Whilst most people are happy to leave the academic study of mathematics to university professors and researchers, the history of math includes a lot of amateurs – people who had other jobs and did math as a hobby.

They, as I’m sure you will if you’re reading this, find math to be something much better and more enriching that its reputation would have you believe.

Sometimes, these math enthusiasts conduct pioneering work in math and advance the forefront of knowledge.

Let’s look at some of history’s best amateur mathematicians

**Oliver Heaviside**

I’m sure that most working adults wouldn’t say that their work inspires them into doing mathematics. But that wasn’t the case for one English engineer, Oliver Heaviside.

Heaviside’s formal education started and finished at school in London in the 1860s. He was an exceptional student at school, but at the age of 16 his family could no longer afford to send him to school.

It was then that he then moved into the telegraph industry, where his uncle was an inventor and businessman. But lack of money wasn’t going to stop him learning here!

Whilst working as an electrician, he taught himself mathematics and physics on the side. At first, his research covered practical and experimental electrical results. He wrote regular articles for a trade paper “The Electrician”.

It was in the 1870s he read the great physicist Maxwell’s work on electricity and magnets. He would later rewrite many of Maxwell’s equations into the form we see them now.

The contributions he made to maths and physics earned him an Honorary degree for the University of Gottingen and a Fellowship to the Royal Society (one of the most prestigious academies for British scientists).

His legacy is remembered by his namesake the “**Heaviside Function**” in mathematics. It just goes to show what you can do when you teach yourself a new skill!

**Mary Everest Boole**

Mary Boole was born in Gloucestershire in England in the 1830s and was the niece of George Everest (after whom the mountain was named!)

She became interested in mathematics at an early age when she had private math tuition in France. She was then taught mathematics by another self-taught mathematician George Boole, who would later become her husband.

She was a librarian by trade, but also privately taught mathematics.

She is remembered for the great contributions she made to education and teaching math. Her book “**Philosophy and Fun of Algebra**” pioneered explaining math like algebra and logic to children. This involved including history and telling stories to keep the attention of children.

Furthermore, she contributed to George Boole’s publication “**The Laws of Thought**” as an editor. She frequently advised George Boole on his work and attended his lectures, which was a radical thing for a woman to do at the time.

Her legacy was continued in her five daughters, Alicia, Ethel, Mary Ellen, Margaret and Lucy.

Alicia was an expert in the fourth dimension, Ethel a great author, and Lucy a brilliant chemist. Lucy went on to become the first-ever female Fellow of the Institute of Chemistry.

One of Mary Boole’s grandchildren, Sir Geoffrey Taylor, went on to be “one of the most notable scientists of this [the 20th] century”

Maybe math does run in the genes!?

**Pierre de Fermat**

Fermat was born in Beaumont-de-Lomagne in France in 1607, and whilst being an avid mathematician on the side, was a lawyer by trade. At university, he studied law, and it wasn’t until he moved to Bordeaux that he started adventuring in maths.

Unlike many mathematicians, he treated his math purely as a hobby. Lots of the theorems and equations he worked on weren’t written up in journals, but in letters to others (like Pascal). He also famously wrote his results as annotations in his math textbooks!

He was a polymath – literally – and made contributions to calculus, geometry, number theory and probability theory to name just a few areas!

But he had also a great weakness. He stated a lot of results but was less reliable at proving them. I find his lack of rigour quite relatable!

He’ll be remembered for “**Fermat’s Little Theorem**“, sure, but more than that for “**Fermat’s Last Theorem**“.

Fermat’s last theorem is an easy theorem to state: there are no whole numbers x, y and z such that **x ^{n} + y^{n} = z^{n} **for any n bigger than 2.

Recall Pythagoras theorem which says that in a triangle the lengths of the edges satisfy: **x ^{2} + y^{2} = z^{2} **? Taking 3, 4, and 5, for example, this is a whole number solution.

But if you change the 2 to anything bigger then there are no whole number solutions, Fermat says.

