1. The concept of the lithosphere, as a hierarchical non-linear (chaotic) dissipative system (Earthquakes and other geological disasters are regarded as critical phenomena in that system) [1-4]

Based on modeling and phenomenology four fundamental paradigms of the predictability of the critical geological phenomena in the lithosphere were discovered [3, 5, 6]:

• Long–range correlations between processes occurring in distant areas [7, 8]. Due to these correlations critical phenomena are formed in large territories (“it is not a fault segment which generates a strong earthquake, but a fault network which generates a sequence of earthquakes”).
• Precursory transformation of the background activity of the system prior to a critical phenomenon. This transformation comprises increase of intensity, irregularity, clustering, and correlation range of the background activity as well as specific changes in size distribution of the events [9-14]. This transformation is reminiscent of an effect know n in statistical physics as asymptotic behavior of the correlation range near the point of phase transition of second kind. However, unlike statistical physics, the problem addressed by Keilis-Borok concerns not the equilibrium state, but the growing non-equilibrium, culminated by a critical phenomenon.
• Similarity of the above precursory transformations in a wide range of conditions. For example in the case of earthquakes, one of the most prominent critical phenomena in the lithosphere, the precursory transformations are similar in the energy range from ergs to 10²⁶ erg, and possibly 10⁴¹ erg [1, 2, 9-14].
• Nature of the precursory transformations; some are “universal”, common for a wide class of non-linear systems; other are Earth-specific [9, 15].

Furthermore, it was discovered that simple lattices of interacting elements that are commonly used in statistical physics display similar kind of predictability with “universal precursors” [14, 16].

Finally, earthquake prediction algorithms were developed and successfully tested worldwide by advance prediction [17-21]. These algorithms are so far the only reproducible and statistically significant ones in existence.

2. Instability of tectonic fault network

• Discovery (by the pattern recognition approach) of mosaic structures around fault intersections (the “nodes”), where instability is concentrated and strong earthquakes nucleate [8, 22-24].
• Discovery of the integral measure of network’s instability caused by the collective behavior of the nodes that controls the nucleation of strong earthquakes [25]. Such nodes were recently discovered in low seismicity regions, such as European platform, where they are associated with the destructive slow movements (‘slow earthquakes’).
• Development of the theory of instability induced by mechanical and chemical rock-fluid interactions [26-28].
• Discovery of Earth-specific features of precursory phenomena in the models of the fault networks [29-32].

3. Theory of disasters’ risk and disasters’ preparedness

• Probabilistic estimation of seismic risk (mathematical economics approach) [33-35].
• Optimization of disaster preparedness measures (optimal control approach) [36-39].

4. Critical phenomena in socio-economic systems.

It was discovered that the “universal” precursors discovered for the critical phenomena in the lithosphere also exist in socioeconomic systems. Therefore the same approach can be used for predictions of the socioeconomic critical phenomena, such as economic recessions [40] and surges of unemployment [41]. Tests by advance predictions are now in progress.

Similar approach with system-specific precursors has been successfully applied to presidential and senatorial elections in the United States, with the established statistical significance of advance predictions [42-44].

5. Theory of seismic surface waves

This theory was developed based on the mathematical theory of operators [45, 46]. Among the important applications of this theory is significant enhancement of the capability to detect underground nuclear explosions (for a nuclear test ban system); enhancement is based on analysis of surface waves. This discovery, made simultaneously by professors F. Press and V. Keilis-Borok, has been the successful turning point of the international negotiations for nuclear test ban treaty conducted in Geneva in the early 60s [47, 48].

6. Establishment of non-uniqueness in seismological inversion and development of methods to reduce it [49-52].

The abovementioned fields of research are rapidly expanding, attracting many independent groups. Among these groups Keilis-Borok remains by far unique: first, - in his broad theoretical approach that combines “universal” and Earth-specific models; and second – in extending research to successful worldwide experiments in actual systematic prediction.

This outstanding list of discoveries is by no means complete. It culminates lifetime achievements in expanding the mathematical foundation of solid Earth sciences by integrating “high” theory and phenomenology. Keilis-Borok’s trademark is to successfully develop the apparently impossible connections between different fields of research and/or different groups of experts. These achievements demonstrate his outstanding visionary qualities.

Keilis-Borok has founded a unique group of “pure” mathematicians working jointly with geophysicists and geologists, with direct involvement of world-famous mathematicians, such as I. Gelfand, L Kantorovich, Ya. Sinai and their schools, and geoscientists, such as F. Press, L. Knopoff, and C. Allègre.

The fundamental results obtained by his group are invariably extended to applications in the “hot” controversial problems, including instability of megacities, political and economic predictions, and detection of underground nuclear explosions.

