, recursively improve itself, and eventually escape human control. I find this framing somewhat misleading. Modern AI systems are not unconstrained intelligences. Transformer-based models operate within very real physical and computational limits: available compute, memory capacity and bandwidth, electrical power, training time, data quality, and the efficiency of optimization algorithms. Recursive self-improvement therefore does not imply that intelligence can increase without bound. The more interesting problem is different: What happens when an increasingly capable optimizer repeatedly optimizes an imperfect objective function without sufficiently independent external correction? We must consider AI as an optimization system. Consider a simplified learning system with parameters $\theta$ and objective function $...

Before beginning, I want to clarify what I mean by a “generalist.” I do not mean someone with superficial knowledge of many fields, but someone capable of handling a substantial range of work across multiple domains, though not with the depth of a specialist in each. This kind of generalist may become particularly valuable in aging societies, where experienced older people represent a large reservoir of accumulated knowledge and judgment that AI can help put to productive use. Modern science has been built on specialization. This specialization was necessary and enormously productive. As scientific knowledge expanded during the twentieth century, no individual could master everything. Mathematics, physics, engineering, biology, and medicine each divided into increasingly sophisticated subfields. By the latter part of the twentieth century, becoming a serious researcher often meant spending many years mastering a progressively narrower area of knowledge. This system produced extraor...