Push ahead Definition 1 of 2Pro Tip 1/3Overcoming Challenges Used when someone insists on continuing something despite having problems. She had to push ahead with her studies, even after falling ill. Pro Tip 2/3Persistence Suggests a strong determination to keep going, often in a difficult situation. The small business had to push ahead despite financial difficulties. Pro Tip 3/3Not Discouraged Implies not being stopped or discouraged by any hindrances. He decided to push ahead with his invention, ignoring the skeptics.