Can Maths Be Self Taught? (Solved & Explained)

I often get emails asking if possible to be a self-taught mathematician and possible to avoid going to college

In this article, we’ll discuss if possible maths can be self-taught.

Yes, maths can be self-taught, will take perseverance and effort through reading maths books and practising problems but can be done.

Students who are interested in pursuing a career as a Mathematician should take as many mathematics courses in high school as possible.

Some problems study maths because they enjoy it. Studying maths for fun!

Many students find mathematics hard because it is abstract, and the more advanced maths one studies the harder it gets.

But that does not mean students don’t want to progress to being a mathematician.

Yes, it’s possible to become a self-taught mathematician. It will take an enormous amount of effort and time but can be achieved.

Becoming a mathematician takes around 10 years of learning and practising mathematics.

Students typically need a Master’s Degree to become a mathematician.

No easy task!

Then there is the expensive of having to pay tuition fees and boarding plus living costs.

Hard enough to study mathematics at college then being self-taught is much harder.

To be honest, the chances of becoming a self-taught mathematician are pretty slim.

But don’t let me put you off, if you have the desire and means by doing so, go for it !!

The easiest way to self-learn Maths (Explained)

There are many good books available explaining mathematics so don’t have too far to find a specific book.

The range of mathematics books now available is enormous.

This list just contains a few suggestions that you should find helpful

A list which is by no means exhaustive, but some popular well-known titles.

Recreational Books

The Colossal Book of Mathematics M. Gardner (Norton 2004)

Over 700 pages of Gardner for under 20 pounds is an astonishing bargain.

You will be hooked by the very first topic in the book if you haven’t seen it before (and probably even if you have): a diophantine problem involving a monkey and some coconuts — can’t say more without writing a spoiler.

In the beginning, about 60 other books by Martin Gardner are listed, none of which will disappoint.

Problem Solving Through Recreational Mathematics Bonnie Averbach & Orin Chein (Dover 2000)

One can never have enough maths puzzles! This is another great collection, from easier ones to some that will leave you stumped, through quite enough variety to please all tastes and to give an introduction to all the main areas of mathematics while you have fun making your way through it.

Lots of practice problems, and hints and solutions to most puzzles.

Game, Set and Math. I. Stewart (Penguin, 1997)
Stewart is one of the best current writers of mathematics (recreational or otherwise).

This collection (which includes a calculation which shows why you need only be marginally the better player to win a tennis match — whence the title) was originally written in French: some of the puns seem to have suffered in translation, but the joie de vivre shines through.

You might also like Stewart’s book on Chaos, Does God Play Dice? (Penguin, 1990).

Excellent writing again but, unlike the chaos books mentioned below, no colour pictures.

The title is a quotation from Einstein, who believed (probably incorrectly) that the answer was no; he thought that theories of physics should be deterministic, unlike quantum mechanics which is probabilistic

How to Think like a Mathematician Kevin Houston (CUP, 2009)

There is lots of good mathematics in this book (including many interesting exercises) as well as lots of good advice.

How can you resist a book the first words of which (relating to the need for accurate expression) are:

Question: How many months have 28 days?
Mathematician’s Answer: All of them

Undergraduates Books

Mathematics: Queen and Servant of Science E.T. Bell (Spectrum, 1996)

Another old gem. An absorbing account of pure and applied mathematics from the geometry of Euclid to that of Riemann, and its application in Einstein’s theory of relativity.

The twenty chapters cover such topics as algebra, number theory, logic, probability, infinite sets and the foundations of mathematics, rings, matrices, transformations, groups, geometry, and topology.

As Martin Gardner says in the foreword: “This continues to be one of the finest of all introductions to the rich diversity of those fantastic structures that mathematicians invent, explore, and apply with such mysterious success to the huge unfathomable world outside the little organic computers at the top of their heads”.

Makers of Mathematics S. Hollingdale (Penguin, 1989)

There are not many books on the history of mathematics that are pitched at a suitable level.

Hollingdale gives a biographical approach that is both readable and mathematical.

An Outer View of the Inner World Mariana Cook (Princeton University Press, 2009)

Another, more modern, biographical approach.

This book gives a compelling and immediate introduction to some of the most amazing mathematicians of our time, not just through a glimpse of their brilliant mathematical work, but also of their experience as fathers, daughters, husbands, wives…

Each portrait is personal and in the voice of the mathematicians themselves.

You will find out what inspired them to pursue maths, and no doubt be inspired yourself to participate in the joy of mathematical discovery.

A Russian Childhood S. Kovalevskaya (trans. B. Stillman) (Springer, 1978)

Sonya Kovalevskaya was the first woman in modern times to hold a lectureship at a European university: in 1889 she was appointed a professor at the University of Stockholm, even though she was a woman (with an unconventional private life), a foreigner, a socialist and a practitioner of the new Weierstrassian theory of analysis.

Her memories of childhood are non-mathematical but fascinating.

She discovered in her nursery the theory of infinitesimals: times being hard, the walls had been papered with pages of mathematical notes.

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Alan Turing, the Enigma A. Hodges (Vintage, 2014)

Great biography of Alan Turing, a pioneer of modern computing.

The title has a double meaning: the man was an enigma himself, and the German code that he was instrumental in cracking was generated by the Enigma machine.

The book is largely non-mathematical, but there are no holds barred when it comes to describing his major achievement, now called the Turing machine, with which he demonstrated that a famous conjecture by Hilbert is false.

The Man Who Knew Infinity R. Kanigel (Abacus, 1992)

The life of Ramanujan, the self-taught mathematical prodigy from a village near Madras.

He sent Hardy samples of his work from India, which included rediscoveries of theorems already well known in the West and other results which completely baffled Hardy.

Some of his estimates for the number of ways a large integer can be expressed as the sum of integers are extraordinarily accurate but seem to have been plucked out of thin air.

Hardy was one of the best mathematicians of the first part of this century.

Always an achiever (his New Year resolutions one year included proving the Riemann hypothesis, making 211 not out in the fourth Test at the Oval, finding an argument for the non-existence of God which would convince the general public, and murdering Mussolini), he led the renaissance in mathematical analysis in England.

Graham Greene knew of no writing (except perhaps Henry James’s Introductory Essays) which conveys so clearly and with such an absence of fuss the excitement of the creative artist.

There is an introduction by C.P. Snow.

The man who loved only numbers Paul Hoffman (Fourth Estate, 1999)

An excellent biography of Paul Erd ̈os, one of the most prolific mathematicians of all time.

Erd ̈wrote over 1500 papers (about 10 times the normal number for a mathematician) and collaborated with 485 other mathematicians.

He had no home; he just descended on colleagues with whom he wanted to work, bringing with him all his belongings in a suitcase.

Apart from details of Erd ̈os’s life, there is plenty of discussion of the kind of problems (mainly number theory) that he worked on.

Surely You’re Joking, Mr Feynman R.P. Feynman (Arrow Books, 1992)

Autobiographical anecdotes from one of the greatest theoretical physicists of the last century became an immediate best-seller.

You learn about physics, about life and (most puzzling of all) about Feynman. Very amusing and entertaining

Final Thoughts

Yes, mathematics can be self-taught. It will require persistence and effort to study math books and practise problems, but it is possible.

So yes, there is plenty of material available to teach yourself maths.

It will take determination and time to self-learn math and even more if you want to become a self-taught mathematician.

The odds will be stacked against you but if you have a strong desire, time and resources it can be achieved.

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