Mathematics plays an important role in today’s world and its diverse applications are everywhere around us. But have you ever wondered which are the most challenging maths?
This article will discuss the hardest maths on Earth and why they are so difficult.
1: Overview of Hard Maths
Maths has been around for centuries but not all maths are equal in terms of difficulty. We can simplify some maths and make them easier and more manageable, but there is a subset of maths which is challenging and mind-bendingly hard.
The most challenging maths endure the test of time because they are not-so-simply solved and they are used in diverse applications.
2: Taxman’s Dream
Probably the king among hard maths is taxman’s dream. It is a type of variational calculus used in tax studies and economics.
It was originally developed to solve a problem posted by the eminent economist Vilfredo Pareto in the early 20th century. The problems posed by this subject are highly complex and require a great deal of mathematical rigor, making it a truly difficult subject to master. The complicated problem posed by this subject can be solved using numerical methods such as the shooting method, the steepest descent method and others.
3: Number Theory
Number theory is the second hardest maths on earth. It takes the form of divisibility, primes, squares, modules and other numerical puzzles.
It is often considered an abstract maths, but it is far from that! In fact, number theory is trusted by cryptographers and computer scientists to keep their data secure. Problems posed by number theory are often difficult to solve and require a deep understanding of abstract mathematical thinking.
4: Algebraic Geometry
Algebraic geometry is an area of maths which combines both algebra and geometry. It deals with equations, curves, surfaces and all kinds of mathematical objects which lie at the intersection of them.
It is a very difficult subject, mostly due to its topological and abstract nature. In order to fully grasp it, one needs to have a solid mathematical understanding and a good grip on abstract thinking.
5: Calculus
Calculus is the language of maths and is used in a vast array of different fields of study and research. It is said to be the single most difficult maths subject and its complexity is only increasing with time. This is because of its highly abstract nature, as well as its vast number of applications.
To be able to understand calculus and to master it, one must spend considerable amounts of time and effort trying to comprehend it.
6: Differential Equations
Differential equations are probably the most challenging of all equations to solve. It is a type of equation which deals with derivatives and requires an understanding of the relationship between an unknown function and its derivatives.
Among the many other applications of this equation, it has been used in practical fields such as engineering, chemistry or physics. Furthermore, due to the complexity of the equation, computer programs have been written to solve it, proving its complexity.
7: Topology
Topology is one of the most difficult math on earth and it is related to geometry, algebra and analysis. It involves the study of shapes and their properties and is a very abstract type of maths. To be able to succeed in topology, one must be able to understand the various properties of shapes, as well as their transformations.
This can prove to be quite a challenge, as it requires a deep understanding of the principles of mathematics.
8: Partial Differential Equations
Partial differential equations (PDEs) are specialized equations which are derived from partial derivatives. These equations involve a complex system of variables and are often used to solve problems related to physics, engineering and chemistry. PDEs are known to be hard equations to solve and it requires a comprehensive understanding of the principles of calculus to be able to work with them.
9: Abstract Algebra
Abstract algebra is an area of maths which deals with algebraic structures such as groups, fields, rings and vector spaces. Problems related to this area can be very difficult to solve and require a deep understanding of abstract mathematics.
Furthermore, the numerous applications of this maths can make it even harder. As such, abstract algebra is one of the most challenging matrices out there.
10: Fourier Analysis
Fourier analysis is an advanced type of mathematics which deals with wave functions. It is used in various applications, such as physics or engineering, where wave functions are necessary to be able to solve problems.
In order to master Fourier analysis, one must be able to understand complex wave equations, as well as the principles of calculus. As such, it is considered to be one of the most difficult maths out there.
11: Combinatorics
Combinatorics is a branch of mathematics which involves the study of combinations and permutations of objects. It can be used to solve problems related to probability and statistics and its applications are vast. The complexity of combinatorics can make it a difficult math to master and usually requires an understanding of basic algebra and calculus.
12: Game Theory
Game theory is a branch of mathematics which deals with decision making and strategy development. Its applications include economics, psychology and engineering, among others.
This type of maths is often considered to be one of the hardest, mostly due to its abstract nature. In order to understand it, one must develop an in-depth understanding of strategy, as well as the principles of game theory.
13: The Bottom Line
In conclusion, while it can be argued that different maths are hard in their own way, the maths discussed in this article are considered to be among the most challenging out there. From calculus to abstract algebra, these maths can cause even the most seasoned mathematicians to break a sweat.
Conclusion
To sum up, the toughest maths on earth are taxman’s dream, number theory, algebraic geometry, calculus, differential equations, topology, partial differential equations, abstract algebra, Fourier analysis, combinatorics and game theory. These maths are known for their complexity and difficulty and require a high level of understanding and proficiency to be able to master them. That being said, it is important to remember that with hard work and dedication, anything is possible.