I think the greatest discovery would be cold fusion. It would be amazing if they could find a way to achieve it cheeply and sustainably.
Having a source of power with such potential readily and safely available would change the way we do everything in the world. Third world countries could have reliable power. Space travel would no longer rely on fission, solar or fossil based fuels.
I believe it would bring on a new advent of civilization. It could be a discovery that is on the same level as fire.
The biggest problem would be letting it see the light of day. The gas and oil companies would have too much to lose. It is likely they would put the full weight of their resources behind keeping it from being adopted.
Much like what has been depicted in the movies, corporate lobbyists and lawyers would do everything they can to stifle that innovation.
The Body/Mind Connection
One of the greatest mysteries of all time has to do with ourselves: discovering the causal links between the (objective/measurable) body and the (subjective/mostly-immeasurable) mind. Currently, we don't know exactly how the mind works and - at best - we have very loose correlations between (objective) physiological changes in the brain/body and (subjective) states of consciousness.
Solving this mystery in the form of a scientific discovery would revolutionize industries of Health & Human Performance to the point where we could all become my powerful (both mentally & physically) human beings.
The A.I. Connection
Artificial Intelligence, once fully developed, would probably be the primary technology used to facilitate to facilitate this process. I would recommend checking out one of Elon Musk's companies called Neuralink: https://www.neuralink.com/
One of the things (of presumably many secret projects) Neuralink is working on is to decrease the amount of time it takes for the mind to access information via a device to connect the human brain with a computer.
Here are some quotes from Elon Musk about this company from his recent appearance on the Joe Rogan Podcast.
You can learn more here: https://www.youtube.com/watch?v=ycPr5-27vSI
Thanks for reading!
The existence of life elsewhere in the universe
The ramifications would be huge.
Religion, individual countries, people's belief systems, etc would all radically change overnight on a global scale.
Especially if contact was made in a public forum where it could not be denied/hidden or otherwise kept secret from the populace.
It could be travelling into Parallel Universes and finding other versions of yourself.
It could be breath taking experience and wondering to see which path was right for your life. Think about your whole life and your choices. You will able to see all options and result. It could be endless travel and you could find out awesome versions of you ever wanted to be.
You could even see one of your version living your dream never able to live on your current life.
There could be different scnerios and learning from all could be amazing experience. Maybe you see concequences of something you always wanted and give up afterthat. Maybe you will find out some choice lead your alternate version some place you could never guess.
Possibilities of many choices and seeing concequences and different version of yourself are pretty amazing idea.
In my opinion the discovery of the true concept of species and life. I am a biology student and I have always questioned the fact that there is no clear concept of what a species is and what life is. Recently the concept of species was considered as members of populations that reproduce or can reproduce among themselves in the wild and not according to a similar appearance and that their decency is fertile, however they were found in a Siberian cave the remains of a woman with Denisovan genome and a Neandentalis, two different species of ancient hominids, this in my opinion revolted this concept.
Without a doubt finding life on other planets would change everything from religion down to our history books. I mean could you imagine if the old historical reports of flying ships were proved real? Or if the nazca lines were really landing strips and communication with aliens? The planet would have a mental break down.
A portable lie detector apparatus.