Mathematically

Mathematically refers to the use of mathematical principles, methods, and techniques in a logical, precise, and systematic manner. It involves employing numbers, symbols, equations, and algorithms to analyze, solve, and describe various phenomena, problems, or relationships. It emphasizes the rigor, accuracy, and abstract nature of mathematics, focusing on verifiable proofs, logical deduction, and the construction of models that accurately represent real-world systems or theoretical concepts. The term suggests a structured, quantitative approach to understanding and expressing ideas, often emphasizing the objectivity and universality inherent in mathematical reasoning.

Mathematically meaning with examples

• To solve the physics problem, we need to approach it mathematically, applying Newton's laws of motion and calculating the relevant forces to determine the object's trajectory. Ignoring these principles makes any attempt to estimate outcome useless. The student's grasp of complex formulas and rigorous application shows an understanding of the mathematical framework.
• The financial model was developed mathematically, using complex algorithms to forecast future market trends and assess investment risks with high degrees of confidence. The model's projections were based on statistical data and are very accurate. The model provides a powerful tool for making informed investment decisions.
• The artist employed mathematical principles mathematically in designing the architectural structure, using geometric proportions and complex calculations to ensure structural stability and aesthetic harmony. The building's facade is a testament to mathematical precision, showcasing symmetrical lines. The architect utilized mathematical theories.
• The scientific paper presented its findings mathematically, expressing the experimental results as equations and statistical distributions to demonstrate the correlation between variables and validate the research hypothesis. The data was rigorously analyzed to confirm the scientific theory mathematically. The authors carefully constructed the information with mathematics.