Column - Why I regret giving a speech about Andrew Wiles
Age 17. I was enthused with maths, a strange choice I know but forgive the youthful naivety. As many do, my school had yearly awards ceremonies for the finest students to dress up, bring their parents and celebrate their success. As someone talkative with a wandering mind I was never invited, but likely for the same ability to not shut up, I was invited at 17 to give a speech at the ceremony for those in the lower age groups.
I was told to speak about 1 inspirational figure, preferably of an academic nature and preferably of my nationality. You may not have heard of my chosen figure, Andrew Wiles, so allow me to introduce you. In 1995 he published a proof of Taniyama–Shimura conjecture, which you likely haven’t heard of; which proved Fermat’s Last Theorem which you may have heard of. Standing unproven for 358 years, it was a mathematical mammoth to topple, for decades it was viewed not only as ludicrously difficult, but at a level of unsolvable that many who worked towards it didn’t really want to admit to people that they actually dreamed of solving it. Wiles himself has alluded in interviews to the fact he didn’t really want people to know, fearing they would brandish it a waste of time. Tireless work day and night for months on end led him to his revelation, one that put him in the conversation for best mathematician alive… So why don’t I like him anymore?
First and foremost I should clarify that I am sure he is a nice gentleman, this isn’t me cancelling him. I do however think that I could not have chosen a worse person to champion to my young teenage audience.
I’d like to present to you an argument for the death of locking yourself away in an office and hustling dusk til dawn on your secret project. The discovery may be brilliant but his methodology was archaic and weak, and nearly cost him everything too. There is no worse image to cast into the view of a child than the scientist and inventor as a Cambridge Professor working in isolation, sometimes skipping meals due to how intensely locked in thought he was.
In the book “Unsolved Problems in Ecology”, Elizabeth Borer posits that large-scale collaboration and working towards fully harnessing the power of global datasets is one of the greatest issues the field faces, with so much untapped potential currently squandered. I don’t think it’s an egregious leap to make to suggest that this is true in a much wider setting than just ecology.
For his work Sir Wiles was knighted, won the Abel’s Prize and the Copley medal, two of math’s answers to the nobel prize. Prizes like the Nobel’s are currently coming under strain however. If I may take you back to 1901 and the founding of the Nobel Prizes, the standard winner in a science category was a man who had his own lab and was a professor at a university and came up with a great idea and then won a prize for his great idea. Pre WW1 nearly all shared prizes went to people who had done separate work on the same topic, such as becquerel and the curie’s. Although they still had a full committee and due process, in truth the nobel laureates picked themselves, you choose whichever discovery published recently you liked the look of the most, and gave the author a medal. By the 1950s most nobel prizes in physics were shared, the 1956 prize went 3 ways to 3 colleagues at Bell Labs for their cumulative team work towards the invention of the transistor and development of semiconduction. Prizes like these for the combined might of a big lab just were not the case historically, but were already normal in physics after WW2. This was not because the individuals got less clever, or were trapped in systems, or a nice sharing attitude. These prizes were shared because if you’re an individual racing against the combined force of an institution to demonstrate something, you’re a pedestrian racing a train. Everyone watching this under the age of 32 will not have been alive to see a solo awarding of the Nobel Prize in Physics. To try to inspire a future physicist with the story of solo greatness is about as up to date as telling future geographers about opportunities for colonial exploits and exploring new unmapped lands.
Other fields like maths, chemistry and ecology would need time to catch up; Elizabeth Borer noted in her piece on collaboration in ecology that the field regularly struggles with “physics envy”, as was the pace of progress and collaboration in physics through the last 75 years. Our story though began with Sir Wiles persevering solo surrounded by stacks of paper in the 1990s, able to make a great breakthrough alone, the soloist therefore did not die with Bell Labs, but even just from the 1990s to now the world has changed irreversibly.
The influence of a truly open and cheap internet on science cannot be understated. Today at the time of recording,13000km away it’s TEMPERATURE X, and humidity Y in the Marshall Islands, with Z chance of rain. The international data at the fingers of everyone is beyond what any of us stop to consider in our daily lives, and the intellect of others is rarely more than an email away if you have the appropriate credentials.
The 2009 Nobel prize for chemistry was shared by an Indian, with US citizenship leading a research lab at Cambridge, a born and raised American leading a large team at Yale and a Jerusalem born woman heading a vast lab at the Max Planck Institute in Hamburg. Venki Ramakrishnan’s book on the whole process of his career that culminated in the prize is a brilliant work and I would encourage anyone interested in becoming a research chemist to read it. At times these winners all disagreed and had heated debates at conferences; but all worked towards a cumulative understanding of the exact structure and subfunctions of the ribosomes. To me this group delightfully represents what it is to do science, and to make great discoveries in the modern information age; a whole slew of different ethnic backgrounds, men and women, large teams of people sharing results with each other.