After support for basic research in the world slowed down with the end of the Cold War, Keilis-Borok initiated a set of projects, demonstrating the crucial practical importance of basic research. The last initiative of such kind is the Study Week “Basic science for survival and sustainable development” under the auspices of the Pontifical Academy of Sciences.

At the peak of the Cold War Keilis-Borok made bold contribution to the détente, reaching understanding with the international experts at the nuclear test ban negotiations, and in earthquake prediction research. In 1963 he has founded the famous International Symposia on Mathematical Geophysics, which brought together leading mathematicians and geoscientists of the East and West. His annual Workshops in the Abdus Salam International Centre for Theoretical Physics (Trieste, Italy) keep bringing together the scientists from all the world.

His unusual position is illustrated by the fact that he was elected in the US National Academy of Sciences 17 years earlier than into the USSR Academy of Sciences. His first Academy -- the American Academy of Arts and Sciences -- elected him simultaneously with A. Sakharov, A. Solzhenitsyn and L. Kantorovich.

The results of Keilis-Borok’s research are unexpected, counterintuitive, and brilliant. His school received wide and fast recognition, reflected in the more than impressive list of the international positions he held during his career.

1. Keilis-Borok,V.I. The lithosphere of the Earth as a non-linear system with implications for earthquake prediction. Review of Geophysics, 1990, 28, 1: 19-34.
2. Keilis-Borok,V.I. Introduction: Non-linear systems in the problem of earthquake prediction. Phys. Earth Planet. Inter., 1990, 61, 1-2: 1-7.
3. Keilis-Borok,V.I. Intermediate-term earthquake prediction. Proc. Natl. Acad. Sci. USA, 1996, 93: 3748-3755.
4. Keilis-Borok,V. What comes next in the dynamics of lithosphere and earthquake prediction? Phys. Earth and Planet. Inter., 1999, 111, 3-4: 179-185.
5. Keilis-Borok,V.I. Symptoms of instability in a system of earthquake-prone faults. Physica D, 1994, 77: 193-199.
6. Keilis-Borok,V.I. Non-seismological fields in earthquake prediction research. In Sir James Lighthill (ed.), A Critical Review of VAN, Singapore-New Jersey-London-Hong Kong: World Scientific, 1996: 357-372.
7. Keilis-Borok,V.I., and L.N.Malinovskaya, One regularity in the occurrence of strong earthquakes. J. Geophys. Res., 1964, 69, 14: 3019-3024.
8. Keilis-Borok,V.I., and F.Press, On seismological applications of pattern recognition. In C.Allègre (ed.), Source Mechanism and Earthquake Prediction Applications, Paris, 1980: 51-60.
9. Caputo,M., P.Gasperini, V.I.Keilis-Borok, L.Marcelli, and I.M.Rotwain, Earthquake's swarms as forerunners of strong earthquakes in Italy. Annali di Geofisica, 1977, XXX, 3-4: 269-283.
10. Keilis-Borok,V.I., and I.M.Rotwain, Two long-range precursors of strong earthquakes. In V.I.Keilis-Borok (ed.), Theory and Analysis of Seismological Observations. Moscow, Nauka, 1979: 18-27 (Comput. Seismol.; Iss. 12, in Russian). English translation: Computational Seismology, Vol. 12, Allerton Press Inc., 1979: 13-21.
11. Keilis-Borok,V.I., L.Knopoff, and I.M.Rotwain, Bursts of aftershocks, long-term precursors of strong earthquakes. Nature, 1980, 283: 259-263.
12. Keilis-Borok,V.I., L.Knopoff, I.M.Rotwain, and C.R.Allen, Intermediate-term prediction of occurrence times of strong earthquakes. Nature, 1988, 335, 6192: 690-694.
13. Knopoff,L., T.Levshina, V.I.Keilis-Borok, and C.Mattoni, Increased long-range intermediate-magnitude earthquake activity prior to strong earthquakes in California. J. Geophys. Res., 1996, 101, B3: 5779-5796.
14. Shebalin,P., I.Zaliapin, and V.Keilis-Borok, Premonitory raise of the earthquakes' correlation range: Lesser Antilles. Phys. Earth and Planet. Inter., 2000, 122, 3-4: 241-249.
