Working as a researcher, discovering new knowledge, changing society, improving our lives. The journey from the first germ of the idea to fulfilment can be a tortuous one. Form some discoveries the world is begging for your answer. For others the world first of all has to realise it has the need and then to realise that a diligent and prescient researcher, via a journey of troughs and peaks, has already found out what you need . Mathematicians are often in the later category.
I found an equation that approximates my work pattern during my PhD:
f(x) = x²sin(x)². It's a combination of a steadily climbing curve and a sine wave.
My work rate started low and climbed slowly, repeatedly dropping to zero - troughs - and returning to the curve - peaks. I wrote this poem in a trough day. The trough days depress. I feel worthless, a drain on society. The peak days remind me that I have to work even harder on the next peak day.
I think I've gone slightly mad during my PhD. I am frequently anxious now. But I'll soon be able to call myself a doctor, so apparently it will be worth it. My proud heart seems to prefer to feel impressive rather than happy.
Technically I have made a discovery. It doesn't seem to matter that it will never be of any use to anybody. They say you've done well if four people read your thesis: you, your supervisor, and your two examiners.
I feel confident in academic circles where I used to feel like an imposter. This is satisfying. They might never be read, but I've published some papers. This is satisfying.
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