Could someone explain what does this quote implies? Any advice on this essay will be appreciated.

"It is by logic that we prove, but by intuition that we discover"

The mathematician Henri Poincaré once said: "It is by logic that we prove, but by intuition that we discover." Discuss this quote and what it means for the way science is advanced. In light of this statement, how should future scientists approach their work? (2000 characters)

The quote asks you to think about why you want to become a scientist. What particular aspect of the field do you want to seriously participate in? For example, Elon Musk once admitted to being afraid of the dark. However, he knew (intuition) that he did not need to be afraid of it (logic). So he sought out the reasons why he should not be afraid of the dark (discover). He realized through research and experimentation that there are light creating elements that are not present in darkness. Based on this understanding, he began to develop a better understanding of how solar panels should work and how it should be created (future scientists approach their work). From there, his scientific mind and interest in evolving technology to our benefit was born and what he has raced to learn more about ever since. I hope that this practical example of the quotation will help you better understand what the writing requirements of your statement are.

The quote talks about how science needs intuition before logic, for even to prove anything scientifically, you need to first discovery it. The essay in my opinion should be about how science requires you to stay intuitive and inquisitive for it to advance and flourish. If we only try to use logic to prove something, and use the same old methods, we shall never think out of the box, we would still be believing that Earth is flat or Earth is the center of the Solar system. All of it was discovered at times when proving any of it was quite difficult. So today when we keep science first and can prove even the smallest theories of physics, one should have stop getting used to this comfort zone where we doubt/ reject all things we cant prove. Instead, one should put forth more intuition based theories and hypothesis, be innovative and try to break some known realities, even if sounds absurd at first. Because the worst thing to happen is that it might be proved wrong, but at least one will learn from it. But the process of trusting your intuition and trying something new is the basis of advancement & an important step before even trying to use logic to prove anything.