Eureka's science wish list for the next 300 years

The Royal Society Exhibition, due to open on Monday, features a wonderful science wish list, jotted down by the 17th century chemist Robert Boyle (of Boyle's law fame).

At a first glance the list is, well, hilarious. "The Emulating of Fish without Engines by Custome and Education only"? You could not make it up. But on closer inspection the list contains surprisingly accurate predictions of things to come:

The Art of Flying - Tick

The making Armor light and extremely hard - Kevlar

Freedom from Necessity of much Sleeping exemplify'd by the Operations of Tea and what happens in Mad-Men - Pro Plus

Potent Druggs to alter or Exalt Imagination, Waking, Memory, and other functions, and appease pain, procure innocent sleep, harmless dreams, etc. - Take your pick

The list captures the contemporary issues, those that Boyle himself was particularly concerned with and also gives a sense of the immense progress in intervening years. These ambitions, which would have read as science fiction in Boyle's day, now (with a few exceptions) read as every day realities.

What might yet be achieved? We compiled our own wish list based on contributions from scientists and Times writers:

Finding alien life - Keith Moore, Royal Society librarian

When I was about knee-height I decided I'd like to get into space by the age of 30. I'm rather offended that this hasn't happened, but if I'm not up there I'd like to think that someone else is out there.

Solving the Riemann Zeta Hypothesis - Jonathan Ashmore FRS, biophysicist University College London

I would love to see one of the big maths problems solved once and for all.

A vaccine to safely and effectively prevent HIV - Dr Evan Harris, former Liberal Democrat science spokesman

The Holy Grail of infectious diseases research needs to be found to save millions of lives and prevent to the ever-increasing cost of maintaining HIV infected people on anti-retrovirals

The sorting of metals - Athene Donald FRS, physicist University of Cambridge

Unless we devise a way to separate, reclaim and reuse metals (efficiently, cheaply and cleanly) we will run out of some high value metals and they contaminate landfill sites. High volumes are produced in cars, mobile phones, batteries etc.

The Acceleration of the Understanding of Afflickshuns of the Mind - Sam Lister, Times Health Editor

Dementia remains woefully underfunded and poorly understood. Its burden on society is increasing rapidly

The Cure of Cancer without Knife, Fire or Poison - Mark Henderson, Times Science Editor

We need treatments for cancer -- and other diseases -- that don't rely on blunt instruments with horrible side effects. There's a good chance that genetic targeting and earlier diagnosis could deliver this.

Memory replacement - Dr Alice Bell, science communication lecturer, Imperial College London

I'd love a simple way of replacing the pointless memories I hold (security code for props cupboard of theatre I worked in when I was 19, lyrics to Wombles Christmas singles...) with stuff I really do need to remember (where I left my passport, the name of the journal where I saw that paper on trust and URL names...). That or a way of injecting the content of a book into my mind without having to take the time to read it. I'm sure google are onto that though.

A time machine - Imran Khan, director Campaign for Science and Engineering

It would be great if we could engineer an Evidence Based Policy generator for Government. Apparently that's unrealistic, though, so I'll settle for a time machine so scientists can go back and fix the problems instead...

And, personally, I'm going for the Higgs boson, which would be the ultimate find in 100 years of particle physics.