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To be a Mathematician…

some ideas I have found useful to revive flagging spirits and keep the great project going.

Cultivate the right attitude for doing maths

Precision, thoroughness and tenacity are obvious skills you will need but in this little post i hope to show there are lots of others too, many of which are applicable to many other areas of life. A love and respect for knowledge in general is also good and resist temptation to think you have the only path to truth. Poets and social scientists are doing good work too, as well as carpenters and nurses. In maths we purify and formalise knowledge, but it is not the only possibility.

Experiment !

Just do it. When we were all little we played so much, and learned so effectively. Experimentation is a kind of play too. Computers also can be mathematical laboratories and give something physical and external to the mind to touch and interact with. Writing code to test and reinforce your mathematical ideas is a great adjunct to the old paradigm of pen and paper. Use both appropriately.

Build your mathematical motivation

Science fiction helps me do this. If you reassure yourself of the worthwhile nature of your study from time to time you will build the energy to bring great efforts to bear on problems. Be a dreamer too and convince yourself of how mysterious and self-improving the subject you are studying can be. Even if you fail, at least you tried and this is so precious.

Mix adrenalised struggle with gentle meditation

It’s a competitive world full of pressures and this goes for education too, but too much of a wrestling match tires you and makes you jaded. Sometimes its good to pick up a recreational book like a Martin Gardner or a Pickover and just wander through it with a peaceful mind. meditation helps us bed down our knowledge into sound foundations, and its fun too. Be like an olympic athlete, sure, and push your limits, but also take time to be a Zen monk and just reflect under a tree !

Court spaciousness

If ideas clog and constipate then separate them and walk through them one by one as if they were in an actual place or virtual reality scape in your mind. Important concepts need to sit in their own domains and not be packed too close to one another. Empty your mind of distractions and learn one thing at a time and learn it well. With enough mental space a kind of claustrophobia is avoided and you have the room to move around ideas and see them from all sides.

Beginner’s mind – the wisdom of going back to basics

Sometimes you will have to erase your mental whiteboard and start afresh. Even the most advanced people have to do this because the conscious mind has limits to how much it can hold at once. Every time you go back to important basic subjects you cement the learning ever stronger. Be glad that you are studying a subject so subtle that going to the basics will yield new insights each time you do it. You’ll always see something new in what you thought was familiar.

Get into “the state” of focused calm

Alpha Rhythms of brain activity are also what meditators seek. In Greg Bear’s “eon” the heroine gets into a state of perfect attention when she is thinking mathematically. watch your state of mind and work towards building your habitual focus. Awareness is a mirror you can polish your whole life.

Deal with and use your errors

Errors are inevitable… don’t berate yourself too much since the more maths you do the more errors you will make. Everyone does it so don’t lose heart, gently correct them and move on. Also errors can give us new ideas when they become like a springboard to dive off into the unknown. We wouldn’t be here without the fundamental creativity of DNA copying, and this process uses its errors to create mutation !

Keep your confidence or morale up

Realise how far you have come and give yourself praise for every small step and insight. Don’t try to run before you can walk, and don’t expect to be equal to the greats overnight. If you are stuck on a problem go back to a simpler case that you can solve, this warms you up and convinces you that you are indeed competent after all.

Cope with math anxiety and number panic

If ideas flood in then slow them down and write them all down. Break apart threatening overcomplex clods into bite sized pieces and write them down on cards. soemtimes the intuition works too fast for the rational mind but its gifts are valuable.Breathe deeply and calm yourself if you get number panic. Run through the thought that panicked you until it loses its sting.

Find your own learning style and modality

Start to observe yourself and your working style so that you can learn in which ways you perform best, and then capitalise on this to speed up and turbo charge learning.

Be playful and side track and be disciplined and keep to the point

Do both in balance. Curiosity leads us down back alleys where treasure and new experiences may be discovered. Discipline to stick to one idea helps you organise too. It shows the subtlety of a subject if you need to embrace both these opposites in a yin-yang synthesis that keeps you on your toes.

Exploit creativity and non linear intuition

Lateral leaps are part of original work, maths is a creative discipline, break the rules if you feel like it. Sometimes that won’t work but when it does it rocks the world.

Savour aesthetics, elegance and beauty

When the mind perceives beauty it always remembers and prioritises what it has seen. Beauty or even just symmetry is a way to order facts that makes it easier for the mind to grasp them fully and appreciate the complex patterns within data effortlessly and enjoyably. If you find a proof elegant chances are you will grow fond of it and internalise its mysteries. Learning shouldn’t always be drudgery and the aesthetics of maths are there for us to enjoy.

Follow your golden path through the landscape

Use your feelings and come back again and again to areas you find beautiful and interesting. We each have a unique sacred path through the mountains of math. Following your own route through the subject may just allow you to contribute soemthing unique, a fruit of your own personal vision. Even if you can’t manage to discover brand new maths, you may be able to explain existing maths in a unique way. Teaching is a challenge that helps the teacher learn. To explain something you know – reordering and rearranging your knowledge for another mind to digest it is the best way to deepen your own understanding. Get some friends together into a study group if you can.

Don’t overdo it

Overwork creates negative emotional associations with the subject, sometimes you have to pull back. Anyway, pulling back and dropping it lets the subconscious loose on a problem. Remember you are a human being as well as a mathematician. Some thrive on competition and others withdraw to a hermit’s cell. Capitalise on your own methods, and learn from other practitioners.

Thanks for listening !


Written by Luke Dunn

October 17, 2008 at 2:14 pm

Posted in Math

Tagged with , ,

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