Discussions, summarized

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• Hacker News1Sharing AI progress in mathematicsLinks to OpenAI's "math" GitHub repository and its preprints folder, which appears to hold mathematical research papers or preprints.Grief and meaning for human mathematicians:A researcher who spent 24 years on Barnette's Conjecture mourns its AI proof, noting he'll never meet its "creator." Others share demotivation, an ERC group's goals solved overnight, and debate whether AI erodes training of future mathematicians or augments them.Concentration of power in proprietary models:Many worry these results come from withheld internal models no one can reproduce, with unknown compute and setups. Some cite Tao's group objecting to strip-mining open problems; others argue open-weight models lag under a year and specialized science tools are always restricted.Significance of results and limits of LLMs:The Unique Games proof would settle many approximation hardness results; others note Barnette, Millennium-problem progress, and huge polynomial exponents. Debate whether LLMs truly generalize or exploit broad coverage plus Lean verification and compute, and whether to fear AI doom.
• Reddit science1A 30-minute soak in a 40°C (104°F) hot bath lowered blood pressure more than 30 minutes of moderate cycling in a small study of 25 adults aged 45–70 with overweight or obesity, and increased blood flow in tiny skin vessels, which may help people who can't exercise get similar blood vessel benefits.A small study of 25 overweight adults aged 45–70 found a 30-minute 40°C hot water soak boosted skin microvascular blood flow and lowered blood pressure more than 30 minutes of moderate cycling, suggesting passive heat therapy may help those unable to exercise, though not replace it.Temporary vs long-term benefits:Users noted that heat-driven vasodilation causes only a temporary BP drop, which the study measured right after the bath. Exercise briefly raises BP but improves vascular function and resting BP over time. Many felt the headline overstated a bath as a substitute for exercise.Sample size debate:Some questioned the 25-person sample. Others, including a science PhD, argued that the required sample size depends on effect size, variability and study design. Easily measured physiological effects like blood pressure often need few subjects, and power analyses guide this.Practical challenges of hot soaking:Users complained that tubs are too small for tall or larger people and that water cools quickly. Some found 40°C uncomfortably hot. Others shared anxiety relief from baths but warned of fainting from low BP and of dysautonomia/POTS risks, suggesting draining the tub before standing.
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