Question

life is made beautiful by two things studing mathematics and teaching mathematics ..who said these words​

Answer 1

life is made beautiful by twice things studying mathematics and teaching was said by David Pleacher

Answer 2

Answer:

Given below is the answer

Step-by-step explanation:

The aesthetic pleasure that arises from the abstractness, simplicity, depth, or orderliness of mathematics is known as mathematical beauty. For example, G. H. Hardy[1] took the position that mathematics is an art form, or at the very least, a creative endeavour. Mathematicians may also describe mathematics (or, at least, some component of mathematics) as beautiful. There are comparisons with poetry and music. Mathematicians refer to a particularly appealing proving strategy as elegant. Depending on the situation, this could mean:

a demonstration that makes the fewest extra assumptions or previous findings.

A proof that is remarkably short.

a demonstration that yields a conclusion in an unexpected manner (e.g., from an apparently unrelated theorem or a collection of theorems).

a demonstration based on new and original insights.

A method of proof that can be easily generalized to solve a family of similar problems.

In the search for an elegant proof, mathematicians[who?] often[how often?] look for different independent ways to prove a result—as the first proof that is found can often be improved. The theorem for which the greatest number of different proofs have been discovered is possibly the Pythagorean theorem, with hundreds of proofs being published up to date.[2] Another theorem that has been proved in many different ways is the theorem of quadratic reciprocity. In fact, Carl Friedrich Gauss alone had eight different proofs of this theorem, six of which he published.[3]

Conversely, results that are logically correct but involve laborious calculations, over-elaborate methods, highly conventional approaches or a large number of powerful axioms or previous results are usually not considered to be elegant, and may be even referred to as ugly or clumsy.

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