15. Kossobokov,V.G., V.I.Keilis-Borok, D.L.Turcotte, and B.D.Malamud, Implications of a statistical physics approach for earthquake hazard assessment and forecasting. Pure and Appl. Geophys., 2000, 157, 11-12: 2323-2349.
16. Zaliapin,I., V.I.Keilis-Borok, and G.Axen, 2000. Premonitory spreading of seismicity over the fault network in S. California: precursor Accord. 20 pp. Submitted to J. Geophys. Res.
17. Molchan,G.M., O.E.Dmitrieva, I.M.Rotwain, and J.Dewey, Statistical analysis of the results of earthquake prediction, based on bursts of aftershocks. Phys. Earth Planet. Inter., 1990, 61, 1-2: 128-139.
18. Kossobokov,V.G., V.I.Keilis-Borok, L.L.Romashkova, and J.H.Healy, Testing earthquake prediction algorithms: Statistically significant real-time prediction of the largest earthquakes in the Circum-Pacific, 1992-1997. Phys. Earth and Planet. Inter., 1999, 111, 3-4: 187-196.
19. Vorobieva,I.A. Prediction of a subsequent large earthquake. Phys. Earth and Planet. Inter., 1999, 111, 3-4: 197-206.
20. Keilis-Borok,V.I., A worldwide test of three long-term premonitory seismicity patterns: a review. Tectonophysics, 1982, 85, 1/2: 47-60.
21. Keilis-Borok,V.I., L.Knopoff, V.Kossobokov, and I.M.Rotwain, Intermediate-term prediction in advance of the Loma Prieta earthquake. Geophys. Res. Letters, 1990, 17, 9: 1461-1464.
22. Gelfand,I.M., Sh.I.Guberman, M.L.Izvekova, V.I.Keilis-Borok, and E.Ja.Ranzman, Criteria of high seismicity, determined by pattern recognition. In A.R.Ritsema (ed.), The Upper Mantle. Tectonophysics, 1972, 13 (1-4): 415-422.
23. Gelfand,I.M., Sh.A.Guberman, V.I.Keilis-Borok, L.Knopoff, F.Press, E.Ya.Ranzman, I.M.Rotwain, and A.M.Sadovsky, Pattern recognition applied to earthquake epicenters in California. Phys. Earth and Planet. Inter., 1976, 11: 227-283.
24. Caputo,M., V.Keilis-Borok, E.Oficerova, E.Ranzman, I.Rotwain, and A.Solovieff, Pattern recognition of earthquake-prone areas in Italy. Phys. Earth and Planet. Inter., 1980, 21: 305-320.
25. Gabrielov,A., V.I.Keilis-Borok, and D.D.Jackson, Geometric incompatibility in a fault system. Proc. Natl. Acad. Sci. USA, 1996, 93 (9): 3838-3842.
26. Barenblatt,G.I., V.I.Keilis-Borok, and M.M.Vishik, Model of clustering of earthquakes. Proc. Natl. Acad. Sci. USA, 1981, 78 (9): 5284-5287.
27. Barenblatt,G.I., V.I.Keilis-Borok, and A.S.Monin, Filtration model of earthquake sequence. Doklady Academii Nauk SSSR, 1983, 269, 4: 831-834 (in Russian).
28. Gabrielov,A.M., and V.I.Keilis-Borok, Patterns of stress corrosion: geometry of the principal stresses. PAGEOPH, 1983, 121, 3: 477-494.
29. Gabrielov,A.M., V.I.Keilis-Borok, T.A.Levshina, and V.A.Shaposhnikov, Block model of dynamics of the lithosphere. In V.I.Keilis-Borok and A.L.Levshin (eds), Mathematical Methods in Seismology and Geodynamics. Moscow, Nauka, 1986: 168-178 (Comput. Seismol.; Iss. 19, in Russian). English translation: Computational Seismology, Vol. 19, Allerton Press Inc., 1986: 168-177.
30. Keilis-Borok,V.I., I.M.Rotwain, and A.A.Soloviev, Numerical modeling of block structure dynamics: dependence of a synthetic earthquake flow on the structure separateness and boundary movements. Journal of Seismology, 1997, 1, 2: 151-160.
31. Gorshkov,A., V.Keilis-Borok, I.Rotwain, A.Soloviev, and I.Vorobieva, On dynamics of seismicity simulated by the models of blocks-and-faults systems. Annali di Geofisica, 1997, XL, 5: 1217-1232.
32. Ismail-Zadeh,A.T., V.I.Keilis-Borok, and A.A.Soloviev, Numerical modelling of earthquake flow in the southeastern Carpathians (Vrancea): effect of a sinking slab. Phys. Earth and Planet. Inter., 1999, 111, 3-4: 267-274.
33. Keilis-Borok,V.I., Ye.V.Vilkovich, G.M.Molchan, Seismicity and principal seismic effects. Geophys. J.R. Astr.Soc., 1970, 21, 3-4: 323-335.
34. Caputo,M., V.I.Keilis-Borok, T.L.Kronrod, G.M.Molchan, G.Panza, E.Piva, V.M.Podgaetskaya, and D.Postpishl, The estimation of seismic risk for Central Italy. Annali di Geofisica, 1974, XXVII, 1-2: 349-365.
