Proofs in Mathematics – Why are they so important and How do they drive our world?

A mathematician is a master of critical thinking, of analysis, and of deductive reasoning. The Mathematics skills travel well, and can be applied in a large variety of situations; and in many different disciplines. Today, mathematical skills are being put to good use in medicine, physics, law, commerce, Internet design, engineering, chemistry, biological science, social science, anthropology, genetics, warfare, cryptography, plastic surgery, security analysis, data manipulation, computer science, and in many other disciplines and endeavors as well.

Proof’s Triumph: Elevating Mathematics Above Other Disciplines

The unique feature that sets mathematics apart from other sciences, from philosophy, and indeed from all other forms of intellectual discourse, is the use of rigorous proof. It is the proof concept that makes the subject coherent, that gives it its timelessness, and that enables it to travel well.

Proof is the heart of mathematics. It distinguishes mathematics from the sciences and other disciplines. Courts of law deal with the burden of proof, juries having to decide whether the case against a defendant has been proven beyond a reasonable doubt. That remaining element of doubt is not acceptable in mathematics. A Mathematical proof must be watertight, establishing the truth of the statement beyond any doubt.

Evolving Theories: The Dynamic Engine of Knowledge Advancement

Experts advance theories based and supported by all available evidence. A given theory will survive for the test of time as long as no evidence is found to cast doubt on it. When there is doubt, experts will conjecture new theories that take into account the latest information. It is in this way that knowledge and learning advances.

A classic illustration of this occurred in 1543 when Copernicus proposed that the earth and the planets orbited the sun, contrary to the scientific belief at that time where the Ptolemaic view was that the sun, moon and stars revolved around the earth.

Nicolaus Copernicus

Nicolaus Copernicus, born on 19th February 1473 and passing away on 24th May 1543, was a person of many talents during the Renaissance. He worked as a mathematician, astronomer, and Catholic canon. Copernicus came up with a new idea about how the universe works. He suggested that the Sun is at the center of the universe, not the Earth. This was different from what most people believed at that time. Interestingly, Copernicus thought of this idea on his own, without knowing about an ancient Greek astronomer named Aristarchus of Samos, who had a similar idea about 1800 years before him.

So what do we mean by a proof?

Put simply, a proof is a chain of reasoning that establishes the truth of a particular statement or a proposition.

There is no other scientific or analytical discipline that uses proof as readily and routinely as does mathematics. This is the device that makes mathematics special: the chain of reasoning, following strict logical rules, that leads to a particular conclusion. It is proof that is our device for establishing the absolute and irrevocable truth of statements in our subject. This is the reason that we can depend on mathematics that was done by Euclid 2300 years ago as readily as we believe in the mathematics that is done today. No other discipline can make such an assertion.


Learning Mathematics can open many career opportunities and doors in the future. Why not connect with us or visit our Tutoring center in Motor City for more information on how Discover Learning can help your child and to book your no-obligation, free trial.

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