260 interesting mathematical topics for essays and research papers (2023)

Mathematics is the science of numbers and shapes. Writing about it can give you a new perspective and help clear up difficult concepts. You can even use math writing as a problem-solving tool.

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In this article you will find many interesting mathematical topics. In addition, you will learn about the math subjects you can choose. And if the idea of ​​letters and numbers makes your head spin, try ours.custom writing service. Our professionals will create a paper for you in no time!

Now let's move on to math writing tips and topics.


  1. 🔝 Top 10 Interesting Mathematicians

  2. ✅ Branches of mathematics

  3. ✨ Fun math themes

  4. 🏫 Math topics for high school

  5. 🎓 Colegio-Mathematikthemen

  6. 🤔 advanced math

  7. 📚 Mathesuche

  8. ✏️ math lessons

  9. 🧮 Algebra

  10. 📏 Geometry

  11. ➗ Calculation

  12. 💵 Economic math

  13. 🔍 References

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🔝 Top 10 Interesting Mathematicians

  1. Number theory in everyday life.

  2. Logistic definitions of mathematics.

  3. Multivariable calculus versus vector calculus.

  4. 4 functional analysis conditions.

  5. Random variable in probability theory.

  6. How is mathematics used in cryptography?

  7. El proposito del algebra homológica.

  8. Concave vs convex in geometry.

  9. The problem of the philosophical foundation.

  10. Is numerical analysis useful for machine learning?

✅ Branches of mathematics

What exactlymathematics? First, it is very old. Even the ancient Greeks and Persians used mathematical tools. Today we consider it an interdisciplinary language.

Biologists, linguists, and sociologists use mathematics in their work. Not only that, we all face it in our daily lives. It manifests itself, for example, in the measurement of time. Many times we have to calculate how much our purchases cost and how much paint we need to buy to cover a wall.

260 interesting mathematical topics for essays and research papers (1)

Simply put, mathematics is a universal problem-solving tool. We can divide pure mathematics into three branches: geometry, arithmetic, and algebra. Let's take a closer look:

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  • GeometryWhen we study geometry, we try to understand our physical environment. Geometric shapes can be as simple as a triangle. Or they can form complicated shapes, like a rhombicicosidodecahedron.

  • arithmeticArithmetic deals with numbers and simple operations: subtraction, addition, division, and multiplication.

  • AlgebraAlgebra is used when the exact numbers are not clear. Instead, they are replaced with letters. Businesses often need algebra to forecast their sales.

It is true that most high school students do not like math. However, that doesn't mean it can't be a fun and engaging topic. In the next section you will find many interesting mathematical topics for your article.

✨ Fun math themes

If you're having trouble getting started on your essay, we've got some fun and interesting math topics for you. They will definitely captivate you and make the writing process enjoyable. Also, funny math topics can show everyone that even math can be fun or even a bit silly.

  1. The connection between mathematics and art: analysis of the golden ratio in Renaissance paintings.

  2. An evaluation of Georg Cantor's set theory.

  3. The best approaches to learning math facts and developing number sense.

  4. Different probability approaches explored by card trick analysis.

  5. Chess and drafts: the use of mathematics in leisure activities.

  6. The five types of mathematics used in computing.

  7. Real applications of the Pythagorean theorem.

  8. An examination of the various theories of mathematical logic.

  9. The application of game theory in the social sciences.

  10. Mathematical definitions of infinity and how to measure them.

  11. What is the logic behind unsolvable math problems?

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  12. An explanation of the mean, mode, and median using math grades in the classroom.

  13. The properties and geometry of a Möbius strip.

  14. Use truth tables to represent the logical validity of a propositional expression.

  15. The relationship between Pascal's triangle and the binomial theorem.

  16. The use of different types of numbers: history.

  17. The application of differential geometry in modern architecture.

  18. A mathematical approach to solving a Rubik's cube.

  19. Comparison of predictive and prescriptive statistical analysis.

  20. Explanation of Koch snowflake iterations.

  21. The importance of limits in analysis.

  22. Hexagons as the most balanced shape in the universe.

  23. The appearance of patterns in chaos theory.

  24. What were Euclid's contributions to mathematics?

  25. The difference between universal algebra and abstract algebra.

🏫 Topics for writing math in high school

When you write a math paper, you want to show that you understand a concept. It can be useful when you need to prepare for an exam. Choose a topic from this section and decide what you want to discuss.

