Why Can’t Math Solve Its Own Problems

Video why can't math solve its own problems

Humans are natural problem solvers. We have an innate drive to seek solutions to challenges that come our way. From climbing mountains to exploring outer space, from curing diseases to unraveling complex relationships, our species has achieved remarkable success in science and technology. This has led to a widespread belief that science alone holds the key to solving any problem, no matter how formidable.

However, the reality is not always so straightforward. Despite our best efforts, there are some problems that remain unsolvable, defying even the most diligent study, hard work, and understanding. In mathematics, a field known for its logical rigor, there exist problems that have stumped even the greatest minds for centuries.

The Riemann hypothesis: a mathematical problem with no solution?

Mathematics students are familiar with the idea that some problems have no solutions. Divide by zero, for example, and the very fabric of spacetime threatens to unravel. But these are more like rule violations than genuinely unsolvable problems. Are there legitimate mathematical problems that are so challenging they may never be cracked by human minds?

The answer is yes. In the year 2000, mathematicians gathered in Paris and identified the seven greatest unsolved mathematical puzzles of our time. These problems are highly advanced and esoteric, far beyond the grasp of the average mathematician, let alone the average person. To make things more enticing, the Clay Mathematics Institute offered a $1 million prize for each of these problems. So far, only one has been solved by the Russian mathematician Grigoriy Perelman, who famously declined both the prize and the Fields Medal, the highest honor in mathematics.

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Among these math mysteries, the Riemann Hypothesis stands out as one of the most accessible to non-specialists. It concerns the distribution of prime numbers, a topic that has fascinated mathematicians throughout history. Prime numbers are those whose only factors are 1 and the number itself, such as 2, 3, 5, and 7. While we know that prime numbers become rarer as we move along the number line, mathematicians still strive to uncover a pattern in their distribution.

To unravel this mystery, mathematicians delve into sophisticated concepts like infinite series and the zeta function. This function, which can be re-written in a peculiar way, has a deep connection to the distribution of prime numbers. Bernhard Riemann, in 1859, extended this concept to include imaginary numbers and proposed that the solutions to the zeta function when it equals zero can offer insight into the distribution of primes. This proposal, known as the Riemann Hypothesis, remains unproven despite 160 years of attempts to crack it.

Aging and cancer: biological problems with no solution?

As human beings, the march of time inevitably takes its toll on our bodies. Aging is an inherent part of our biological existence, leading to the gradual deterioration of our tissues and, ultimately, death.

This process stands in stark contrast to the unlimited growth and division seen in unicellular organisms like bacteria. In multicellular organisms, including humans, cells are tightly regulated and have a limited number of divisions, known as the Hayflick limit. This limit helps prevent uncontrolled growth and the development of cancer. Even stem cells have their own division limits. As we age, our organs weaken, our immune systems decline, and eventually, we succumb to the inevitable.

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One crucial factor in cell division control is telomeres, structures found at the ends of our chromosomes. Telomeres, like the plastic aglets on shoestrings, experience shortening with each cell division. This shortening can lead to the loss of important DNA and trigger a state of crisis, in which cells undergo controlled cell death called apoptosis. Even cells that avoid crisis eventually reach a state of senescence, where they can no longer reproduce. Senescent cells likely contribute to aging-related diseases.

It might seem logical to imagine a “fountain of youth” that removes the limits on cell division and prevents cells from entering senescence. In essence, immortal cells would be the key to everlasting youth. However, this is precisely how cancer cells behave. In a tragic trade-off, cells can either grow old and die or become immortal and cancerous. As one mentor memorably put it, “The only way to avoid cancer is to die of something else first!”

Finding a cure for cancer has been a long-standing hope for many. However, the complexity of the disease and the ability of cancer cells to develop resistance to treatments have presented significant hurdles. Moreover, cancer is not a single disease but a collection of hundreds or even thousands of different diseases, each with its own genetic profile. This genetic variability makes it challenging to find a universal cure. While progress has been made in treating specific types of cancer, a universal solution remains elusive.

Willful ignorance: a social problem with no solution?

While there are many significant problems in the world, one that affects all of us is willful ignorance. In an era of seemingly unlimited access to information and knowledge, many people choose to remain ignorant or ignore the truth.

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We live in a time when powerful technology, like smartphones, enables us to connect with the world and access vast amounts of information. Yet, we often use these devices to watch trivial videos or engage in pointless arguments on social media. Instead of embracing the potential for enlightenment, we succumb to willful ignorance.

The problems of poverty, violence, authoritarianism, and societal divisions are ultimately solvable. Progress has been made, and the world continues to improve in many ways. However, one problem that defies easy solution is the phenomenon of willful ignorance. It is a fundamental flaw in human nature that some people choose not to be educated or refuse to accept the truth. This problem is amplified by confirmation bias, tribalism, and a culture of sensationalism perpetuated by media outlets and social media platforms.

This toxic combination has given rise to the proliferation of fake news and misinformation. False narratives spread rapidly across the internet, leading to real-world consequences. From conspiracy theories triggering violence to the rejection of life-saving vaccines, willful ignorance poses a significant threat to society.

Efforts to combat this problem by promoting education often fall short. Merely being educated does not guarantee immunity to misinformation or the ability to discern truth from falsehoods. People can be educated and still hold incorrect beliefs. The backfire effect, confirmation bias, and tribal loyalties all contribute to the persistence of willful ignorance.

In the age of social media, fake news has become a pervasive problem. Even reputable news outlets can unwittingly promote misinformation, leading to public confusion. The consequences can be dire in areas that require accurate information, such as public health. The anti-vaccine movement, fueled by fake news and distrust in established institutions, has led to a resurgence of preventable diseases and avoidable deaths.

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Profit-driven industries have capitalized on scientific illiteracy and the public’s susceptibility to fake news. Pseudoscience and alternative medicine have gained a significant following, despite their lack of evidence and potential harm. The spread of misinformation not only jeopardizes personal health but also erodes trust in scientific advancements.

Furthermore, willful ignorance has fueled political polarization and societal divisions. People are unwilling to engage in meaningful dialogue and instead entrench themselves in their own beliefs. Social media, designed to connect people, has ironically become a breeding ground for hostility and the spread of misinformation.

Tackling willful ignorance will require more than just education. It will require a fundamental shift in our cultural mindset, one that values critical thinking, open-mindedness, and a commitment to truth. Recognizing and confronting our own biases and tribal affiliations is a necessary step towards bridging societal divides.

A solution when there is no solution

As we navigate life, we come to the realization that there are many things beyond our control. Our circumstances, genetics, and even our own thoughts and emotions elude our grasp. The world is full of unsolvable problems, and we must learn to accept our limited power over them.

Embracing the concept of accepting the things we cannot change and finding the courage to change the things we can is essential. The Serenity Prayer by Reinhold Niebuhr encapsulates this idea:

“God, grant me the serenity to accept the things I cannot change,
Courage to change the things I can,
And wisdom to know the difference.”

Alternatively, a more light-hearted take on this sentiment suggests relying on coffee to change what we can and wine to accept what we cannot.

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In the face of unsolvable problems, we must come to terms with the limitations of our control. By doing so, we can find peace and focus our energies on the issues where we can make a positive difference.

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