Princeton's Internal Predictions

In mid-July, Shen Qi returned to Princeton.

There were still more than three months until the International Congress of Mathematicians in late October.

There's much speculation about who will win this year's Fields Medal.

The IMU statement reads, "What troubles us is that, although we have decided to award all four Fields Medal slots, we still find it difficult to make a decision on selecting the four best among so many outstanding mathematicians."

"The selection process is proceeding in a tense but orderly manner, under the premise of fairness and impartiality."

"This International Congress of Mathematicians will last for nine days, and on the ninth day, we will announce the winners of this year's Fields Medal."

The above is the official news from IMU, which can be summarized into two points:

Four people won awards;

2. Still under evaluation.

The most pressing issue for the Princeton Mathematics Department recently is, of course, the Fields Medal.

More than a dozen mathematicians from the department have been invited to the Mathematicians' Congress in October, among whom two are expected to win the prize: Professor Faltings and Shen Qi. The two of them won the Breakthrough Prize in Mathematics a few months ago, each receiving a prize of $1 million.

Faltings received the highest-level qualification to give a one-hour report at the International Congress of Mathematicians, while Shen Qi's was 45 minutes.

During Wednesday coffee at Princeton University's Mathematics Department, Professor Faltings, the 1986 Fields Medal winner, released a set of research data. "Considering factors such as research achievements, research direction, age, qualifications, and reputation, I believe that Simon Blund of the University of Munich and Joseph Ayoub of the École Normale Supérieure are almost certain to secure both Fields Medal awards. Through mathematical processing, I obtained data showing that Simon Blund's probability of winning is 65.76%, and Joseph Ayoub's is 57.35%."

Professor Faltings's words stirred up a great deal of discussion.

Professor Muller commented. "Simon Blund is a genius. I often interacted with him when I was teaching in Germany. Grader gave Blund a 65.76% chance of winning, which I think is conservative. His chance of winning is at least 70%, and I expect more than 70% of the judges to vote in favor of Simon Blund."

Simon- Blund was a German mathematician, a fellow German of Muller and Faltings.

Another German woman in the café, Mary, also thought highly of Simon Blund: "This is Simon's last Fields Medal; he should receive it."

Faltings wrote a set of data on the blackboard:

[Simon Blund, German nationality, 39 years old, University of Munich, Differential Geometry, Partial Differential Equations, 1 hour (45 minutes, 30 minutes), 65.76%]

Faltings said, "I still maintain that Simon Blund's chances of winning are 65.76%, and even so, he is the biggest favorite."

The customers in this coffee shop are all industry insiders; they all understand the rules of the game.

Simon- Blund, a German mathematician at the University of Munich, specializes in Differential Geometry and Partial Differential Equations, and has achieved outstanding research results in these two fields.

Simon- Blund was qualified to give a one-hour presentation at this International Congress of Mathematicians, whereas at the previous two congresses he gave 45-minute and 30-minute presentations, respectively.

Simon Blund, who rose to fame at a young age and became a legend in his youth, has competed for the Fields Medal twice. Now 39 years old, this is the last time he will compete for the Fields Medal.

Overall, it is a reasonable prediction that this 39-year-old German mathematician has secured a Fields Medal Prize this year with the highest probability of 65.76%.

Even Shen Qi and Faltings acknowledged this fact.

"I know Simon very well because our research areas are very similar," said Italy mathematician Faltings, whose expertise also lies in Differential Geometry and Partial Differential Equations.

Shen Qi sipped his coffee, remaining silent. In his view, if Simon Blund won this year's Fields Medal, then his colleague Faltings would have to wait until next year.

Faltings continued the betting on the blackboard:

[Joseph Ayoub, French national, 39 years old, Algebraic Geometry, ENS Paris, 1 hour (45 minutes, 30 minutes), 57.35%]

French mathematician Joseph Ayoub is in a similar situation to Simon Blund; he has a background and qualifications, is 39 years old, and is competing for the Fields Medal for the last time.

Joseph Ayoub's winning probability of 57.35% is lower than Simon Blund's 65.76%. Faltings offered his professional explanation. "If the 'Ayub Conjecture' were 100% complete, then Ayoub's winning probability would be adjusted to 100%. Unfortunately, the 'Ayub Conjecture' is only around 60% complete, so I predicted his winning probability to be 57.35%."

"Joseph Ayoub is ranked second, no objections." Everyone agreed with Professor Faltings' professional prediction.

Shen Qi asked with great curiosity, "Professor Faltings, based on your mathematical methods and Probability Statistics system, who is the mathematician with the third-highest winning rate this year?"

Faltings wrote on the blackboard:

[Jordi Williamson, Australian, 38 years old, University of Freiburg, Lie Theory and Representation Theory, 1 hour (45 minutes), 48.03%]

The two European mathematicians with the highest and second-highest winning rates are highly regarded within Princeton University's Mathematics Department.

However, when it came to the Australian mathematician Williamson, who ranked third, divisions arose within Princeton University's Mathematics Department.

"Grader, I see now. Your ranking is based on the candidates' age. The closer a candidate is to 40, the higher their chances of winning in your prediction system," Director Feierman questioned. "According to this setting, Alessio and Qi have no hope this year."

Yes, Shen Qi understood now. Professor Faltings' ranking was based on seniority.

Of course, seniority has its prerequisites. Australian mathematician Williamson has made extremely significant contributions to the field of Lie Theory and Representation Theory, and can be considered the leading figure in this research field in our time.

"Jordi Williamson is an outstanding mathematician, and I acknowledge his significant contributions to Lie Theory and Representation Theory. However, Grader, I still feel that the odds of winning the Fields Medal for Jodi Williamson are set too high, artificially inflated. Normally, the probability of the Fields Medal being awarded to a mathematician in Lie Theory and Representation Theory would not exceed 40%." Feierman, Fields Medal winner in 1978, based on his own experience, suggested that Professor Faltings lower the odds of winning for Jodi Williamson.

"I will recalculate Jodie Williamson's odds tonight, but there's no denying he's one of the frontrunners for this year's Fields Medal." Faltings, editor of the Annals of Mathematics, has his own sources of information and unique methods of computational statistics.

Shen Qi habitually did some quick calculations. According to Professor Faltings' professional predictions, almost 2.5 winners of this year's Fields Medal were already decided. In Professor Faltings' predictive system, my chances of winning were probably less than 5%.