# 30+ New Math Extended Essay Topic Ideas

Writing a 4000-word math extended essay may seem ridiculous. Math may be a highly practical subject, but theoretical study on mathematics-related concepts cannot be written off.

There exists a myriad of these concepts, consider the brief list below:

• Math Constants – Explore various constants, their history, properties, and applications in different fields. Eg. 𝝿 (pi), e (euler’s number), and φ(golden ratio).
• Number Theory – Investigate aspects of prime numbers, number sequences, and theorems in number theory such as Fermat’s Last Theorem.
• Geometric Applications – Explore application of geometry in modern and ancient art as well as in architecture.
• Probability Theory – Delve into statistical forms; standard variation, variance, mean etc.
• Calculus – Write a math extended essay on the fundamental theorem of calculus; its history, proof, and application, along with concepts like differentiation, integration, optimization, and their application in other industries.
• Graph Theory – Study the various types of graphs; eulerian, hamiltonian, tree etc. You can also look into graph algorithms and network flow theorems.
• Fractals – Explore various fractal dimensions such as Mandelbrot and Julia sets, and the application of Fractals in art.
• Game Theory – Analyze the different theorems in the game theory; Nash Equilibrium, Prisoner’s Dilemma, Evolutionary Game Theory etc, and examine possible niche of game applications in the emerging Artificial Intelligence (AI) technology.
• Coding Theory – Explore math-computer science concepts like Error Correcting Codes, Linear Codes, Non-linear Codes, Performance Analysis, as well as future trends in coding theory.
• Linear Algebra – Investigate linear transformations, matrix factorization,  Eigenvalues and Eigenvectors, together with the extended application of algebra in computer science, cryptography, computer graphics, and AI.
• Complex Analysis – Research complex analytical theorems like the Cauchy-Riemann Equations, Gamma Function, Residue Theory, and immense application of Complex Analysis in Fluid Dynamics, Quantum Mechanics, Fractal Geometry, Number Theory, Electrical Engineering, and Signal Processing.
• History of Mathematics – Track the journey of math all the way from Ancient Times, Islamic Golden Age, Renaissance, Modern, and Contemporary Mathematics in your math extended essay.
• Mathematical Analysis – Explore multitudes of mathematical analytical methods such as Calculus, Riemann Hypothesis, Fourier Analysis, Lebesgue Integration and Measure Theory, Complex Analysis, Functional Analysis and many more.
• Cryptanalysis – Research the modern cryptanalysis techniques, Frequency Analysis, Major Codebreaking Milestones, as well as the interaction of Cryptanalysis with other computer-mathematical concepts such as Information Theory, Quantum Computing, Steganography, and Cryptocurrency.

The above list seems to serve justice right? Not yet. We are yet to give you the 30 direct topics you can immediately dive into.

Here they are:

## 30+ Math Extended Essay Topics

1. Exploring the mathematical properties and applications of fractals.
2. Analyzing the mathematics behind encryption algorithms like RSA or AES.
3. Investigating the history and significance of Fermat’s Last Theorem.
4. Exploring the mathematics of origami and its applications.
5. Analyzing the concept of infinity and its various mathematical implications.
6. Investigating the mathematics of music theory and harmony.
7. Exploring the mathematics of prime numbers and their distribution.
8. Analyzing the use of mathematical modeling in predicting the spread of diseases.
9. Investigating the mathematics behind the concept of chaos theory.
10. Exploring the applications of game theory in real-world scenarios.
11. Analyzing the mathematics of graph theory and its applications.
12. Investigating the concept of non-Euclidean geometry and its implications.
13. Exploring the mathematics of cryptography and its role in secure communication.
14. Analyzing the mathematics behind the traveling salesman problem and its solutions.
15. Investigating the use of mathematical modeling in climate change predictions.
16. Exploring the mathematics of symmetry and its applications in various fields.
17. Analyzing the history and significance of Euler’s formula.
18. Investigating the mathematics of data compression techniques.
19. Exploring the mathematics of complex numbers and their applications.
20. Analyzing the mathematics of number theory and its significance.
21. Investigating the concept of mathematical proof and its role in mathematics.
22. Exploring the mathematics of network theory and its applications in social networks.
23. Analyzing the use of mathematical optimization in resource allocation.
24. Investigating the mathematics of statistics and its role in data analysis.
25. Exploring the mathematics of differential equations and their applications.
26. Analyzing the mathematics behind the Monty Hall problem and its solutions.
27. Investigating the concept of mathematical symmetry groups and their properties.
28. Exploring the mathematics of chaos theory and its applications in various fields.
29. Analyzing the use of mathematical modeling in financial markets.
30. Investigating the mathematics of quantum mechanics and its mathematical foundations.

Do not get it wrong, because it’s a math extended essay does not mean there will be no practical calculations within. If your topic has anything to do with math equations then definitely you can not evade calculations.

However, if you are in need of help with either the essay, calculations, or the entire EE altogether, we are here for you. Our star team is ready to crunch the numbers for you as well as draw a good math extended essay to put you in A-grade positions. You only have to reach out.