Why Study Mathematics?
There are at least two good answers to the question posed in the title, both of which can be encapsulated in the alternative title:
Maths is BEST
On the one hand, Mathematics is a fascinating and exciting subject in its own right. On the other hand, Mathematics is the language of modern Business, Engineering. Science and Technology.
This leads to a very wide range of potential careers for graduates with Maths-based degrees, as we shall see below.
Recent Developments
Some areas of mathematics, such as Euclidean geometry, have existed for thousands of years. This leads to a common misconception that Maths is finished, all the answers are at the back of the book and there is nothing more to be done. On the contrary, Maths is very much alive and well. If we think of the last 30 years, it could be argued that Maths has entered a new Golden Age. Two themes can be identified, underpinned by a third.
1. Problems which have exercised minds for hundreds of years have finally been solved.
2. New areas of Mathematics have sprung up in response to the needs of other disciplines such as Physics, Chemistry, Biology and Economics.
3. Advances in computing power mean that calculations which would have taken more than a life-time 30 years ago can now be done in a few seconds.
Examples of old problems which have been solved (and the number of years taken to find a full solution) include
- The Four Colour Theorem (125 years )
- Fermat’s Last Theorem ( 357 years )
- Kepler’s Sphere-Packing Problem ( 387 years ).
Details can be found in books and on websites. Suffice to say that, in each case, the statement of the problem is simple but the proof is very hard. That is part of the fascination of Mathematics!
This still leaves plenty unfinished business.
There are plenty of problems to which NOBODY knows the answers !
This comes as a surprise to many people but is another aspect of the fascination and excitement of Mathematics.
New Areas of Mathematics
Many activities involve the construction of mathematical models in which the resulting equations are so complicated that the current body of mathematical knowledge is inadequate to provide an answer. Research is then needed to extend existing theories to cope with these new problems. We shall discuss briefly a few examples which, between them, illustrate the all-pervasive nature of Mathematics in the modern world.
1. Mathematical Finance
All the major banks and finance houses employ teams to develop models to predict the future behaviour of share prices on the Stock Exchange, interest rates and many other economic indicators. Major roles are played by the areas of probability and statistics which could be said to model the Mathematics of Uncertainty.
2. Nonlinear Dynamical Systems
A good example is provided by the weather which is constantly changing (dynamic)
and modelled by very complicated (nonlinear) equations. Forecasts are based on measurements from satellites, weather stations, etc. However, whenever a measurement is made, small errors will arise. Often these have no effect but in some situations, as time goes by, they not only persist but get worse and calculations eventually become worthless. This is linked to a phenomenon called chaos. Mathematical advances could lead to long-range forecasts becoming more reliable.
3. Liquid Crystal Displays (LCDs)
Think of a plasma screen television. You will probably be aware that Physics, Chemistry and Engineering have been involved in its construction but Mathematics has also played a role. Attempts are constantly being made to improve picture quality, e.g. to cope with footballers moving quickly. Examples of LCDs are all around us. In my own Department at Strathclyde there is an internationally-renowned research group collaborating with colleagues in other disciplines to produce better LCDs.
4. Security
Security issues dominate our lives in various shapes and forms. Consider internet shopping, where the buyer is required to type in a credit card number and other personal details. To avoid a hacker emptying out the buyer’s bank account, the details of the transaction have to be encrypted (scrambled) at the buyer’s end and decrypted (unscrambled) at the seller’s end so that the hacker can make no sense of them as they go down the wire. Number Theory provides the key. Thus one of the oldest and most beautiful branches of Mathematics has really come into its own, even if it has had to wait 2000 years to find an everyday use!
Careers
Given the range of applications listed above, it is no surprise that career opportunities for graduates in the mathematical sciences are enormous. Everyone knows that teaching and lecturing are options but that is only the start.
- The financial sector takes a large percentage who become accountants, actuaries, traders on the Stock Exchange, fund managers, investment analysts, bankers, etc.
- Statisticians are employed by government departments, health boards and pharmaceutical companies.
- The IT sector employs Maths graduates as programmers and systems analysts.
- Although some industries have declined in recent years, opportunities still exist in Research and Development.
- Less obvious destinations include jobs in business, such as Personnel Management.
Employers are looking for people who can think logically, analyse a situation rigorously and then make a sensible decision on the basis of their conclusions. These so-called transferable skills are an integral part of a mathematician’s training and make Maths graduates highly marketable. Indeed such graduates can do ALMOST ANYTHING !
Conclusion
Studying for a Maths-based degree keeps many doors open. At the same time you can enjoy a subject that combines elegance and beauty with relevance to the world in which we live.
Article by: Professor Adam McBride, Department of Mathematics, University of Strathclyde
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