Mathematics Is A Toolbox of Methods and Languages
- Medicine, climate science, economics, and even social sciences use mathematics to test ideas, spot patterns, and make predictions.
- This makes maths both powerful and problematic: powerful because it adds precision, problematic because its reliability depends on the assumptions, data, and ethics of how it is used.
Statistics As Proof of Effectiveness
- In medicine, statistical analysis is used to determine the effectiveness of treatments, identify risk factors for diseases, and make predictions about patient outcomes.
- For example, clinical trials rely on statistical methods to compare the outcomes of different treatment groups and determine whether a new drug is more effective than a placebo.
- Key Concepts:
- Randomized Controlled Trials (RCTs): These trials use randomization to eliminate bias and ensure that the results are statistically valid.
- P-values: A measure of the probability that the observed results occurred by chance. A low p-value (typically less than 0.05) indicates that the results are statistically significant.
- Confidence Intervals: These provide a range of values within which the true effect of a treatment is likely to lie.
Mathematics makes medical knowledge claims more trustworthy, but only if the trials are well-designed and the data is unbiased.
Climate Science Models The Unobservable
- Scientists use mathematics to create models, simulations of the climate system that let them test how the atmosphere, oceans, land, and ice interact over time.
