The Most Useful Form of Mathematics for Humankind, Ranked

Voting rules: Choose the form you think is the most useful!

Updated on May 5, 2024 06:58

Throughout history, the application of mathematics has profoundly impacted various aspects of human life, from solving everyday problems to advancing scientific and technological frontiers. By identifying which mathematical concepts are deemed most useful, educators and students alike can focus their efforts on areas guaranteed to have the most significant practical implications. This site allows users to contribute to a continuously updated ranking of mathematical concepts based on perceived utility and effectiveness. By casting votes, users help shape a consensus on the importance of these mathematical tools, aiming to guide future educational and research priorities. Whether you are deeply embedded in the field of mathematics or simply have an appreciation for its impact, your input is invaluable.

What Is the Most Useful Form of Mathematics for Humankind?

1

59
votes
Statistics

Statistics is helps in making informed decisions based on data analysis.
Statistics is a branch of mathematics that involves collecting, organizing, analyzing, interpreting, and presenting data. It provides techniques for quantifying uncertainty and making reliable inferences from available information. Statistical methods are widely used in various fields, including medicine, social sciences, economics, and business.

Descriptive Statistics: Summarizing and representing data using measures such as averages and percentages.

Probability: Studying the likelihood of different events occurring in a given situation.

Statistical Inference: Drawing conclusions about a population based on a sample.

Hypothesis Testing: Determining the truthfulness of a statement about a population based on evidence from a sample.

Regression Analysis: Examining the relationship between a dependent variable and one or more independent variables.
2

31
votes
Calculus

Calculus - important in various fields such as engineering, physics, economics, and more.
Calculus is a branch of mathematics that deals with continuous change and motion. It encompasses two main branches: differential calculus, which focuses on rates of change and slopes of curves, and integral calculus, which deals with accumulation and area under curves. Calculus provides a powerful framework for understanding and solving problems in physics, engineering, economics, and other scientific fields. It is considered one of the most challenging subjects in college due to its abstract concepts and complex problem-solving techniques.

Differential Calculus: Deals with rates of change and slopes of curves.

Integral Calculus: Concerned with accumulation and area under curves.

Fundamental Theorem of Calculus: Connects the concepts of differentiation and integration.

Limits: Examines the behavior of functions as inputs approach certain values.

Derivatives: Measures the rate of change of a function.
3

17
votes
Algebra

Algebra - used in solving real-world problems and helps in understanding relationships between variables.
Algebra is a Quizlet set that focuses on the fundamental principles and concepts of algebra. It covers various topics related to equations, expressions, functions, and graphs. The set helps students build a strong foundation in algebraic thinking and problem-solving.

Number of terms: 500

Total flashcards: 1000

Concepts covered: Variables, linear equations, inequalities, factoring, polynomials, quadratic equations, exponents, and logarithms

Difficulty level: Intermediate

Language: English
4

18
votes
Geometry

Geometry - used in architecture, design, and understanding the physical world around us.
Geometry is a Quizlet set that covers various concepts and topics related to the study of shapes, angles, and spatial relationships. It provides a comprehensive review of geometry principles and formulas.

Number of flashcards: 200

Topics covered: Points, lines, angles, triangles, quadrilaterals, circles, polygons, transformations, and 3D shapes

Difficulty level: Intermediate

Images included: Yes

Audio pronunciations: No
5

24
votes
Number theory

Number theory - essential in cryptography, coding theory, and computer science.
Number theory is a branch of mathematics that deals with the study of integers and their properties. It explores the fundamental nature of numbers, relationships between them, and various mathematical structures that can be built using integers.

Prime Numbers: Number theory extensively studies prime numbers, which are integers greater than 1 that cannot be divided evenly by any other integer except 1 and themselves.

Divisibility: Number theory investigates divisibility properties, including factors and multiples of numbers.

Congruences: Congruences are an important concept in number theory, dealing with the equivalence of numbers modulo a given integer.

Diophantine Equations: Number theory addresses Diophantine equations, which are polynomial equations with integer solutions.

Arithmetic Functions: Number theory studies various arithmetic functions, such as the Euler's totient function and the Möbius function.
Number theory in other rankings
- Position 3 of 10 in Most advanced math topic
6

19
votes
Probability

Probability - essential in understanding risk and uncertainty in various fields such as finance, insurance, and more.
Probability is a branch of mathematics that deals with the likelihood and uncertainty of events occurring. It is widely used in various fields to make predictions and informed decisions based on available data. Probability enables us to quantify and understand the chances or odds of different outcomes.

Probability Theory: Probability theory provides a systematic framework to study and analyze uncertain events.

Probabilistic Modeling: Probability allows us to model and represent real-world uncertainties in a mathematical form.

Statistical Inference: Probability is used to draw conclusions and make inferences from observed data.

Risk Assessment: Probability is crucial in assessing and managing risks in various situations and industries.

