As wishlists go, it was both visionary and practical, but more than anything it reveals the scope and almost limitless ambition of science in the 17th century.

In 24 handwritten notes, Robert Boyle, co-founder of the Royal Society, set forth the most pressing problems for scientists to solve. The issues ranged from the secret of eternal youth and healing wounds from afar, to the construction of an unsinkable ship and the ability to harness the power of the hysterical.

The list was drawn up in the 1660s, soon after the Royal Society was formed, and goes on public display for the first time next week as part of an exhibition at the scientific body's London premises to celebrate its 350th anniversary.

Boyle's notes appear alongside rare and previously undisplayed manuscripts, instruments, portraits and books that chart the history of science from the society's earliest days. Among them are the first sketches of nebulae by Sir John Herschel, who visited South Africa with a telescope in the 1830s, and Newton's death mask.

Boyle was an enduring and influential figure who brought great minds into the fold of the organisation. His wishlist for scientists begins, simply, with "The Prolongation of Life", a laudable goal considering life expectancy at birth at the time was less than 40 years old.

Boyle also ponders the development of a means to recover youth, or at least some of its outward signs. Perhaps false teeth and hair colouring will one day be possible, he speculated.

Many of the problems Boyle set out had clear practical applications, such as perfecting "the art of flying". It was nearly a century since Leonardo da Vinci had sketched out designs for ornithopters, but it would be another century yet before the Montgolfier brothers achieved the first hot air balloon flight.

Boyle's hopes for a way to "cure wounds at a distance, or at least by transplantation" have become a reality, with the advent of organ transplants and robotic surgical tools that can be operated from thousands of miles away.

"As you go down Boyle's list, some of the things sound quite silly, but then you realise we've kind of done them," said Keith Moore, the society's librarian.

Boyle also hoped scientists would find ways for people to work underwater and develop a ship that could sail in all winds and was impossible to sink. "I'm not sure we've managed that yet," said Jonathan Ashmore, fellow of the Royal Society and a spokesman for the exhibition. "But the way the list was put together is impressive, with very far-sighted and visionary ideas coupled with very down-to-earth, practical ones."

The most radical items on Boyle's list touch on human physiology and the brain. In one note, he suggests scientists might devise ways to live on a minimal amount of sleep by studying the effects of tea and also "mad-men", who appeared to need very little. In another, he wonders if understanding hysterical people and those with epilepsy might help scientists recreate their "great strength and agility".

Boyle, regarded by some as the father of chemistry, had great faith in the power of pharmaceuticals and encouraged his fellow chemists to develop potent mind-altering drugs, and pills to relieve pain and induce restful sleep and sweet dreams. A more curious route of inquiry was "Attaining Gigantik Dimensions", presumably a reference to the possibility of enlarging the human race.

"This document provides us with an amazing window into one of the most extraordinary minds of the 17th century," said Ashmore. "Boyle's predictions on the future of science are quite remarkable. His hopes for the cure of diseases by transplantation and drugs to appease pain and aid sleep have both become inherent features of contemporary medicine and yet these were predictions he was making over 300 years ago. We have also seen numerous of his other predictions realised in various ways, including flight, modern healthcare prolonging life, Kevlar body armour, underwater exploration and GPS navigation."

This year, the Royal Society is holding a series of meetings to thrash out the future priorities for modern science. Feeding the world and providing ample green energy will certainly feature, as will enduring questions on the nature of ageing and consciousness.

"What I'd really like scientists to do is find evidence for alien life. I've been waiting a long time ... they should pull their fingers out," said Moore.

Several documents from the 20th century reveal the Royal Society's increasing role in advising government and addressing industrial or occupational issues. In the early 1900s, the society established a committee to investigate the unusually high rates of cataracts among glassblowers. The problem was traced to the intense glare of the molten glass, prompting the scientist, William Crookes, to design darkened safety spectacles. In doing so, he also invented sunglasses. Years later, the society's fellows drew up blueprints for ship mines, studied the possibility of extracting alcohol from horse chestnuts and drafted secret reports on the effects of atomic bombs.

"These guys were interested in everything and the emphasis on rationality when faced with the complexity of the world really comes through," said Ashmore.

New goals – the next 30 years?

Sources of clean, green energy Plenty of energy reaches the Earth in the form of sunlight, but major scientific advances are needed to harness solar energy efficiently. Attempts to master fusion power by creating a tiny star on Earth are under way.

Feeding the world

A perfect storm of climate change, growing human population and water shortages are predicted to put food production under extraordinary strain. Scientific advances in agriculture and desalination are much needed.

Slowing and reversing ageing

The ageing effects of our lifestyles and environment are becoming clear, but scientists know little about the genetics of ageing and how to affect it.

Greater knowledge of consciousness

Giant leaps in neuroscience have failed to explain the nature of consciousness and how it arises. Some scientists believe that consciousness is an emergent property that is inevitable when a critical number of brain cells are interconnected. Others suspect we are missing a fundamental ingredient that gives rise to the conscious mind.

Extraterrestrials

Decades of searching for signs of alien life have so far turned up a blank, yet the question of whether life on Earth is a one-off is among the most compelling in science. Many scientists believe that basic alien life, in the form of microbes, may be relatively common, with intelligent life much rarer.