100 Fascinating Math Research Topics To Consider

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Mathematics is incredibly important in improving our understanding of the world around us. This subject is not simply about handling numbers and equations. It predominantly focuses on solving complex problems in novel ways and making predictions. If you have enrolled in a math course, then as a part of your assignment, you might have to work on exemplary math research topics. Particularly, by conducting mathematics research, you may analyze further and make valuable contributions to your field of study.

Typically, mathematics is a broad discipline that includes several branches and sub-branches such as arithmetic, algebra, calculus, probability, trigonometry, topology, and so on. So, when it comes to research, you can very well consider any of the topics related to the sub-fields of mathematics.

Since the subject is wide, many students experience difficulties with identifying a good research topic. Therefore, to simplify the research topic selection process, in this blog, we have presented a list of outstanding mathematics research topics suggested by subject experts. Additionally, we have shared how to find the right topic for math research. Keep on reading to get interesting math research ideas.

Know How to Choose a Math Research Topic

The success of your research paper mostly depends on the topic you select. Hence, it is necessary to choose a unique topic that has an excellent research scope. If you are confused about how to identify an appropriate topic for your math research paper, then without any hesitation, follow these guidelines.

  • First, explore all the areas of mathematics and identify the one that interests you. It can be applied mathematics, pure mathematics, or interdisciplinary, but the chosen field should reflect your interest and expertise.
  • On the selected area, narrow down your focus to a particular problem. Better give preference to your research scope and then pick a topic that has enough resources and is manageable to finish within the timeframe.
  • Conduct a thorough literature review to learn about the current state of research in your chosen field. Find any gaps, issues, or unsolved concerns that can serve as the foundation for your study topic.
  • Create a precise and well-thought-out research question based on your investigation and literature review. Make sure your study question is specific, measurable, achievable, relevant, and time-bound (SMART).
  • Examine the viability of your research topic in terms of the available resources, data, and research techniques. But make sure your topic is reasonable and doable within the scope of your project.
  • Seek feedback from mentors, advisers, or professionals in the field to validate your study topic and improve your ideas. Their thoughts might help you discover potential problems and areas for improvement.

List of the Best Math Research Topics


Math Research Topics

We know the troubles involved in identifying the research paper topics on mathematics. Therefore, here, we have analyzed and prepared a list of amazing math research topics on different themes. Explore the entire list and work on any topic that meets your needs.

Simple Math Research Topics

  1. Study the Artin-Wedderburn theorem.
  2. Examine the key principles of calculus.
  3. Explore the Jacobson density theorem.
  4. Evaluate the various ways to calculate net worth.
  5. Discuss the significance of the Binomial theorem.
  6. Explore the role of statistics in business.
  7. Conduct a comparative analysis of multivariable and vector calculus.
  8. Examine the different ways to identify critical points in graphs.
  9. Discuss the different methods to calculate the slope of a curve.
  10. Conduct a comparative analysis of sine, cosine, and tangent.

Interesting Math Research Ideas

  1. Explore the best ways to solve linear equations.
  2. Figure out the best methods to solve the matrix.
  3. Identify the effective ways to find the probability of rolling two dice.
  4. Compare quadratic and linear equations.
  5. Explore the various mathematical logic theories.
  6. Explain the ways to solve Sudoku with the help of mathematics.
  7. Explore the workings of an acute square triangulation.
  8. Analyze the connection between the Binomial theorem and Pascal’s triangle.
  9. Evaluate the set theory of Georg Cantor.
  10. Study the contributions of Euclid to the mathematics field.

Unique Math Research Paper Topics

  1. Explore the significance of Scholz’s conjecture.
  2. Evaluate the conditions of functional analysis.
  3. Examine the importance of the Tree automation.
  4. Evaluate the De Finetti theorem in probability and statistics.
  5. Study the concept of hyperboloid in 3D geometry.
  6. Explore Sphericon.
  7. Analyze the Diophantine Equations and find their solutions.
  8. Examine the applications of modular arithmetic in cryptography.
  9. Focus on the Riemann Hypothesis and its implications.
  10. Discuss the workings of the Back-and-forth method.
  11. Study stochastic differential geometry.
  12. Examine the theory of linear speedup in mathematics.
  13. Explain geometric flows in the Hermitian Geometry.
  14. Explore the fundamental theorem of Fischer’s natural selection.
  15. Evaluate De Moivre-Laplace theorem.