Randomness: Probability is closely related to the concept of randomness and the generation of random events.
7

17
votes
Linear algebra

Linear algebra - essential in machine learning, computer graphics, and optimization.
Linear algebra is a branch of mathematics that focuses on the study of vector spaces, linear transformations, and systems of linear equations. It deals with the properties and operations of vectors and matrices, allowing for the representation and manipulation of complex systems in a concise and efficient manner.

Vectors and Matrices: Linear algebra involves the use of vectors and matrices to represent and operate on data and systems.

Linear Transformations: It studies the properties of linear transformations and their effects on vectors.

Systems of Linear Equations: Linear algebra provides methods for solving systems of linear equations and finding their solutions.

Eigenvectors and Eigenvalues: It explores eigenvectors and eigenvalues, which play a vital role in understanding the behavior of linear transformations.

Vector Spaces: It examines the properties and structure of vector spaces, allowing for the analysis of geometric concepts.
8

6
votes
Differential equations

Differential equations is important in modeling various phenomena such as population growth, chemical reactions, and more.
Differential equations is a branch of mathematics that deals with equations involving derivatives. It is particularly useful in understanding and analyzing change and rates of change in various scientific and real-world phenomena. Differential equations provide powerful tools for modeling dynamic systems and predicting their behavior over time.

Application: Used extensively in physics, engineering, economics, biology, and other fields

Types: Ordinary differential equations (ODEs) and partial differential equations (PDEs)

Order: Refers to the highest derivative involved in the equation

Linear vs. Nonlinear: Can be classified as either linear or nonlinear depending on the terms involved

Solutions: May have analytic solutions or require numerical methods for approximation
9

6
votes
Patrick M. Emerson · CC BY-SA 4.0

Game theory

John von Neumann

Game theory - useful in understanding strategic decision-making in economics, politics, and more.
Game theory is a branch of mathematics and economics that studies the strategic interactions between multiple players or decision-makers. It provides a framework to analyze and predict the outcomes of such interactions and helps in making rational decisions in competitive situations.

Strategic Interactions: Examines how choices and actions of one player affect the choices of other players.

Payoff Matrix: Represents the outcomes and payoffs associated with different choices made by players.

Nash Equilibrium: A solution concept that identifies stable outcomes when no player has an incentive to unilaterally change their strategy.

Cooperative Game Theory: Focuses on how players can cooperate to achieve mutually beneficial outcomes.

Non-Cooperative Game Theory: Analyzes strategic interactions where cooperation between players is not assumed.
Game theory in other rankings
- Position 10 of 10 in Most useful thing about mathematics for humankind PDF
10

3
votes
Topology

Topology - used in understanding the shape and structure of objects and spaces.
Topology is a branch of mathematics that studies the properties of space that are preserved under continuous transformations, such as stretching, bending, and twisting. It deals with the concept of proximity and connectivity between various objects within a space.

Homeomorphism: A continuous function that establishes a relationship between two spaces, preserving their topological properties.

Compactness: A property that captures the idea of being finite in size and not having any 'holes' or 'gaps'.

Connectedness: The property of a space that ensures there are no separate or disjoint pieces within it.

Separation Axioms: Different levels of separation that a topological space can possess.

Metric Spaces: A specific type of topological space equipped with a distance function.

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Discussion

Ranking factors for useful form

Applicability

The usefulness of a particular form of mathematics depends on its practical applications in various fields such as engineering, finance, physics, statistics, and computer science.
Accessibility

The ease with which people can learn and apply the concepts and techniques of a form of mathematics is also an important factor. If a form of mathematics is too challenging to learn, it may not be as useful.
Versatility

The ability of a form of mathematics to solve a wide range of problems in different contexts is also an important factor. The more versatile a form of mathematics is, the more useful it is likely to be.
Impact

The impact of a form of mathematics on society, economy, and technology is also an important factor. A form of mathematics that leads to significant advancements in these areas is likely to be very useful.

About this ranking

This is a community-based ranking of the most useful form of mathematics for humankind. We do our best to provide fair voting, but it is not intended to be exhaustive. So if you notice something or form is missing, feel free to help improve the ranking!

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196 votes
10 ranked items

Voting Rules

A participant may cast an up or down vote for each form once every 24 hours. The rank of each form is then calculated from the weighted sum of all up and down votes.

More information on most useful form of mathematics for humankind

Mathematics is an essential field of study that has been shaping our world for centuries. From ancient civilizations to modern times, mathematics has played a critical role in advancing science, technology, and engineering. It is a tool that allows us to understand the complexities of the universe, make predictions, and solve real-world problems. But, with so many branches of mathematics, it can be challenging to determine which form of math is the most useful for humankind. In this article, we explore the different types of mathematics and try to answer the question, "What is the most useful form of mathematics for humankind?"