The reason I have clung so tightly to the Nobel prizes while narrating this story to you is because of why those 3 won the award… Those 3 won the award because the Nobel Committee is limited to a maximum of 3 winners per year. There were easily 5 or 6 names who made big contributions to the structure of the ribosome, and deciphering which 3 to give it to was a harder task than deciding that the total collection of discoveries around the ribosome deserved a prize. Of those 5 or 6 big names, each worked with a dozen or more collaborators, very smart individuals who provided them with ideas; ran tests and solved their problems. To give every person who made significant input intellectually to the problem a prize would result in perhaps 100 or more Swedish gold medals being handed out. As time has progressed this has gone from being a rare problem that struck when a discovery was clearly collaborative, to a yearly nightmare. Awards in science and maths now fight to remain relevant and respectable while plucking out 1 to 3 candidates for a prize worked towards by dozens.
While I would not wish to argue for the abolition of prizes, they do great work in inspiring and spreading the word of great work, the image that they promote in the modern age has to be questioned. The idea of one or three people winning a prize obscures from the public the process of what science is.
At 17 I loved the ideal of a shutaway working hard in their genius cover to produce mastery. There’s something enticing about the idea that one good thought and it could be you, the person who found an obsession then found themselves overrun with invites to awards ceremonies. But what should we sell to people? If it is wrong to mislead people with the idea of individual heroism in the modern age, what should the inspiration be? At a surface level the story that a big group of 20 or 30 people in a lab did lots of experiments and slowly chugged towards an outcome seems rather turgid; like hey maybe if you work really hard one day you too could be a member of a whole room of people trying to do something… it just doesn’t inspire in the same way. On a deeper level though I would argue that a great collaboration is more impressive. To be a part of a great global collaboration is to have the chance to lay the last brick of the next Sistine Chapel; to look at things greater than you ever could’ve achieved in your whole lifetime and say “that wouldn’t have happened if it weren’t for me”, the chance to share thoughts with great minds from Kyoto to Cairo and together step back and admire the enormity.
If I could go back to that speech now, not only would I not like to talk about someone other than Andrew Wiles; but I’d like to reject the whole premise of talking about 1 inspiration, I think everyone should be greedy and insist that they are inspired by dozens of people, and the products of their works. However, if I did have to give another telling of the life and work of Andrew Wiles it would be more like this:
A promising hardworking university student, Wiles’ let his boyhood obsession with Fermat’s Last Theorem drive him towards an understanding of elliptic curves that got him under the wing of John Coates to study a PhD. The accomplished Coates solved Iwasawa theory in the 1970s, continuing on from the work of the American Barry Mazur who had analysed all the subsections of Fermat’s Last Theorem and broken down which separate proofs would need to be established before the big one could be taken down.
Under Coates, Wiles excelled and continued to let his passion drive him to be curious and absorb as much of Coates’ knowledge as he could in those 4 years. After nearly abandoning Fermat’s theorem entirely Wiles read of the breakthrough work by another american, Ken Ribet, who proved a key element of the theorem; Wiles’ years of study on the matter already allowed a spark to be lit in him by this discovery, as he was one of the handful of people able to grasp just how important Ribet’s contributions could go on to be.
Working tirelessly in his academic position, Wiles was elected into the Royal Society; an immense feat that would mark the pinnacle of the career of anyone less driven than himself. This great honour was not enough for Wiles who saw the many jigsaw pieces of Fermat’s Theorem slowly falling into place through the years and could not escape the lure of adding more pieces. 5 years after his ascension to the Royal Society, he released his now infamous proof of the Tanyama-Shimura conjecture. The final piece in the 358 year jigsaw of proving Fermat’s Last Theorem. To stand back and enjoy the final image, the completed jigsaw was a once in a lifetime opportunity. Barry Mazur at age 65 got to see the puzzle of his dreams solved; with a catch. Once Wiles’ works were released from his solo studies; an error was found. When he attempted to quickly patch up this error it seemed to keep pulling apart and the hole was clearly not so trivial. It took a full year and the assistance of one of his PhD students to finally fix it in 1995, finally granting the long history of contributors their complete success.
In the proceeding 30 years since this great feat people have been able to use this discovery to generalise towards other problems in Number Theory; and when interviewed in 2016 Wiles’ takeaway message to those wishing to follow in his footsteps was simply:
Always pursue the problem that matters the most to you.