Why the History of Sciences is Sometimes More Important Than Sciences Themselves
Let me tell you a story.
You have all probably heard of Fermat’s Last Theorem at least once in your life. However, in the unlikely case you have not, here it is:
Proposed in 1637, this problem was firtly solved by the renowned British mathematician Andrew Wiles. However, it is worth noting that his (incredible) work was only the top of the iceberg. In reality, hundeds of mathematician had attempted to give a solution to this mystifying problem, dismally failing. Wiles’ solution not only required an incredible amount of ingenuity, technicality and persistence, but also a deep knowledge of very different and seemingly unrelated areas of Mathematics. One of these areas is that of elliptic curves.
Elliptic curves are a fairly technical topic, and we are not going to develop them in this article. However, for our purposes it is vital to mention that they belong to a branch of Mathematics completely irrelevant to that of Number Theory — the one at which Fermat’s Last Theorem belongs.
Back in 1957, when the theory of elliptic curves was being developed and revolutionized, Japanese Mathematicians Yutaka Taniyama and Goro Shimura formulated the namesake conjecture (which is now a theorem known as the modularity theorem).
Their work received little attention from the public, mainly because the topic of elliptic curves is not so easy to explain to the broad public (as opposed to Number Theory and Fermat’s theorem). However, German Gerhard Frey made an observation directly connecting Fermat’s Last Theorem and the Taniyama-Shimura conjecture. While this conjecture seemed to be one of the many more of Mathematics, through Frey’s work it was instantly brought to the number one of conjectures the mathematical community seeked to prove.
At this point, it is worth mentioning that Fermat’s Last Theorem was being attempted for more than 350 years from Mathematicians, with all possible means and with the newest and most well-developed theories. To no avail. At one point, mathematicians seemed to have no alternatives in approaching this enormously hard problem. However, the above observation showcased a connection between two distinct branches of Mathematics, and opened new opportunities ahead of Mathematicians around the globe that were keen to spend countless months attempting a problem that may as well have no solution at all.
One of these Mathematicians was Andrew Wiles. The British succeeded in proving the conjecture, after more than 7 (yes, 7!) years of exclusively trying to solve it! His solution (firstly presented during June 1993 at Cambridge at the form of a lecture) received broad media coverage, as he finally cracked the hardest unsolved problem in the world.
Wiles quickly rose to become a hero, a mathematician in par with Gauss, Euler and Euclid. He earned or accepted multiple prizes, gave many interviews, became a cult hero for the mathematical community, and so on. Needless to say, he undoubtedly was deemed the best mathematician of the 90s — by far.
You might ask — and you will have every right to do so — what about Shimura, Taniyama, and Frey? Well — we must firstly state that it was not only them that contributed to solving Fermat’s Theorem. However, they were the one to implement the connection between this problem and elliptic curves, thus paving the way for Wiles to perform his magic and… boom! Problem solved.
They deserved some acknowledgement, too, didn’t they?
Well, they did get some acknolwedgement, sort of. Or at least their theorems. While every newspaper extensively focused on Wiles as a person, their only referral to the Japanese was that Wiles proved the Taniyama-Shimura conjecture, thus solving Fermat’s Last Theorem — and that’s it. While Taniyama had passed away long before Wiles announced his proof, Goro Shimura didn’t hesitate hiding his dissapointment at an interview that his contributions to solving the theorem were condensed in a reference of a subset of Wiles’ work.
This story, which I first read at [1] inspired my deep perception of the importance of acknowledging the work of scientists through their own lifes, shortcomings and breakthroughs. While most Mathematicians have probably a learnt a good amount of theorems attributed to Leonhard Euler, most Physicists have been bamboozled by works of Einstein at least once in their lives, and I cannot think of a Chemist not knowing Curie’s contributions to the science, I think most of perspective scientists neglect to attempt exploring the lives of these incredible individuals.
I think this perspective incorporates a theme I partly developed at one of my previous posts — that of getting to know people as individuals and not citations, scores and numbers. Personally, I have attempted to follow this approach whenever I am working on science projects, whether it that be developing a paper on trigonometry or performing research on graph theory. In both of my scientific endeavors, I attempted to include brief notes, in which I either developed a bit on the biographies of Mathematicians mentioned throughout the paper, or I provided a short historical background, as well as some supplemental information on the matter.
