Lootman wrote:But is maths that important? As a kid I was fast and accurate at mental arithmetic. Before calculators and computers, and when money was pre-decimal and measures were pre-metric, that came in handy. Not so much now. Applied maths is mainly useful only if you want to be an engineer, and the pay is poor there. Pure maths is really just a convention that teaches you nothing about the real world - the ultimate left-brained luxury.
From personal experience, advanced maths is rather important if you want to be an Actuary!! I woudn't write off Engineering as a high earning career for applied maths; it pays relatively badly in the UK but much better in some other countries (particularly America).
A key mathematical skill is being able to tell if an answer "looks reasonable". You don't need to get the exact answer, just to have a feel if the figures are "roughly right" or "precisely wrong". Lots of people are at a huge disadvantage because they often can't see when a mathematical answer is "obviously wrong". Those of us with a decent maths background generally spot these errors because we've spent so much time doing maths we've got better instincts. The technique of solving maths problems by guessing the answer and working back to the question is quite commonly used.
There's a lot of advanced maths underpinning the modern world, lying hidden beneath the surface (e.g. weather forecasting relies heavily on the binomial theorem). Yes, you don't need stuff like calculus, group theory or topology for everyday life. But sometimes a bit of advanced maths separates those who can do from those who can't.
An understanding of probability, statistics and risk theory makes life much easier and less stressful (for one thing you're far less likely to waste resources worrying about the extremely low probability events that causes the man on the Clapham Omnibus to waste lots of resources). Game theory is extremely useful in modelling people's behaviour, particularly in fields such as economics and military strategy.
Most of us who invest in the stockmarket apply game theory and probability theory to some extent. We just don't necessarily realise it.
Linear programming is extremely useful when dealing with everyday problems involving allocation of resources (most people use it regularly, such as when deciding what to buy given a limted budget, though they don't formally reduce matters to simultaneous equations and optimised utility functions). Some years ago I helped a client out with a problem regarding allocating work to different departments which was reducible to multiple simultaneous equations which were quickly solved by a brute force spreadsheet.
The Pareto distribution explains a huge amount about life in general (80% of outcomes are due to 20% of causes) - it's one of those bits of maths that is highly influential economics and human psychology than anything else. And I'm a far better gambler because I know a lot about probability and statistics.
https://en.wikipedia.org/wiki/Pareto_distributionPure Maths doesn't have everyday uses but it has been used to develop all sorts of real world applications, most of which are discovered many years after the maths was discovered. For example, modern cryptography (which underpins the internet, including browser encryption for shopping online) relies heavily upon the work of Srinivasa Ramanujan, an Indian mathematician who died in 1920 and IMHO is the most influential mathematician since Euler (the film about his life, "The Man Who Knew Infinity", starring Dev Patel and Jeremy Irons, is worth a watch (link below)).
Most of the mathematics of General Relativity was developed in the 1850s by Bernard Riemann and was long though to be of no practical use. As for Quantum Mechanics, that draws upon all sorts of maths which was though to be totally impractical yet it's now the basis for a huge part of the modern economy (e.g. semiconductors).
Here's the trailer for "The Man Who Knew Infinity"
https://www.youtube.com/watch?v=oXGm9Vlfx4wAnd what was actually said was probably paraphrased.
Two of the ladies I studied with are now quite active in promoting females in STEM in the UK (in addition to the other bits of their careers) - they would be horrified to hear the conjecture posted! (if taken at face value)
(the other is more sanguine)
