Patience, effort, and perseverance will lead to….. proven Conjecture!
Mathematics is a fundamental part of life that has its roots in the practical world. Understanding different mathematical concepts and applying logical reasoning to them is the basic requirement of mastering mathematical concepts. Conjecture is one such concept, based on thorough reasoning and brainstorming, and has been widely used in mathematics and other scientific fields for years.
Though the importance of conjectures is not limited to scientific fields, they are widely used in daily-life scenarios. In this article, we have explained certain real-life examples of conjectures. Before covering them, let’s get the hang of their history and meaning.
Understanding the history of Conjecture
In simple terms, Conjecture is an educated guess backed up by relevant and informative data and has the potential to get proven or demonstrated. Mathematicians constantly work hard to prove or refute the mathematical statements or judgments proposed several years back but have not yet been proven. Once that statement or a judgment is proved, it will be called a theorem.
Concluding conjectures is necessary, as conjectures pave the way to various important scientific and mathematical discoveries that can benefit humankind. Conjectures are those lighthouses that, once discovered and operated, will brighten the secrets of a large part of the sea (fields of mathematics).
Mathematical history is full of interesting yet brain-stimulating conjectures. Some of those conjectures were solved relatively fast, and some took more than 100 years and the brainstorming of various legendary mathematicians to conclude. The interesting part is some of the conjectures that originated several years back are not yet solved!
Some popular conjectures in the history of mathematics are-
- Fermat’s theorem: Before delving deep into Fermat’s theorem, notice that it is a theorem; that is, it is a proven conjecture. It took 300 years and the joint efforts of several great mathematicians of various decades to finally solve Fermat’s problem. Fermat’s theorem was based on number theory, and solving the problem led to the development of cryptography methods.
- Poincare problem: Originated in 1904 by the French scientist Henri Poincare, the problem focused on the characteristics of a sphere in three dimensions. After 20 failed attempts, and several ups and downs, the problem was finally solved by a Russian mathematician, Grigori Perelman, in 2003. However, the efforts of various mathematicians throughout the years led Perelman to the final step of solving the problem.
- Riemann Hypothesis: Riemann hypothesis is still a hypothesis, and efforts to solve it are constantly being made. The Riemann hypothesis was devised in 1859, focusing on prime numbers. The problem focuses on explaining how the prime numbers are distributed among all the integers, in real life or in theory. After various efforts and attempts, several pieces of evidence to solve the problem have occurred, but the problem remains unsolved.
The list of conjectures is indeed interesting and a long one. We hope that by now you have a solid idea of what conjectures are.
Real-life examples of Conjectures
Conjectures are not limited to theoretical aspects of mathematics and scientific fields; they have their uses in multiple practical fields and scenarios. Some real-life examples of conjectures are-
1. Algorithms and Heuristics in computer science
Computer science is an ever-blooming field where discoveries are made almost every day. Those discoveries are not the result of one or two days of hard work. Various conjectures are proposed regarding the suitability and effectiveness of the algorithms and heuristics, which are then rigorously tested, and then finally proved and applied in computer science, resulting in great discoveries.
2. Studying market trends
Marketing behavior or trends is dynamic. One day it’s blooming like a flower, and the other, it sinks like a heavy stone. Studying and predicting market behavior requires conjectures. Based on the available data and information, conjectures can help forecast the market trends and make the necessary requirements in case of need.
3. Evolutionary theories
A widely discussed theory of evolution states that human ancestors were apes. Over thousands of years, we have evolved from apes to humans in physical appearance, skills, and intelligence. It is a conjecture, an educated guess backed up by some evidence, though still not proven. Similarly, various conjectures on evolutionary theories are useful to enhance human knowledge and shed light on the secrets of human existence.
4. Study of extinct species or genetics
Dinosaurs are considered to be the most fearful creatures to have ever existed on the planet Earth. But have you seen them? Various species are now extinct but were believed to be present thousands of years back. There is no proof that dinosaurs roamed the planet ever or how they disappeared from the face of the planet. But various hypotheses or conjectures focus on their existence, and to prove the said conjectures, scientists are constantly working.
5. Drug testing and development
Conjectures or hypotheses regarding the effectiveness and potential use of the drug are important to further develop and test the drugs or medicines. The conjectures also help in further experimentation and performing necessary changes to the drug to make it suitable for use.
6. Artificial intelligence
Various softwares and models that operate on artificial intelligence technology have been designed and developed. Before designing and developing such machine learning models, scientists form certain conjectures for their practicality, usefulness, and applicability. Those conjectures are also useful for future discoveries in artificial intelligence.
The multiverse theory, a highly fascinating theory with lots of potential, is a conjecture based on proven quantum mechanics. Various other conjectures related to the universe exist that scientists constantly test and try to prove.
8. Finding secrets of oceans
Oceans are mysterious, and several conjectures revolve around oceans’ secrets. These conjectures are not just some fun or interesting flukes to attract people towards oceans and oceanography; rather, several pieces of evidence exist behind those conjectures that help in scientifically exploring the depths of the oceans to prove the findings of the oceans.
9. Archaeological research
Conjectures are widely used in archaeological research. The evidence, such as ancient objects, monuments, etc., of rich heritage and vast history of humankind are constantly being found, though one can never be sure of the history of those ancient objects or monuments. Archaeologists form various conjectures and work according to them to make sense of the found evidence and carry out future research.
10. Product designing
Product designing is another highly common real-life example of conjectures. Businesses or companies launch products only after constantly searching and understanding various market and consumer factors. Those factors are not concrete, resulting in companies or businesses developing conjectures. The formed conjectures act as a blueprint for present and future actions and outcomes, respectively.
Conjectures are a part of daily life. Conjectures play a significant role in human life, from making crucial decisions and solving a problem to forming lasting interpersonal relationships. They are also valuable tools for exploring new possibilities. Conjecture is a great example of discovery-based learning and represents problem-solving skills in action. It works as a map that helps scientists or laymen to identify paths toward discoveries.
I am Sehjal Goel, a psychology student, and a writer. I am currently pursuing my Masters’s from Banaras Hindu University, Varanasi. Child psychology has always fascinated me and I have a deep interest in learning about disabilities in children and spreading awareness regarding the same. My other areas of interest are neuropsychology and cognitive psychology. Connect me on Linkedin