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Math Blab

A Blog for Math & Science

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2021-07-30 20:12:45

    What is Math?

    Mathematics is everywhere and we all learned it at some point, but what is mathematics, really? A search on the internet will yield many different interpretations. According to Google, mathematics is “the abstract science of number, quantity, and space.” Here is a collection of how some of history’s greatest minds described mathematics.

    An intellectual game
    “Mathematics is a game played according to certain simple rules with meaningless marks on paper.”—David Hilbert

    “Pure mathematics is the world’s best game. It is more absorbing than chess, more of a gamble than poker, and lasts longer than Monopoly. It’s free. It can be played anywhere—Archimedes did it in a bathtub.”—Richard J. Trudeau

    “Mathematics is about making up rules and seeing what happens.”—Vi Hart

    “Mathematics is like checkers in being suitable for the young, not too difficult, amusing, and without peril to the state.”—Plato

    “Mathematics is an independent world created out of pure intelligence.”—William Woods Worth

    A tool for the sciences
    “Mathematics is the tool specially suited for dealing with abstract concepts of any kind and there is no limit to its power in this field.”—Paul Dirac

    “Our physical world doesn’t have just some mathematical properties, it has only mathematical properties.”—Max Tegmark

    “Mathematics serves as a handmaiden for the explanation of the quantitative situations in other subjects …”—H. F. Fehr

    “In order to understand the universe, you must know the language in which it is written. And that language is mathematics.”—Galileo

    A search for pattern, order, and structure
    “A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.”—G. H. Hardy

    “Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them.”—Joseph Fourier

    “Go down deep enough into anything and you will find mathematics.”—Dean Schlicter

    Logic and reasoning
    “All Mathematics is Symbolic Logic.”—Bertrand Russell

    “Pure mathematics is, in its way, the poetry of logical ideas.” –Albert Einstein

    “Mathematics is the supreme judge; from its decisions there is no appeal.“—Tobias Dantzig

    Which do you believe best describe math?

    Mathematics can, on the one hand, be thought of as an incredible lens through which to see the world; an important knowledge available to all, that promotes empowered young people ready to think quantitatively about their work and lives and that is equitably available to all students through study and hard work. On the other hand, mathematics can be thought of as a subject that separates children into those who can and those who cannot, and that is valuable as a sorting mechanism, allowing people to label some children as smart and others as not smart.

    — Jo Boaler, Mathematical Mindsets

    Fractal Geometry – The Geometry of Nature

    Self-similarity, the property of exhibiting patterns that repeat on different scales, is evident just about everywhere you look. Objects with this property are known as fractals thanks to the work of mathematician Benoît Mandelbrot in 1975.

    Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line… Nature exhibits not simply a higher degree but an altogether different level of complexity. The number of distinct scales of length of natural patterns is for all practical purposes infinite. The existence of these patterns challenges us to study these forms that [traditional plane geometry] leaves aside as being ‘formless’. – Benoît Mandelbrot

    1729

    The number 1729 has an interesting story in mathematics involving the extraordinary Indian mathematician Srinivasa Ramanujan. G. H. Hardy accounts:

    “I remember once going to see him (Ramanujan) when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to be rather a dull one, and that I hoped it was not an unfavourable omen. ‘No’, he replied, ‘it is a very interesting number; it is the smallest number expressible as the sum of two [positive] cubes in two different ways.’”

    Ramanujan had a knack for numbers. Growing up in India at the turn of the 20th century, Ramanujan was largely self-taught. Over his short life time (aged 32), he independently developed nearly 4,000 results in mathematics. He kept his results (without proofs) in notebooks that modern mathematicians are still looking into this day. Nearly all of his results have been proven to be true and have driven research in number theory for the past century. Recently, one of Rumanujan’s results, previously unknown to mathematicians, was an important piece to a 2006 publication.

    More at https://en.wikipedia.org/wiki/Srinivasa_Ramanujan

    “[Mathematics] is the work of the human mind, which is destined rather to study than to know, to seek the truth rather than to find it.”

    — Évariste Galois | Mathematician, who by age 20, solved the 350 year old problem of describing which polynomials are solvable by radicals (turns out there are only nice general formulas [like the quadratic formula] up to degree 4)