In education — and in life — what we believe about a challenge often matters as much as the challenge itself.

A growing body of research suggests that mindset plays a critical role in learning and achievement. Carol Dweck’s well-known work on growth mindset shows that students who believe their abilities can develop through effort tend to outperform those who view intelligence as fixed. In fact, a 2019 study published in Nature involving over 12,000 ninth-grade students across the United States found that teaching students a growth mindset led to measurable improvements in academic performance, especially among students who were initially underperforming.

Similarly, studies on stereotype threat by researchers like Claude Steele and Joshua Aronson demonstrate that when students are led to believe a task is particularly difficult for people like them, their performance can suffer — not because of a lack of ability, but because of how expectations shape behavior.

In short: research points to a powerful truth — what we think is possible influences what we actually achieve.

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A Story That Proves the Point

In 1939, a graduate student named George Dantzig walked into his statistics class at the University of California, Berkeley — a few minutes late.

On the blackboard were two math problems. Assuming they were the homework assignment, Dantzig copied them down and began working on them at home.

They were unusually difficult. But because Dantzig thought they were simply homework, he didn’t assume they were impossible — he assumed they just required more effort. After several days of intense focus, he solved one and turned it in to his professor.

Weeks later, his professor, Jerzy Neyman, called him in with incredible news: the problems weren’t homework. They were two of the most famous unsolved problems in statistics — and Dantzig had solved one of them.

His work later became part of his Ph.D. dissertation, and Dantzig would go on to become a pioneer in mathematics, founding the field of linear programming and transforming industries from logistics to computer science.

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The Takeaway

George Dantzig didn’t know the problem was "unsolvable," so he solved it.

The lesson is simple but profound:
It’s often not ability that limits us — it’s belief.

As educators, leaders, and lifelong learners, we must constantly ask ourselves: Are we setting ceilings over our own potential (or our students') by labeling challenges as too hard, too unlikely, or too ambitious?

Of course, belief and effort work best when paired with opportunity, resources, and support. But believing that growth is possible is the essential first step.

Imagine what’s possible if we approached challenges the way Dantzig did — not weighed down by assumptions, but fueled by effort, curiosity, and a mindset open to possibility.

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Because sometimes, not knowing something is “impossible” is exactly what makes it possible.