Maths in one form or another has been used to make quantitive predictions since the time of the ancient Babylonians. But when did maths start to be used to make predictions of new objects or phenomena?
John Couch Adams used mathematics (perturbation theory if you really want to know) to predict the position of Neptune by mid-September 1845. He communicated the results immediately to Challis at Cambridge and a month later to Airey the Astronomer Royal. Independently, Urbain Le Verrier also did and presented the results publicly in Paris to Academy of Sciences on 10th Nov 1845. It was these latter predictions that helped Galle at Berlin observatory find the planet. Needles to say there was quite a to-do about who actually predicted the planet first. Either way we can date the discovery of a new object by mathematics to as early as 1845.
And we’ve been predicting where unknown objects exist from the apparently errant behaviour of objects we know about ever since, right up to the modern day where we are predicting where planets are around in other solar systems.
What about mathematical prediction of phenomena? Well, we have look to 1900 and 1905. Max Planck, frustrated about the lack of his progress in solving what was known as the ultraviolet catastrophe or black body problem suggested a mathematical model that could fit the the known experimental evidence of his day. It was of course that electromagnetic energy could only be emitted in integer multiples of hf, where f is the frequency of the emission and h is the Planck constant, which of course means it can only be emitted in quanta, and quantum theory was born. At the time Planck did not think this was what happened in reality. It took a certain clerk in a Swiss patent office, Albert Einstein, working on the photoelectric effect to show these quanta were real physical entities.
Of course there been well documented examples since then of finding new phenomena by applying mathematical theories to physics and science.
These have been two great leaps in the way maths is applied to science, physics in particular. So what is the next leap? When will it happen? [Imagine picture of hungry cat waiting for scrumptious pussy meat!]
So what has all this got to do with science fiction (apart from the obvious giant leaps in maths leading the way to a vast improvement in the understanding of the sciences, which in turn, has form the basis for many stories in science fiction)?
There is the timing aspect of things. Science fiction such as exploring new places and unknown worlds, and commenting on the way our future is unfolding has and will always be with us. But science fiction built on potential technology advances and explaining how they work comes in waves that follow on from improvements in maths. The bigger the bound in maths, the bigger the bound in science.
I think we are due for a new leap in maths. I can’t put my finger on why I think so, just call is a gut feel… I think it might be something to do with the maths about maths , or meta-maths if you want to pedantic. When I’ve sussed it out, you can bet I’ll be writing a science fiction story about it! Well, what else would expect this gal do about it?