It’s apparently not quite as easy to prove as it is to say, unfortunately. In the margin of his textbook ‘Diophantus’ he wrote:

“I have a truly remarkable proof of this theorem which my margin is too small to contain”

It’s a shame that he didn’t write it down, however, because it took hundreds of years and hundreds of mathematicians before it was solved by Andrew Wiles in 1995.

It’s safe to say that if Fermat had proved his last theorem, it was in a completely different way to Wiles – who had to take a detour to elliptic curves through the work of many mathematical geniuses before him to reach his proof.

Most people agree Fermat never proved his theorem and was mistaken. But it makes you think – what if there is a ‘remarkable’ proof of the theorem which we’ve missed all this time?

**Thomas Bayes**

Our next amateur mathematician is Presbyterian minister Thomas Bayes.

He was born in 1701, and his life followed two parallels: math and religion. At university, he studied logic and theology, and following his degree, he became a church minister.

In Bayes’ time, math, science and the church were far more interconnected circles.

Whilst Bayes’ first published work was theological, his second was a defence of Newton’s famous theory of calculus. It came as a response to yet another church minister, Bishop George Berkeley’s criticism of Newton’s work.

But the thing which Thomas Bayes is most famous for is his eponymous **‘Bayes Theorem’**.

It’s arguably the most important theorem in probability and tells us what the probability of an event happening is conditional on some other event happening.

He thus pioneered Bayesian inference; a way of using probability to predict things and test hypothesis.

The basis of Bayesian inference is this: our aim is to predict *parameters – *for example the number of calls a call center receives in an hour, or the probability of a football team winning.

First we have our initial beliefs about the parameter – how many calls *we think* the call center gets an hour, on average.

Then we have some data from trying to find the parameter (i.e. counting calls or watching the football team play).

Then we update our belief about the parameter by multiplying our initial beliefs and the likelihood of the data we collect.

Bayesian inference differs from other methods of hypothesis testing because it treats parameters as random and not fixed.

All this to say that his math revolutionized applied probability.

For his work, he was elected Fellow of the Royal Society. And if you ever want to start an argument in science department, ask someone if they’re a Bayesian or a frequentist (but that’s a story for another time!)

**Marin Mersenne**

Our final pioneering amateur math contributor is another clergyman, and a contemporary of Fermat.

Mersenne was born near Oizé in France in 1588. His education was in theology and Hebrew at a Jesuit (a Catholic religious order) College in Le Mans.

Marin Mersenne became a friar, was ordained as a priest, and engaged in teaching philosophy and theology throughout the 1610s. It wasn’t until a decade later when he settled in the convent of the annunciation that he started his studies in math as well as music. He was in good company too!

During this time, he met the mathematicians Descartes and Roberval and physicists Galileo Galilei and Huygens.

His first mathematical work, L’Harmonie Universelle, was published in 1636 about the relationship between music and maths. It looks at all aspects of musical theory; practical, theological, stylistic.

But it’s legacy is in it’s formulation of ‘Mersenne’s Laws’. They describe how the frequency of a note played on a string relates to the string’s length, tension, and mass.

However, Mersenne is arguably best well known for his influence on number theory.

A lot of number theory focuses on prime numbers – numbers with precisely two factors.

Prime numbers are the ‘building blocks’ of all other whole numbers. Every whole number can be written uniquely as the product of prime numbers.

Mersenne studied numbers of the form where p is prime, so called ‘Mersenne numbers’. He then came up with an incorrect list of prime numbers which he said gave prime Mersenne numbers.

He may have been wrong about whether they were prime, but the fact remains that calculating Mersenne numbers is an easy way to find large prime numbers.

The largest prime number that we currently know of is a Mersenne number. This is thanks to a collective online effort called the ‘Great Internet Mersenne Prime Search’. Anyone with a computer can download the programme, and it will use your computer to help test whether huge Mersenne numbers are prime.

It goes to show how many math problems of the past have nowadays become projects for big computing power. Computers may not be able to solve all problems, but their computing power certainly helps!

## Conclusion

Amateurs have contributed to many fields of endeavor. Amateur mathematicians have made significant contributions to math over the centuries. If you have a love of math, you could make a breakthrough.