As you've probably noticed by dying or even finishing a run, you'll always receive a score down at the bottom of your run summary/breakdown. This score will be shown on the global Leaderboard.
You can check out the leaderboard on the steam community hub of the game.
In the upper right corner, you can click on "View Stats" -> "Global Leaderbords". There you can see the leaderboards for all 3 difficulty settings.
Here's the current leaderboard for the "Insurmountable" difficulty mode of the game:
Who's going to be the 10th to join the ranks?