Also Read: 10 Major Importance of Math in Our Daily Life

Advanced Math Research Topics

  1. Examine the minimum overlap issue.
  2. Describe the Bernoulli scheme.
  3. Analyze the crucial aspects of non-Euclidean geometry comprises.
  4. Figure out the ways to use elementary embedding in model theory.
  5. Explore the different cases of algebraic cycles.
  6. Examine the Fourier series.
  7. Conduct a comparative analysis of various types of knapsack issues.
  8. Discuss the oblivious transfer.
  9. Compare Ruella Zeta and Riemann functions.
  10. Study the basic properties of holomorphic functions.

Applied Math Research Topics

  1. Examine the uncertainty principle.
  2. Assess the statistical signal process.
  3. Examine the dimensions used to investigate fingerprints.
  4. Explore the predictive models.
  5. Analyze the significance of step-stress modeling.
  6. Examine the process of the statistical signal.
  7. Explain the Lorentz-FitzGerald contraction hypothesis in relativity.
  8. Evaluate the rule of the perpendicular axes.
  9. Describe the best ways to solve simultaneous equations.
  10. Identify the use of algorithms in probabilistic modeling.

Algebra Research Topics

  1. Analyze the Abel-Ruffini theorem.
  2. Discuss the Morita duality in algebraic structures.
  3. Analyze and describe the Noetherian ring.
  4. Focus on the representation of linear algebraic groups.
  5. Study algebraic invariants of topological structures.
  6. Examine the usage of F-algebras.
  7. Present a two-dimension analysis of the Gram-Schmidt process
  8. Explain the differences between eigen vectors and eigen values.
  9. Conduct a comparative analysis of epimorphisms and monomorphisms.
  10. Discuss the Descartes Rules of Signs.

Math Research Paper Topics on Geometry

  1. Study the real-life uses of a rhombicosidodecahedron.
  2. Explore the Klein bottle.
  3. Examine the reasons for the requirement of n-dimensional vectors.
  4. Present a comparative analysis of various relationships between lines.
  5. Explore the Riemannian manifolds in Euclidean space.
  6. Explore the notions associated with manifolds of Dirac
  7. Analyze the ways to solve Heesch’s problem.
  8. Research the usage of the geometry of M.C. Escher.
  9. Study Archimedean solids.
  10. Evaluate the usage of geometry in the paintings of Picasso

Math Research Ideas on Calculus

  1. Assess the applications of L’Hopital’s rule
  2. Explore the usage of predicate calculus
  3. Evaluate the ratio and root tests
  4. Discuss the extreme value theorem.
  5. Figure out the best ways to estimate the Taylor series of a function.
  6. Identify the best ways to resolve the phenomenon of Runge.
  7. Analyze the distinctions between algebra, calculus, and trigonometry.
  8. Evaluate the impact of nonstandard analysis on the theory of probability.
  9. Explore how integral becomes inaccurate
  10. Explain how the methods of rings operate

Also Read: 11 Best Math Books To Augment Your Skills

Business Mathematics Research Topics

  1. Study the markup and markdown notions.
  2. Explain how to calculate interest rates easily.
  3. Present thorough research on debt amortization.
  4. Discuss the benefits and downsides of Annuities.
  5. Discuss how to estimate sales tax.
  6. Explain the economic lot scheduling problem.
  7. Provide a comparative analysis of the use of different types of charts.
  8. Investigate the main factors of the stock market crash.
  9. Examine the distinction between a mortgage and a loan.
  10. Conduct a comparative analysis of consumer and business mathematics.
  11. Discuss how loans operate.
  12. Analyze how a critical path analysis works.
  13. Analyze the discount factor.
  14. Discuss the best moment to employ multi-period models.
  15. Investigate how various businesses use statistics.


All the topics and ideas recommended in the list above will help you to come up with a fantastic math research paper deserving of top grades. In case, you require any other original math research paper topics or if you want math research help from an expert, call us immediately.


Jacob Smith Research Paper Topics Reading Time: 7 minutes

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