Do Mathematicians Have Modest Goals?

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In summary, the article explores the motivations and aspirations of mathematicians, questioning whether their goals are modest or ambitious. It discusses the nature of mathematical research, the pursuit of knowledge, and the often understated significance of their contributions to both the field of mathematics and society at large. The piece highlights how the perception of modesty in their goals may mask the profound impact and complexity of their work.
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From the Introduction to
https://arxiv.org/abs/2106.11285

"Since the dawn of time, human beings have asked some fundamental questions: who are we? why are we here? is there life after death? Unable to answer any of these, in this paper we will consider cohomology classes on a compact projective manifold that have a property analogous to the Hard-Lefschetz Theorem and Hodge-Riemann bilinear relations."
 
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It would have been really cool if a paper began,

"Since the dawn of time, human beings have asked some fundamental questions: who are we? why are we here? is there life after death? Unable to answer any of these, in this paper we will prove the Riemann Hypothesis."
 
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FAQ: Do Mathematicians Have Modest Goals?

What is the meaning behind the phrase "Mathematicians Have Modest Goals"?

The phrase "Mathematicians Have Modest Goals" is often used humorously to highlight the grand ambitions and challenging problems that mathematicians aim to solve. Despite the seemingly modest wording, the goals of mathematicians can be incredibly complex and ambitious, such as proving long-standing conjectures or developing new theories.

Who coined the phrase "Mathematicians Have Modest Goals"?

The phrase is not attributed to a specific individual but has been used informally within the mathematical community to emphasize the contrast between the modesty of the wording and the actual significance of the mathematical problems being tackled.

Can you give an example of a "modest goal" in mathematics?

An example of a "modest goal" in mathematics might be proving the Riemann Hypothesis. While it sounds straightforward to "prove a hypothesis," the Riemann Hypothesis is one of the most famous and long-standing unsolved problems in mathematics, with significant implications for number theory and the distribution of prime numbers.

Why do mathematicians use humor in phrases like "Mathematicians Have Modest Goals"?

Humor is often used in the mathematical community to bring a sense of camaraderie and to lighten the mood when dealing with complex and sometimes frustrating problems. It also serves to make the field more approachable and to acknowledge the inherent challenges in mathematical research.

How does the phrase "Mathematicians Have Modest Goals" relate to the broader scientific community?

The phrase reflects a broader theme in the scientific community where seemingly simple questions can lead to profound and far-reaching discoveries. It underscores the idea that modest beginnings can result in significant advancements, a concept that is applicable across various scientific disciplines.

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