Typically, the first solution to come to mind is to build a time machine, go back in time and somehow prevent the OTHER scientist from completing their work. Makes perfect sense...
But what happens when your prized invention IS the time machine? And you are indeed the first person to invent it? Then as soon as someone else comes along and invents their time machine, the first thing they'll do is go back in time killing you in order for THEM to be the first person to invent the time machine...
This starts a chain as such:
1. X invents a time machine. Glad to be first.
2. Y invents a time machine, goes back in time, kills X BEFORE inventing the time machine. Becomes first.
3. Z invents a time machine, goes back in time, kills Y BEFORE inventing the time machine. Becomes first...
...
ad infinitum.
So, since everyone who invents a time machine ultimately dies BEFORE inventing the time machine, no one will ever have invented a time machine... And hence no time machine.
The logic is unassailable!