In this article, I will elaborate on why I choose to approach science this way, and why I think it is important that special emphasis is put on schools and universities on this aspect of sciences.
It is inspiring!
To me, it really means nothing learning obscure theorems and lemmas that bear no connection to real life — instead, I find it much more interesting to learn about the background. Scientists are not just a BA, a Masters and a PhD. They are many more than that. Each scientist is characterized by small, indefinite details that distinguish them from their peers and make them stand out as a unique member of the community.
And this is actually how we choose our idols, anyway — or how we should ideally choose them. We use to get inspired by each person’s work and accomplishments through learning about their hardships, their failures and setbacks, and subsequently realizing that they are just as common as we think we are — they faced the same difficulties, were posed the same problems, and most of them found their way to success after countless years of studying.
I think that realizing that the Andrew Wiles’s of this world are not superhumans created in a lab at New York, and instead are normal — although quite brilliant — people is deeply inspiring for us all, since learning through their difficulties helps us acquire a deeper knowledge and experience in walking our own life path.
It has great educational value!
Hard theorems and proof don’t pop out of nowhere. They are formulated throughout the years after careful consideration and study from dozens of different scientists. Take Goldbach’s conjecture — one of the most famous unsolved problems of Mathematics — for example. It’s original statement, proposed at 1742 by Christian Goldbach, was:
Every integer that can be written as the sum of two primes can also be written as the sum of as many primes as one wishes, until all terms are units.
As a reminder, a prime is a number greater than 1 not divisible by any number other than 1 and itself. However, Goldbach used the convention of considering 1 as a prime number. Later on, he formulated a second, similar, conjecture:
Every integer greater than 2 can be written as the sum of three primes.
Euler, to whom Goldbach had written about his conjectures, summed them up in what we now call Goldbach’s conjecture:
Every positive even integer can be written as the sum of two primes.
Since then, more than 100 mathematicians have published research on this conjecture, each one proving partial results at it (but with no full solution known up to this point). Now, picture this: imagine you are a prospective scientist aiming to tackle this enormously hard problem. What better point to start than studying the successes or failures of the past? Well, that’s precisely what Uncle Petros forgot to do:
After years of fruitless work, Petros arrives at an important intermediate result, which he prefers not to disclose in order not to reveal the object of his research and involuntary helping someone else working on the same problem. Later he comes to an even more important result and decides finally to publish it. He sends it to Hardy, whose answer, however, is disappointing: the same discovery had already been published by a young Austrian mathematician ([2]).
It is therefore vital to study their predecessor’s work, and use their attempts creatively in order to perform new, original discoveries.
I think this view is underlined by a holistic perspective to science, which suggests the third — and final — reason of approaching science this way:
The ethical factor:
Well, science is not mine. Tuum est (taken from UBC’s motto, pun fully intended). Science is not a stubborn man’s ownership — instead, it is the height of collaboration, cooperation and combined effort. Throughout the last centuries, scienticts have continuously been in touch with each other, and very rarely great scientific discoveries were solely made by one person.
Take Wiles’ example — in order to be able to complete the proof, dozens of mathematicians had already paved the way for him.
On the other hand, during the Medieval Ages (and of course even before that), scienticts used to work isolated, refusing to share their discoveries with their colleagues, out of fear that they would steal their innovations. One characteristic example is that of Isaac Newton, who allegedly had discovered the foundations of what we now call Calculus back in 1666, he did not bother publish anything relevant to it until 1693 (in part!) and 1704 (in full!) — and that because Gottfried Leibniz first published his work on the subject in 1684, resulting at a major controversy between two of the greatest scientists humanity has ever seen!
References:
[1]: Singh, S. (1997), Fermat’s Last Theorem. New York City, NY: HarperCollins Publishers LLC.
[2]: “Uncle Petros and Goldbach’s Conjecture” Wikipedia, Wikimedia Foundation, en.wikipedia.org/wiki/Uncle_Petros_and_Goldbach%27s_Conjecture. Accessed 13 Jan. 2024.
