PhD Thesis Acknowledgement

In April 2024 I defended my PhD Thesis, entitled: New methods for the integration of distributions of vector fields. 


I want to share here the acknowledgement section:

In reflecting upon the journey that led to the completion of this thesis, a famous phrase attributed to Isaac Newton comes to mind: "If I have seen further, it is by standing on the shoulders of giants". However, in my own judgement, this statement might be more accurately extended to include not only giants: "If I have seen further, it is by standing on the shoulders of giants - and ants".

Let me explain. The lesser-acknowledged, yet equally vital, contributions of numerous individuals have been the foundation upon which the academic progress has been built. These ants, often unnamed and unrecognized, are akin to the countless mathematicians whose quiet yet essential contributions have paved the way for larger discoveries.

We can think of this using the analogy of the evaporation of a liquid, where some molecules rise out of the surface due to the momentum provided by others. Or like Neil Armstrong, who was the first human to step on the moon, but he would have never done it without the enormous team of anonymous engineers, mathematicians and physical trainers behind him.

It goes without saying that I don't mean Gauss, Einstein or Terry Tao are common molecules, just like the rest of us. But it is also true that, in my opinion, without the others they would have never reached the heights they did. Moreover, it is easy to be Gauss and dedicate yourself to mathematics. The difficult thing is, in my humble opinion, dedicating to this task knowing that you are contributing (infinitesimally) to the development of humanity, but you will never leave anonymity. It's like being a fan of Cádiz football club: you will never win a league, but you enjoy the journey.


This is a reminder that achievements in science are seldom solo endeavors but rather a collective symphony of efforts, even if at the end of the day, the individual is the one who has to take the final step. And my acknowledgement is a tribute to all those ants who have helped humanity to progress.

I want to bring out of anonymity, even if it is only during the brief temporary bubble that lasts while these words are in the reader's mind, to those who have directly influenced the mathematical journey of this ant that is me, since they have been my local giants. I would like to especially thank Conchi Muriel, and Adrián Ruiz, whose guidance and support have been fundamental. But also I want to name other mathematicians like José Antonio Álvarez, Juan Luis Romero, Luis Giraldo, Antonio Aizpuru, Quico Benítez, Paola Morando, Artur Sergyeyev,... and teachers like Luis Fernández and Don Andrés Agüeras, whose teachings and advice have deeply shaped my understanding and appreciation of mathematics.

It is my hope that this thesis will be seen as the work of an ant that infinitesimally contributed to the future of mathematics and human knowledge.


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