35. Keilis-Borok,V.I., T.L.Kronrod, and G.M.Molchan, Seismic Risk for the Largest Cities of the World; Intensity VIII or More. The Geneva Papers on Risk and Insurance, 1984, 9 (? 32): 255-277.
36. Keilis-Borok,V.I., L.V.Kantorovich, and G.M.Molchan, Seismic risk and principles of seismic zoning. In V.I.Keilis-Borok (ed.), Computational and Statistical Methods for Interpretation of Seismic Data. Moscow, Nauka, 1973: 3-20 (Comput. Seismol.; Iss. 6, in Russian). English translation: M.I.T. Special Report, 1975.
37. Keilis-Borok,V.I., G.M.Molchan, A.Kh.Koridze, T.L.Kronrod, and O.D.Gotsadze, An insurance-oriented pilot estimation of seismic risk for rural dwellings in Georgia. The Geneva Papers on Risk and Insurance, 1984, 9 (? 77): 85-111.
38. Kantorovich,L.V., and V.I.Keilis-Borok, Earthquake prediction and decision making: social, economic and civil protection aspects. In International Conference on Earthquake Prediction: State-of-the-Art, Strasbourg, France, 15-18 October 1991, Scientific-Technical Contributions, CSEM-EMSC: 586-593.
39. Keilis-Borok,V.I., and I.Primakov, Earthquake prediction and earthquake preparedness: The possibilities to reduce the damage from earthquakes. In G.Verri (ed.) Proceedings of the International Scientific Conference EUROPROTECH. Udine, May 6-7-8, 1993: 17-46.
40. Keilis-Borok,V., J.H.Stock, A.Soloviev, and P.Mikhalev, Pre-recession pattern of six economic indicators in the USA. Journal of Forecasting, 2000, 19, 1: 65-80.
41. Keilis-Borok,V.I., A.A.Soloviev, C.B.Allègre, A.N.Sobolevskii, and M.D.Intriligator, 2000. Pattern of macroeconomic indicators preceding the acceleration of unemployment in France. Submitted to American Economic Review.
42. Lichtman,A.J. and V.I.Keilis-Borok, Aggregate-level analysis and prediction of midterm senatorial elections in the United States, 1974-1986. Proc. Natl. Acad. Sci. USA, 1989, 86: 10176-10180.
43. Keilis-Borok,V.I., and A.Lichtman, Understanding and prediction of large and complex unstable systems in the absence of basic equations: concepts of selforganization and similarity. In G.Costa, G.Calucci, and M.Giorgi (eds) Proceedings of the First International Symposium on Conceptual Tools for Understanding Nature. Trieste 26-28 September 1990: 145.
44. Keilis-Borok,V.I., and A.J.Lichtman, The self-organization of American society in presidential and senatorial elections. In Yu.A.Kravtsov (ed.), Limits of Predictability, Springer-Verlag, Berlin-Heidelberg, 1993: 223-237.
45. Keilis-Borok,V.I., M.G.Neigauz, and G.V.Shkadinskaya, Application of the theory of eigenfunctions to the calculations of surface wave velocities. Review of Geophysics, 1965, 3, 1: 105-109.
46. Andrianova,Z.A., V.I.Keilis-Borok, A.L.Levshin, and M.G.Neigauz, Seismic Surface Love Waves. Consultants Bureau, New York, 1967.
47. Keilis-Borok,V.I., 1959-1961, 1987. Series of papers on nuclear explosion recognition. Proc. Geneva conference of technical experts for verification of compliance to Nuclear Test Ban Treaty.
48. Keilis-Borok,V.I., and T.B.Yanovskaya, Dependence of surface waves spectrum on a source depth within the Earth's crust. Izvestia AN SSSR. Geophysics, 1962, 11: 1533-1539 (in Russian).
49. Keilis-Borok,V.I. Seismology and logics. In Solid Earth and Interface Phenomena. Washington, The M.I.T. Press, 1964: 61-79 (Research in Geophysics, Vol. 2).
50. Asbel,I.Ja., V.I.Keilis-Borok, and T.B.Yanovskaya, A technique of a joint interpretation of travel-time and amplitude-distance curves in the upper mantle studies. Geophys. J.R. Astr.Soc., 1966, 11, 1-2: 57-66.
51. Keilis-Borok,V.I., and T.B.Yanovskaya, Inverse problems of seismology (structural review). Geophys. J.R. Astr. Soc., 1967, 13: 223-234.
52. Keilis-Borok,V.I., The inverse problem of seismology. In Mantle and Core in Planetary Physics. Academic Press Inc., New York, 1971: 242-274.