  1. Explain why we need the Pythagorean theorem.

  2. What is an exaggeration?

  3. Describe the difference between algebra and arithmetic.

  4. When do you not need a calculator?

  5. Find a connection between math and the arts.

  6. How do you solve a linear equation?

  7. Discuss how to determine the probability of rolling two dice.

  8. Is there a connection between philosophy and mathematics?

  9. What kinds of math do you use in your daily life?

  10. What are numerical data?

  11. Explain how to use the binomial theorem.

  12. What is the distribution law of multiplication?

  13. Discuss the key concepts of ancient Egyptian mathematics.

  14. Why do so many students dislike math?

  15. Should mathematics be compulsory in school?

  16. How to perform an equivalent transformation?

  17. Why do we need imaginary numbers?

  18. How is the slope of a curve calculated?

  19. What is the difference between sine, cosine, and tangent?

  20. How do you define the cross product of two vectors?

  21. What do we use differential equations for?

  22. Examine how it calculates the average value.

  23. Define linear growth.

  24. Give examples of different types of numbers.

  25. How do you solve a matrix?

🎓 University math topics for a job

Sometimes it takes more than formulas to explain a complex idea. Therefore, knowing how to express yourself is crucial. This is especially true for college level math. Consider the following ideas for your next research project:

  1. Why do we need n-dimensional spaces?

  2. Explain how card counting works.

  3. Discuss the difference between a discrete and continuous probability distribution.

  4. How does the encryption work?

  5. Describe extreme problems in discrete geometry.

  6. What can make a math problem have no solution?

  7. Study the topology of a Möbius strip.

260 interesting mathematical topics for essays and research papers (2)
  1. What is K-theory?

  2. Discuss the central problems of computational geometry.

  3. Explain the use of set theory.

  4. Why do we need boolean functions?

  5. Describe the most important topological concepts in modern mathematics.

  6. Study the properties of a rotation matrix.

  7. Analyze the practical applications of game theory.

  8. How do you solve a Rubik's cube mathematically?

  9. Explain the mathematics behind the Koch snowflake.

  10. Describe the paradox in Gabriel's horn.

  11. How are fractals formed?

  12. Find a way to solve sudoku with math.

  13. Why is the Riemann Hypothesis still unresolved?

  14. Discuss the themes of the Millennium Prize.

  15. How are complex numbers divided?

  16. Analyze degrees in polynomial functions.

  17. What are the main concepts of number theory?

  18. Compare the different types of statistical methods.

🤔 Advanced math topics to write an article

Once you have passed the basic math tests, you can move on to the advanced section. This area includes topology, combinatorics, logic, and computational mathematics. Check out the list below to find interesting topics to write about:

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  1. What is an abelian group?

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  2. Explain the orbit stabilizer theorem.

  3. Discuss what makes Burnside's problem so influential.

  4. What are the fundamental properties of holomorphic functions?

  5. How does Cauchy's integral theorem lead to Cauchy's integral formula?

  6. How are Picard's two theorems related?

  7. When is a trigonometric series called a Fourier series?

  8. Give an example of an algorithm used for machine learning.

  9. Compare the different types of backpack problems.

  10. What is the minimal overlap problem?

  11. Describe Bernoulli's scheme.

  12. Provide a formal definition of the process for a Chinese restaurant.

  13. Discuss the logistics map related to chaos.

  14. Why do we need Feigenbaum's constants?

  15. Define a difference equation.

  16. Explain the use of the Fibonacci sequence.

  17. What is an international transfer?

  18. Compare the Riemann and Ruelle zeta functions.

  19. How to use elementary embeddings in model theory?

  20. Analyze the problem using Kunen's axiom of totality and the inconsistency theorem.

  21. How is Lie algebra used in physics?

  22. Define various cases of algebraic circles.

  23. Why do we need étale cohomology groups to calculate algebraic curves?

  24. What is non-Euclidean geometry?

  25. How can two lines be ultraparallel?

📚 Mathematical research topics for an article

Choosing the right topic is crucial to the success of your mathematics research paper. It has to be hard enough to be engaging, but without going beyond your skill level. If possible, stick to your specialty. This way your task becomes more manageable. Here are some ideas:

  1. Write about the history of calculus.

  2. Why are unsolved math problems important?

  3. Find the reasons for the gender differences in mathematics students.

  4. What are the hardest math questions being asked today?

  5. Examine the notion of operator spaces.

  6. How can we design a train schedule for an entire country?

  7. What makes a number big?

260 interesting mathematical topics for essays and research papers (3)
  1. How can infinities have various sizes?

