The best way to respond to: is mathematics useful to a variety of people without knowing the proofs?

Yes, mathematics is useful to a variety of people without knowing the proofs as it helps in problem-solving, decision-making, analysis, and critical thinking.

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Mathematics has always been regarded as an instrumental tool in various fields of life, such as science, engineering, economics, and finance, to name a few. From the simple calculation of everyday life to advanced scientific discoveries, math is everywhere. Fortunately, using algebra, geometry, calculus, and other mathematical concepts do not necessarily require one to know all the nitty-gritty details about every theorem and proof from their respective books. People who do not know how to prove theorems, still find math very pertinent to their life, passions, and career.

In fact, using math to solve problems, analyze situations, and make informed decisions is the crucial aspect, mastering the proof is merely a part of the process. As scientifically expressed by Carl Friedrich Gauss, “Mathematics is the queen of sciences and arithmetic the queen of mathematics.” In essence, mathematics is not only about finding the correct answer to a problem but also the process used to reach that solution is crucial. Hence, regardless of one’s mathematical proficiency, knowing the fundamental structure and foundation of math is of utmost importance.

Interesting facts about the utility of math without proofs include the following:

  1. Despite being a theoretical physicist, Albert Einstein was also skilled in mathematics and has contributed remarkably to calculus, geometry, and algebra.

  2. Math is very much relevant to art as well. Fractals, for instance, are known for the beautiful design patterns that are an extension to the concept of self-similar geometric shapes with intricate structures.

  3. The International Mathematical Olympiad is arguably the most famous math competition globally and is held annually. It is sponsored by the International Mathematical Union and is considered to be the most prestigious academic competition for high school students.

  4. Apple co-founder Steve Jobs once said, “I think everybody in this country should learn how to program a computer because it teaches you how to think.” This holds true not only for programming but also for math.

  5. Mathematics has applications across environments such as medicine, finance, architecture, sports, and other fields apart from science and engineering.

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Here’s an example of a table demonstrating the utility of math without proofs:

Field Utility of Math
Engineering Engineers use math to design, test, develop machines, and other equipment.
Business and finance Math is critical in understanding and analyzing data, making informed decisions, and performing financial analysis.
Art Fractals, geometry, and other mathematical concepts are the fundamental structures of modern art.
Sports Statistical modeling and analysis, geometry, and calculus are essential in sports, analyzing performance, evaluating risk, and making strategies.
Medicine Medical image processing, algorithm design, and statistical analysis all have their basis in math.

In Conclusion, Mathematics is a versatile tool used to solve real-world problems. The ability to prove a theorem is not the only parameter to gauge mathematical proficiency. In addition to memorizing theorems, understanding the logic, and reasoning ability is also essential. As Richard Feynman, a Nobel Prize-winning theoretical physicist, rightly stated, “I learned very early the difference between knowing the name of something and knowing something.”

See a video about the subject.

In the YouTube video “Anyone Can Be a Math Person Once They Know the Best Learning Techniques | Po-Shen Loh | Big Think”, Po-Shen Loh argues that anyone can understand mathematics if they focus on the principles of reasoning and learn at their own pace. He believes that this would make mathematics the easiest subject to understand.

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Proofs are important because proofs are just understanding how we know that something is true. This is what mathematics is all about!

What if all you care about is using the results of mathematics: you don’t particularly care about why it works, just how to use it. Should you still care about proofs?


I am teaching infinite series in calculus at the moment, so I will use an example from this subject to illustrate some reasons why.

One result which is important in the study of infinite series is that if a and r are two real numbers then:

a+ar+ar2+ar3+ar4+⋯=a1−r if −1<r<1.

I am sure you will be interested in these topics as well

Why are proofs important in mathematics?
According to Bleiler-Baxter & Pair [22], for a mathematician, a proof serves to convince or justify that a certain statement is true. But it also helps to increase the understanding of the result and the related concepts. That is why a proof also has the role of explanation.
What is math accepted without proof?
Statements which are assumed to be true without mathematical proof are said to be axioms.
How useful is mathematics?
As a response to this: It gives us a way to understand patterns, to quantify relationships, and to predict the future. Math helps us understand the world — and we use the world to understand math. The world is interconnected. Everyday math shows these connections and possibilities.
Why is mathematics important to humans?
As a response to this: Mathematics provides an effective way of building mental discipline and encourages logical reasoning and mental rigor. In addition, mathematical knowledge plays a crucial role in understanding the contents of other school subjects such as science, social studies, and even music and art.
What is mathematical proof?
Response: mathematical proofis an argument which convinces other people thatsomething is true. Math isn’t a court of law, so a “preponderance of theevidence” or “beyond any reasonable doubt” isn’t good enough.
Is math proof good for a kid?
As an answer to this: Learning how to come up with a math proof is good for a kid. It’s a problem-solving activity. Students believe what they are told by their teachers, especially in math class, and with good reason because math teachers rarely teach an untrue theorem, and proofs often are used instead of good explanations.
What is mathematics and why is it important?
Mathematics is about understanding the laws behind numbers, algebra and geometry. It is about nding new and non routine ways to look at these systems and to explain strange phenomena that we may encounter. To make it more interesting, we can even change the laws to create new systems and then study them.
What is a bad argument in mathematics?
Mathematics is really about proving general statements via arguments, usually called proofs. As you no doubt know from arguing with friends, not all arguments are good arguments. A “bad” argument is one in which the conclusion does not follow from the premises, i.e., the conclusion is not a consequence of the premises.
Can mathematical proofs connect purely mathematical notions?
Response will be: Mathematical proofs can only connect purely mathematical notions—or so it seems. The received view was that our evidence for Church’s Thesis is quasi-empirical. Attempts to find convincing counterexamples to Church’s Thesis have come to naught.
Is math proof good for a kid?
The reply will be: Learning how to come up with a math proof is good for a kid. It’s a problem-solving activity. Students believe what they are told by their teachers, especially in math class, and with good reason because math teachers rarely teach an untrue theorem, and proofs often are used instead of good explanations.
What is an example of a mathematical proof?
Answer will be: A mathematical proof is an argument that deduces the statement that is meant to be proven from other statements that you know for sure are true. For example, if you are given two of the angles in a triangle, you can deduce the value of the third angle from the fact that the angles in all triangles drawn in a plane always add up to 180 degrees.
Should I proofread my math?
Proofread!When time is short, it may be tempting to finish the last line of your proof, throwon a quick Q.E.D., and hand in your writing, but this is a terrible idea. Math is hard to write,and it is nearly impossible to write it without at least a few typos.

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Such different mathematics