# The Path of Thought

Alain Connes is a French mathematician and one of the greatest mathematicians of our time. He revolutionized the theory of von Neumann algebras and solved most of the problems posed in this field, in particular the classification of type III factors. For these works, he was awarded the Fields Medal in 1982. In September 2001, he was awarded the Crafoord Prize, awarded by the Royal Swedish Academy, for his important works in the field of the theory of exterior algebras and for the foundation of noncommutative geometry, which sees its application in quantum physics.

For this same work, the CNRS awarded him its 2004 gold medal. Alain Connes is also the winner of the Clay Research 2000 prize. To reward this innovative work at the border of the mathematical and physical worlds, he also received the AmpÃ¨re prize 1980 from the Academy of Sciences.

Sir Roger Penrose is a British mathematician and mathematical physicist who brought an original and exceptional vision of the laws of nature. It introduces original mathematical methods from algebraic geometry and differential topology in order to easily extract from the equations of the theory of general relativity their predictions concerning cosmology. He has received several prizes and awards, including the 2020 Nobel Prize for his work showing that the formation of black holes is a robust prediction of the general theory of relativity and the 1988 Wolf Prize which he shared with Stephen Hawking for the " Penrose-Hawking singularity theorem". Penrose made contributions to the mathematical physics of general relativity and cosmology.

###### Abhay Ashtekar, Gravitation, Geometry and Quantum

Abhay Vasant Ashtekar is director of the Institute for Gravitational Physics and Geometry at Pennsylvania State University; Evan Pugh Professor of Physics and Eberly Professor at the College of Science. he holds a Distinguished Visiting Research Chair at the Perimeter Institute in Canada. He is also a member of the advisory boards of several institutions around the world.

As the creator of the Ashtekar Variables, he is one of the founders of quantum gravity and loop quantum cosmology. He has also written a number of books and texts on loop quantum gravity that are accessible to non-physicists. In 1999, Ashtekar and his collaborators were able to calculate the entropy of a black hole, matching a legendary 1974 prediction by Hawking. Roger Penrose described Ashtekar's approach to quantum gravity as "the most important of all attempts" to "quantize" general relativity.

Abhay Ashtekar was elected a member of the National Academy of Sciences. He received the first Gravity Prize from the Gravity Research Foundation, Massachusetts and the Einstein Prize.

Jean-Pierre Luminet is emeritus research director at the CNRS at the Marseille Astrophysics Laboratory, after having been a long-time member of the Universe and Theories Laboratory of the Paris-Meudon observatory. In 1978 he was the first to digitally simulate the appearance of a black hole surrounded by an accretion disk, producing a virtual photograph confirmed forty years later by the first telescopic image of a giant black hole obtained by the 'Event Horizon Telescope.

From 1995 he worked on the topology of the Universe, and in 2003 proposed to interpret certain anomalies of the cosmic microwave background as resulting from a space with positive curvature with the topology of the dodecahedral space of Poincaré.

He is the winner of numerous prizes, including the 1999 Georges Lemaître Prize, the 2007 European Prize for Science Communication, the Kalinga Prize and the UNESCO Einstein Medal in 2021. The asteroid (5523) Luminet, discovered at the observatory Palomar in 1991, bears his name in tribute to his work.

He is also an Officer of Arts and Letters. In a prolific body of work wanting to link science, history, music and art, he has published more than thirty works including essays, novels and collections of poems, translated into a dozen languages.