  2. What is the best math strategy to win a game of Go?

  3. Analyze the natural occurrences of random walks in biology.

  4. Explain what kind of mathematics was used in ancient Persia.

  5. Discuss how Iwasawa's theory relates to modular forms.

  6. What role do prime numbers play in cryptography?

  7. How did the study of mathematics develop?

  8. Browse the different solutions for the Tower of Hanoi.

  9. Search Napier's bones. How can you use them?

  10. What is the best mathematical way to find someone lost in a maze?

  11. Investigate the traveling salesman problem. Can you find a new strategy?

  12. Describe how barcodes work.

  13. Study some real examples of chaos theory. How do you define them mathematically?

  14. Compare the effects of various innovative math equations.

  15. Explore the seven bridges of Koenigsberg. Match the problem with the city of your choice.

  16. Discuss Fisher's Fundamental Theorem of Natural Selection.

  17. How does quantum computing work?

  18. Choose an unsolved math problem and tell what makes it so difficult.

✏️ Research topics in mathematics didactics

For many teachers, the hardest part is keeping students' interest. When it comes to math, it can be especially challenging. Making complicated concepts easy to understand is crucial. That is why we need to investigate the didactics of mathematics.

  1. Compare traditional methods of teaching mathematics with unconventional methods.

  2. How to improve mathematics education in the United States?

  3. Describe ways to encourage girls to pursue STEM careers.

  4. Should computer programming be taught in high school?

  5. Define the objectives of teaching mathematics.

  6. Find out how you can make math more accessible for students with learning disabilities.

  7. At what age should children start practicing simple equations?

  8. To examine the effectiveness of gamification in the teaching of algebra.

  9. What do students gain by participating in math competitions?

  10. What are the benefits of not using standardized tests?

  11. Describe the causes of “math anxiety”. How can you get over it?

  12. Explain the social and political relevance of mathematics lessons.

  13. Define the main problems of mathematics education in public schools.

  14. What is the best way to get children interested in geometry?

  15. How can students improve their mathematical reasoning outside of the classroom?

  16. Discuss the benefits of using technology in teaching mathematics.

  17. How does culture affect your teaching of mathematics?

  18. Discover the history of teaching algebra.

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  19. Compare the teaching of mathematics between countries.

260 interesting mathematical topics for essays and research papers (4)
  1. How does dyscalculia affect the daily life of a student?

  2. In which school subjects can mathematics be integrated?

  3. Has a math degree gained value in recent years?

  4. What are the disadvantages of common basic patterns?

  5. What are the benefits of an integrated mathematics curriculum?

  6. Discuss the benefits of Mathcamp.

🧮 Algebra topics for a job

The elegance of algebra comes from its simplicity. This gives us the ability to express complex problems in short equations. The world changed forever when Einstein wrote the simple formula E=mc². If you have a term paper to write for his algebra class, look no further! Here are some brilliant tips:

  1. Give an example of proof by induction.

  2. What are F-algebras for?

  3. What are number problems?

  4. Show the meaning of abstract algebra.

  5. Examine the peculiarities of Fermat's Last Theorem.

  6. What are the fundamentals of algebra?

  7. Explore the relationship between algebra and geometry.

  8. Compare the differences between commutative and noncommutative algebra.

  9. Why is Brun's constant relevant?

  10. How are squares factored?

  11. Explain Descartes' rule of signs.

  12. What is the quadratic formula?

  13. Compare and define the four types of sequences.

  14. Explain how partial fractions work.

  15. What are logarithms used for?

  16. Describe Gaussian elimination.

  17. What does Cramer's rule say?

  18. Investigate the difference between eigenvectors and eigenvalues.

  19. Analyze the Gram-Schmidt process in two dimensions.

  20. Explain what "area" and "domain" mean in algebra.

  21. What can you do with determiners?

  22. Learn about the origin of the distance formula.

  23. Find the best way to solve math problems.

  24. Compare relationships between different systems of equations.

  25. Find out how the Rubik's cube is related to group theory.

📏 Geometry topics for a research paper

Shapes and space are the two basic elements of geometry. Since its appearance in antiquity, it has become an important field of study. The latest addition to geometry, topology, examines what happens to an object as you stretch, shrink, and bend it. Things can get pretty crazy from here! The following list contains 25 interesting geometry topics:

