Alexander Grothendieck
Revolutionized algebraic geometry and homological algebra
Most quoted
"The most important thing is to never lose your sense of wonder, your curiosity, and your courage to explore the deepest mysteries of the universe through mathematics, for it is in this exploration that we truly discover ourselves, our potential, and our profound connection to the cosmos, and inspire others to embark on their own journeys of discovery, contributing to the ever-expanding frontiers of human knowledge."
— from Récoltes et Semailles
"The greatest discoveries in mathematics are often the result of a deep sense of intuition, a willingness to embrace the unknown, and a profound commitment to pushing the boundaries of human knowledge, even when faced with seemingly insurmountable obstacles, for it is in these moments that true breakthroughs occur, transforming our understanding of the world and opening up new avenues of inquiry."
— from Récoltes et Semailles
"Mathematics is a journey into the heart of the cosmos, a quest for ultimate understanding and enlightenment, a dialogue with the divine, and a reflection of our innate capacity for creation and discovery, a path that leads to a deeper appreciation of the universe, our place within it, and the profound interconnectedness of all things, inspiring us to live more thoughtfully and purposefully."
— from Récoltes et Semailles
All quotes by Alexander Grothendieck (685)
I am not really doing research, just trying to cultivate myself.
If there is one thing in mathematics that fascinates me more than anything else (and doubtless always has), it is neither ‘number’ nor ‘size’, but always form.
The harmony between the two complementary aspects of the mathematician’s craft—discovery and rigorous proof—is perhaps the most delicate and elusive that exists.
The essential thing is to have the courage to go to the end of an idea.
It’s better to do good mathematics than to correct the errors of others.
I have had the good fortune to be able to devote my life to the search for truth, and to have discovered a small part of it.
The rising sea (my method) allows one to see the dry parts (the problems) from a higher viewpoint, so they become smaller and easier to cross.
I have never written a single line that was not the fruit of long and painful reflection.
The pursuit of truth for its own sake is the only thing that counts.
I have always preferred to work in the shadows.
The notion of topos is the bed in which all of geometry sleeps.
I can assure you that, for my part, I never had the ‘taste’ for power, nor for money, nor for honors—even the most legitimate ones.
I believe that the only science that is truly ‘pure’ is the one that is done without any thought of application.
The future is hidden behind the men who make it.
It is in the nature of things that the essential is simple, and the simple is essential.
A proof only becomes a proof after the social act of ‘accepting it as a proof’.
I have always been more interested in understanding than in proving.
The creative principle resides in mathematics. In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed.
The world of mathematical ideas is a living, evolving organism.
There is no ‘rigorous’ definition of rigor.
Contemporaries of Alexander Grothendieck
Other Mathematicss born within 50 years of Alexander Grothendieck (1928–2014).