Even today, there are scientific phenomena that defy explanation. If history is anything to go by, resolving these anomalies could lead to a great leap forward, so what are the greatest mysteries, and what scientific revolutions might they bring?

1 The missing universe

Everything in the universe is either mass or energy, but there's not enough of either. Scientists think 96% of the cosmos is missing. They have come up with names for the missing stuff - "dark energy" and "dark matter" - but that doesn't really tell us anything about them. And it's not as if they're not important: dark energy is continually creating new swaths of space and time, while dark matter appears to be holding all the galaxies together. No wonder cosmologists are searching for clues to their whereabouts.

2 Life

I know you think you're more than a sack of molecules, but why? Next time you see a tree, ask yourself why that is alive when your wooden dining table is not. The phenomenon we call life is something that biologists have almost given up trying to define - instead they're investigating ways to make different combinations of molecules come alive. Bizarrely, the best hope is similar in chemical terms to laundry detergent.

3 Death

Here's the flip side: in biology, things eventually die, but there's no good explanation for it. There are hints that switching genes on and off controls ageing, but if our theory is right, those switches shouldn't have survived natural selection. Then there's the argument that an accumulation of faults does us in. However, there are plenty of whales and turtles who seem to age ridiculously slowly - if at all. Of course, if we can work out why, that could be great news for future humans (if not for the planet).

4 Sex

Charles Darwin might have fathered 10 children, but he couldn't understand why almost everything in biology uses sexual reproduction rather than asexual cloning - sex is a highly inefficient way to reproduce. We still don't know the answer. The suggestion that sex's gene shuffling makes us more able to deal with changing environments seems plausible, but the evidence is scarce. At the moment, sex only seems to exist to give males some role in life.

5 Free will

If you want to keep your sanity, look away now. Neuroscientists are almost convinced that free will is an illusion. Their experiments show that our brains allow us to think we are controlling our bodies, but our movements begin before we make a conscious decision to move. Some researchers have already been approached to testify in court that the defendant is not to blame for anything they did. A scary legal future awaits.

• Michael Brooks is a consultant for New Scientist and the author of 13 Things That Don't Make Sense, published by Profile on Thursday