Only through mistakes can there be discovery or progress, as the speaker asserts. I tend to agree. Although we should not lose sight of the fact that the attitude plays a vital role on reaching success when encountered mistakes, in final analysis, it is true that mistakes can help us to make discovery or progress to an extreme extent.
To begin with, during one's lifetime, everyone inevitably faces with a various mistakes around the corner. Without these mistakes we will not grow up at all. When a child is learning how to walk, before he/she can walk alone without the parents' help, he/she falls over himself/herself frequently. From the experience of numerous tumbles, he/she eventually can walk by himself/herself. To some extent, we human have the inherent nature to amass experience from the mistake. Students also always make mistakes. The manifestation of this is that the homework that corrected by teachers. Few students would argue he/she never makes mistakes even though he/she was the best student in the class. Without the mistakes, student would never know where is wrong in his/her homework, and therefore he/she would never get progress at school. For example, one student answer the question what is 3 add 3 and the answer is 7, and then teacher will correct the answer. And if the student understands the rule, he/she will answer rightly next time. Therefore he/she makes progress on math.
In addition, discovery or progress is from the experience of failures or mistakes when it comes to some famous person in the human history. History is replete with such kind of persons. The light bulb discovered by Edison who came through more than 1000 failures during the process of the trial. Marie Curie who discovered the radium also encountered numerous failures and eventually made progress on physic and chemistry. The chief reason why we make mistakes is that we must do something violate the objective law somewhere. And by virtue of analysis of the situation, we can draw a conclusion to solve the problem and then put this into practice and at last get the result, whether fail again or success.
Nevertheless, we should not lose sight of the fact that the attitude of the one who gets success when come up against the failure plays a vital role in the pursuing for progress. If Marie or Edison gave up during research on the bulb and radium, there would be no way that we can realize the bulb and radium if no other does the research. Thus failure and mistake are not bad things, the important thing is how we deal with them, choose to give up or continue to find where is wrong and then put in practice.
To sum up, mistakes are like catalyzer when pursuing success, and we should have positive attitude to deal with them and never give up until get progress.