  1. What are the Archimedean solids?

  2. Find real uses for a rhombenosidodecahedron.

  3. What is studied in projective geometry?

  4. Compare the most common types of transformations.

  5. Explain how acute quadratic triangulation works.

  6. Discuss the configuration of the Borromean ring.

  7. Investigate solutions to the Buffon's needle problem.

  8. What is special about right triangles?

260 interesting mathematical topics for essays and research papers (5)
  1. Describe the notion of Dirac manifold.

  2. Compare the different relationships between the lines.

  3. What is the small bottle?

  4. How can geometry be transferred to other disciplines such as chemistry and physics?

  5. Explore Riemann manifolds in Euclidean space.

  6. How do you prove the angle bisector theorem?

  7. Look up M. C. Escher's use of geometry.

  8. Find applications for the golden ratio.

  9. Describe the meaning of the circles.

  10. Examine what the ancient Greeks knew about geometry.

  11. What does congruence mean?

  12. Examine the use of Euler's formula.

  13. How are CT scans related to geometry?

  14. Why do we need n-dimensional arrays?

  15. How can you solve Heesch's problem?

  16. What are hypercubes?

  17. Analyze the use of geometry in Picasso's painting.

➗ Calculus topics to write an article

You can describe calculus as more complicated algebra. It is a study of changes over time that provides useful information about everyday problems. Applied analysis is necessary in a variety of fields such as sociology, engineering, or economics. Check out this list of engaging topics in a calculus problem:

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  1. What are the differences between trigonometry, algebra, and calculus?

  2. Explain the notion of limit.

  3. Describe the standard formulas needed for derivatives.

  4. How are critical points located on a diagram?

  5. Evaluate the application of L'Hôpital's rule.

  6. How is the area between the curves defined?

  7. What is the calculation basis?

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260 interesting mathematical topics for essays and research papers (6)
  1. How does multivariate calculus work?

  2. Discuss or use Stokes theorem.

  3. What does Leibniz's integral rule say?

  4. What is the Itô stochastic integral?

  5. Investigate the impact of non-standard analysis on probability theory.

  6. Explore the origins of computing.

  7. Wer war Maria Gaetana Agnesi?

  8. Define a continuous function.

  9. What is the Fundamental Theorem of Calculus?

  10. How is the Taylor series of a function calculated?

  11. Discuss ways to resolve Runge's phenomenon.

  12. Explain the extreme value theorem.

  13. Why do we need the predicate calculus?

  14. What are linear approximations?

  15. When does an integral become improper?

  16. Describe root and ratio tests.

  17. How does the ring method work?

  18. Where do we apply calculus in real situations?

💵 Business math topics to write

You don't have to be an entrepreneur to appreciate business mathematics. His topics range from credit and loans to insurance, taxes and investments. Even if you are not a mathematician, you can use it to manage your finances. Sounds interesting? Then take a look at the list below:

  1. What skills do you need for business math?

  2. How interest is calculated?

  3. Compare business and consumer math.

  4. What is a discount factor?

  5. How do you know that an investment makes sense?

  6. When does it make sense to replace a loan with another loan?

  7. Find useful financing techniques that anyone can use.

  8. How does critical path analysis work?

  9. Explain how credit works.

  10. What areas of work use Operations Research?

  11. How do companies use statistics?

  12. What is the economic problem of batch programming?

  13. Compare the use of different types of charts.

  14. What Causes a Stock Market Crash?

  15. How is present value calculated?

  16. Explore the history of revenue management.

  17. When are multi-period models used?

  18. Explain the consequences of depreciation.

  19. Are pensions a good investment?

  20. Would the United States benefit financially from phasing out the penny?

  21. What caused the housing crisis in the United States in 2008?

  22. How is sales tax calculated?

  23. Describe the terms ups and downs.

  24. Examine the math behind debt relief.

  25. What is the difference between a loan and a mortgage?

With all these ideas, you are perfectly equipped for your next math problem. Good luck!

🔍 References

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