From the beginning of human existence, numbers have always been captivating. This attracted popular thinkers to solve the underlying mysteries with natural numbers. Being the global natural language, mathematics has many branches with the oldest as number theory (Zhao et al. 46). Every generation of mathematics experts is fascinated by number assumptions. A good comprehension of this theory is significant in many fields today such as software engineering. Being the king of pure math, number theory forms the basis of cryptography which is taking a great revolution in recent days. There are two different periods in history that represent the evolution of number theory. First was the invention of the greatest common divisor algorithm which is a strategy to simplify fractions by the use of geometrical viewing. This method of working with numbers step by step has always been used in calculations of area, volumes, and lengths. The second important period was the formalization of existing scattered methods while providing the answers to unsolved mathematics problems. This was a breakthrough in mathematics because it formed the foundation for future mathematicians.
There are many devised theorems in mathematics with each having its inventor. The arithmetic theorem links prime and natural numbers stating that exceptional products of prime can represent integers larger than one. This theorem joins unusual things with natural and regular numbers. Spacing between natural numbers follows a regular trend while serial prime numbers vary (Bansal et al., 2019). The algebra theorem associates zeros with polynomials and states that numbers alone are not sufficient to form algebraic equations. The foundation of the algebra theorem is the need for complex numbers when evaluating all roots.
In the composite number system, every nonconstant has exactly n roots. The theorem is also classified as being existence because it states that the roots are there but does not guide on tracing them. The calculus theorem links integrals and derivatives thus it is all about the connection of change and accumulation. The theory states that it is not obvious for integrals and derivatives to be related but the degree of change of any integral is a result of the function of the collected values. The theorem has a defined computational tool where integrals can be devised through the construction of antiderivatives.
The linear algebra theorem is essential in mathematics for relating the row space of an object with its null space. Subspaces are major concerns of this theorem where some are said to be orthogonal. Pythagoras’ hypothesis deals with triangles and outlines that the square of a hypotenuse is the same as the square of the two other sides in any right-angled triangles. It lists a computational method of calculating the lengths of sides and thus it is not grouped as an existential aspect. Geometry being one of the important sections of mathematics has the midpoint theorem. The theory is prominent in coordinate geometry and argues that the midpoint of a line section is typical of the endpoints (Kitzes, 2017). There must be two known terms in the process of using this theorem. Notably, this theory is incorporated with other theories majorly algebra and calculus.
The binomial hypothesis notes that a rise in power results in a lengthy expansion thus complicating a calculation. The theorem assists in the expansion of any equation which is elevated to any fixed power. The greens theorem is also popular in mathematics because it shows the relationship between a surface and line integral. The theory makes it easier to incorporate derivatives in a particular plane. Given a line integral, translating it into a surface or double integral is possible using the greens theorem.
Experts in mathematics are viewed to be of high intellectual capacity and had a great contribution to the statistics field. George Boole English man was a renowned mathematician whose work revolved around logical ideas. His logic work developed Boolean algebra which is the center of every math. Although he wasn’t professionally trained in mathematics he acquired knowledge through the class session he handled as a school teacher to perfect his mathematical skills. He played a key role in providing materials on linear transformation and differential equations for the mathematical journal of Cambridge (Wasserman et al. 78). His mathematics effort was recognized with an award of gold medal for his expertise in merging calculus algebra. It became evident that logic should be associated with math and not philosophical science. Its evident Boolean work had a positive impact and this contributed greatly to the development of mathematics. His effort led to his promotion to head of mathematics and later received an honorary degree. Many probability theories of statistics use the basis of Boolean algebra.
German mathematician Leonhard Euler is known to take part in the formation of every section of mathematics. He had a powerful skill of high memory and concentration that would enable him to recite a complex set of numbers. Euler number which was named after him plays a significant role in mathematics. He made several notable contributions to mathematics that set a foundation in statistics and probability studies. He introduced Greco-Latin squares that are used for design in other disciplines. Euler emphasized the problems associated with observational error and math statistics that can ruin a good structure model. A notable contribution in the field of mathematics was the innovation of the calculus of deviations.
Carl Gauss is another prominent personality in the field of mathematics. He invented the Gauss distribution concept which is very essential in probability and statistics (Schukajlow et al. 317). Gauss founded the algebraic theorem that brings the notion of more than one solution to any algebra equation. The idea of fitting a line to data points commonly used in reversion breakdown is attributed to Gauss since he introduced the least-squares method. Nevertheless, Carl was the first human to identify a pattern in prime numbers and this is a major idea in mathematics.
Another major contributor in the field of mathematics is Gottfried Leibniz. He is considered the forefather of today’s reasoning and systematic theories (Kitzes et al.,2017). The development of calculus is a significant achievement attributed to Leibniz. By inventing a number the counting machine, he is known as the grandfather of computing due to the great ideas he incorporated into the progression. While developing the counting machine, he laid a strong foundation for combinations and complex probabilities. Gottfried drafted several properties of sets among them uniqueness, disjunction, union, and void set. John Venn was another remarkable person in mathematics by invented the Venn diagrams used in the rationality and possibility of sets. He is also known for his statistical book; the logic of sense which majorly outlines the idea that forecasting is the best way of determining probability rather than using learned assumptions. His diagrams are vastly used in various calculations, for example, while working with sets.
Works Cited
Bansal, Kshitij, et al. “HOList: An Environment for Machine Learning of Higher-Order Logic Theorem Proving.” International Conference on Machine Learning. PMLR, 2019.
Kitzes, Justin, et al., editors. The Practice of Reproducible Research: Case Studies and Lessons from the Data-Intensive Sciences. Univ of California Press, 2017.
Schukajlow, Stanislaw, et.al. “Emotions and Motivation in Mathematics Education: Theoretical Considerations and Empirical Contributions.” ZDM 49.3 (2017): 307-322.
Wasserman, Nicholas, et al. “Mathematics Teachers’ Views about the Limited Utility of Real Analysis: A Transport Model Hypothesis.” The Journal of Mathematical Behavior 50 (2018): 74-89.
Zhao, Jing, et al. “Multi-View Learning Overview: Recent Progress and New Challenges.” Information Fusion 38 (2017): 43-54.