The Oxford English Dictionary defines 'mathematics' (2010) as "the abstract science of number, quantity, and space, either as abstract concepts (pure mathematics), or as applied to other disciplines such as physics and engineering (applied mathematics)". There are many "branches" of mathematics from simple numbers to algebra, calculus, equations, geometry, probability and statistics. It's used in such diverse disciplines as science, art, economics, and sport. Galileo Galilel even described mathematics as the language of the universe ('Galileo Galilei 1564–1642 Italian physicist and astronomer', 2006).
Mathematics is fundamental to everyday life, from managing your daily accounts through to answering some of science's more complicated questions. It's something you often don't realise you're using - for example, the game of snooker is all about angles and the force and direction applied to the balls in play - all of which can be described in mathematical terms. When you decide if you can make it across a road before that car comes...? You're estimating your speed of the car and comparing it to your walking speed to judge if you can make it. You may not be writing it down to calculate it precisely - but that's what your brain is doing.
Mathematics has developed and grown over the years, and new areas have been "invented" as our understanding of the universe has grown. Interestingly, it took until the 3rd century for the number zero to be "invented" (Oxford University, 2017), and we now have negative numbers, imaginary numbers, prime numbers, and the concept of orders of infinity as well as mathematical models to describe how the world works.
In order to understand how important mathematics is to you, it's perhaps easier to imagine what a world without mathematics would be like. Some of the things you would have to do without are (Mathematics Teacher Training, no date):
Mathematics has come a long way in recent years thanks in part to the invention of computers and the ability to do many calculations per second. Applied mathematics in the world of engineering has given us the ability to create mathematical models to help predict almost anything from the behaviour of a crowd to how a building copes in an earthquake. Such models allow us to test theories without having to conduct live experiments - which can prove costly or be potentially hazardous to living things.
The use of mathematics to crunch big data sets is also an increasing trend. Trying to spot patterns or anomalies to help predict the future in areas such as weather forecasting, seismology, global warming will help keep us safer in the future. Or for a more personal touch, without such large dataset crunching algorithms, you wouldn't have the "you might also like these" links when you shop on line. In sports like tennis too - looking at the statistics of matches played helps determine training regimes to help improve performance.
There are various unsolved mathematical problems - some of which carry can earn the solver a substantial monetary reward - such as the Clay Mathematics Institute's Millennium Prize Problems. There are seven Millennium Prize Problems, only one of which has been solved so each one carrying a $1 million prize (Clay Mathematics Institute, 2025).
Put simply - without mathematics the human race wouldn't be where we are today. It's one of the few subjects which cuts across all disciplines, and while you may not think you're using mathematics in your daily life - you are definitely benefiting from its existence!
Clay Mathematics Institute (2025) The Millennium Prize Problems. Available at: https://www.claymath.org/millennium-problems. (Accessed: 28 July 2025).
'Galileo Galilei 1564–1642 Italian physicist and astronomer' (2006) in W. F. Bynum and R. Porter (eds) Oxford Dictionary of Scientific Quotations. Available at: https://www.oxfordreference.com/display/10.1093/acref/9780198614432.001.0001/q-author-00007-00000477?rskey=zAsrUi&result=1. (Accessed: 28 July 2025).
'mathematics' (2010) Oxford English Dictionary. Available at: https://www.oxfordreference.com/display/10.1093/acref/9780199571123.001.0001/m_en_gb0504840?rskey=xMVgxi&result=1. (Accessed: 28 July 2025).
Mathematics Teacher Training (no date) Try to imagine a world without mathematics. Available at: https://teachingmathsscholars.org/news/try-to-imagine-a-world-without-mathematics. (Accessed: 28 July 2025).
University of Oxford (2017) Earliest recorded use of zero is centuries older than first thought. Available at: https://www.ox.ac.uk/news/2017-09-14-earliest-recorded-use-zero-centuries-older-first-thought. (Accessed: 28 July 2025).
Multiplication by Chris Liverani is used under Unsplash licence
Liane Frydland
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Professional Institutions are specialist organisations which offer guidance, support and training for their members. The main ones for Mechanical engineers are listed below.